Methods and apparatus for implementing and/or using amplifiers and/or for performing various amplification related operations

Description of equivalent WO 2007002770 A2

0001METHODS AND APPARATUS FOR IMPLEMENTING AND/OR USING AMPLIFIERS AND/OR FOR PERFORMING VARIOUS AMPLIFICATION RELATED OPERATIONS

FIELD OF THE INVENTION

0003[0001] The present invention relates to amplifier methods and apparatus and, more particularly, to methods and apparatus for implementing and/or using amplifiers and/or for performing various amplification related operations.

BACKGROUND

0005[0002] Delta Sigma (ΔΣ ) modulators are devices for causally computing a discrete valued (often two-valued) digital approximation or near representation of an analog or virtually continuous valued digital signal. The representation is typically a high rate (e.g., high clock rate) signal quantized to a small number of discrete levels (e.g., two). ΔΣ modulators are often used in analog-to-digital conversion and also in digital-to-analog conversion. ΔΣ modulators that produce two level representations are good candidates for use in conjunction with switching amplifiers because such amplifiers have essentially two power efficient states and operate by switching between the states.

0006[0003] While the use of Delta Sigma modulators as part of a power amplification device has been tried for some high frequency applications, e.g., RF applications, the use of Delta Sigma modulators has generally been limited due to the signal distortions introduced by the known implementations. While the use of high accuracy, and thus high cost, switching components can help reduce the amount of distortions as compared to implementations which use lower cost components, the distortions introduced by known Delta Sigma modulator based amplifers still remains too high for many applications particularly wireless communications applications where the power efficiency advantages of Delta Sigma modulator based amplifiers would be particularly desirable.

0007[0004] In view of the above discussion, it should be appreciated that there is a general need for improved ways of performing amplification and implementing amplification devices. With regard to Delta Sigma modulators, while amplifiers which use Delta Sigma modulators are ^ifJ' <img file="WO2007002770A2_D0001.tif" /> Sffiϊi'a neei iir4m^'proved methods and apparatus which allow for the use of Delta Sigma modulators in amplification devices. Accordingly, there is a need for improved methods and apparatus for implementing amplifiers which use Delta Sigma modulators. In view of the distortion issues associated with the use of Delta Sigma modulators in power amplifiers, it would be beneficial if ways of reducing, compensating or eliminating distortions introduced into a signal as the result of using a Delta Sigma modulator could be developed. While some improvements may be directed to improved circuitry or apparatus, other improvements may be directed to the signals which are processed by Delta Sigma modulators or ways in which a power amplifier using a Delta Sigma modulator is controlled.

SUMMARY

0009[0005] Methods and apparatus for implementing and/or using amplifiers and performing various amplification related operations are described. The methods are well suited for use with, but not limited to, switching type amplifiers. Various methods and apparatus of the invention can be used to perform power amplification operations, e.g., using one or more S-type or D-type amplifiers.

0010[0006] The described methods and apparatus can be used in a wide range of applications. Various embodiments are well suited for wireless transmission applications, e.g., in a base station or wireless terminal. Other embodiments are well suited for audio and other applications where an amplifier is used. The methods and apparatus are not limited to these applications but can be used in other applications as well.

0011[0007] Power efficiency can be important in amplifiers for transmitters yet stringent linearity requirements often render the amplifiers very inefficient, on the order of 5 to 10 per cent for wireless base-stations in many existing systems. Switching amplifiers can be very power efficient but are normally not used for wireless applications because, in known systems, the high frequency signals used in wireless applications can not be sufficiently accurately reproduced using switching amplifiers.

0012[0008] The methods and apparatus described herein allow for the use of switching amplifiers while reducing and/or compensating for distortions that the use of such amplifiers would normally create. The described methods and apparatus can be used alone or in '^■combination with vktϊbfeπσvel signaling schemes which can make it easier to compensate for the non-ideal behavior of switching amplifiers in such a way as to enable practical application in wireless transmission and/or other applications.

0013[0009] The fidelity of switching type amplifiers can be improved using the described methods and/or apparatus, so that such amplifiers can, in some form, be applied to a wide variety of applications where power amplifiers are used, including, e.g., audio applications.

0014[0010] While various embodiments have been discussed in the summary above, it should be appreciated that not necessarily all embodiments include the same features and some of the features described above are not necessary but can be desirable in some embodiments. Numerous additional features, embodiments and benefits of various embodiments are discussed in the detailed description which follows.

BRIEF DESCRIPTION OF THE FIGURES

0016[0011] Figure 1 is a drawing of an exemplary simple first order Delta-Sigma modulator in accordance with various embodiments.

0017[0012] Figure 2 is a drawing of an exemplary form for a DeltaSigma modulator in accordance with various embodiments.

0018[0013] Figure 3 is a drawing of an exemplary second order DeltaSigma modulator in accordance with various embodiments.

0019[0014] Figure 4 is a drawing of an exemplary frequency shifting DeltaSigma modulator in accordance with various embodiments.

0020[0015] Figure 5 is a drawing of a representative circuit form of an exemplary switching amplifier, filter and load, in accordance with various embodiments.

0021[0016] Figure 6 is a drawing illustrating the concept of DeltaSigma correction in accordance with various embodiments. [0017] Figure 7 is a drawing illustrating an exemplary correction calculation module and describing exemplary correction calculation in accordance with various embodiments.

0022[0018] Figure 8 is a drawing illustrating a correction compution module coupled to a complex Delta-Sigma modulator module in accordance with various embodiments.

0023[0019] Figure 9 is a drawing illustrating an exemplary direct modulation scheme in accordance with various embodiments.

0024[0020] Figure 10 is a drawing illustrating a Real form of an exemplary direction modulation scheme in accordance with various embodiments.

0025[0021] Figure 11 is a drawing illustrating a re-ordered real form of an exemplary direct modulation scheme in accordance with various embodiments.

0026[0022] Figure 12 is a drawing illustrating exemplary waveforms from an exemplary reordered real form of a direct modulation scheme in accordance with various embodiments.

0027[0023] Figure 13 is a drawing illustrating a time varying quantizer form in accordance with various embodiments.

0028[0024] Figure 14 is a drswing illustrating an exemplary four phase carrier clock implementation of an exemplary direct modulation scheme in accordance with various embodiements.

0029[0025] Figure 15 is a drawing illustrating an alternative frequency shifting DeltaSigma form used in various embodiments.

0030[0026] Figure 16 is a drawing illustrating an alternative equivalent first stage that may be used in the frequency shifting DeltaSigma of Figure 15.

0031[0027] Figure 17 is a drawing illustrating a DeltaSigma modulator module being used to modulate a single clock in accordance with various embodiments. '^"' [OOioj Figure'Wi'l'a "drawing illustrating an exemplary DeltaSigma modulator module including a two level quantizer used in various embodiments.

0032[0029] Figure 19 is drawing illustrating exemplary possible descision regions for an exemplary embodiment.

0033[0030] Figure 20 is a drawing illustrating exemplary six and eleven point constellations used in various embodiments.

0034[0031] Figure 21 shows an exemplary constellation that may be used if a clock that is 8 times the carrier frequency is available, in accordance with various embodiments.

0035[0032] Figure 22 is a drawing illustrating exemplary receiver based calibration in accordance with various embodiments.

0036[0033] Figure 23 is a drawing illustrating an exemplary time varying Thevenin equivalen circuit.

0037[0034] Figure 24 is a drawing of an exemplary time varying Thevenin equivalent circuit, filter and load in accordance with various embodiments.

0038[0035] Figure 25 is a drawing of an exemplary wireless communications system, e.g., OFDM wireless communications system, in accordance with various embodiments.

0039[0036] Figure 26 is a drawing of an exemplary base station in accordance with various embodiments.

0040[0037] Figure 27 is a drawing of an exemplary wireless terminal, e.g., mobile node, in accordance with various embodiments.

0041[0038] Figure 28 is a drawing of a flowchart of an exemplary method of operating a device including a delta sigma modulator and a correction computation module in accordance with various embodiments. DETAILED DESCRIPTION

0042[0039] To gain an understanding of the various features and benefits of the invention, an understanding of Delta Sigma modulators and their effects, alone and in combination with switching type amplifiers, is useful.

00432.1 Signal representation via sigma delta.

0044[0040] A smooth real valued function/taking values in the range [-1,1] can be "weakly" approximated arbitrarily accurately by a function / taking only the values ±1. "Weak" approximation means that for any suitable smooth function g the integral J (f(^x) ~ f (^χ))g(^x)dx will be relatively small in magnitude.

0045[0041] ΔΣ modulation applies the same principle. A low-pass (e.g., smooth) signal U of bandwidth 2W_βHz is approximated by a discrete signal V with clock frequency

0046Z₀=(OSR)W _β where OSR is an Over-Sampling-Ratio. For purposes of explanation, the discrete valued signal can be thought of as a discrete valued function (e.g., two valued) changing value only on clock boundaries or as a series of discretely scaled δ functions, possibly convolved with a square pulse.

0047[0042] ΔΣ can be applied to both continuous-time and discrete-time signals. We shall focus primarily on discrete-time signals which may be produced by sample-and-hold operations applied to a continuous-time signal.

0048[0043] A simple ΔΣ modulator 100 for a discrete-time signal U 102 is depicted in Figure 1. Exemplary ΔΣ modulator 100 includes an adder 104, a clock 106, an integrator 108 and a comparator 110 coupled together as shown in Figure 1. Integrator 108 includes an adder 112 and a register 114. In each clock cycle register 114 saves the digital output of adder 112. The inputs to the adder 112 are the previously stored value in the register 128 and the difference signal D 116. Thus, the output of the adder 112, which is stored in the register as 5 122, is the integral (time sum) of the difference signal D 116. A comparator 110(1 bit in this example), or quantizer, quantizes the signal S 122, e.g., according to its sign, to e.g. +1. This signal may be scaled to some other value, e.g., ±A to produce the approximation V 124. For simplicity we will assume unity scaling, absorbing it into the quantizer. Thus, the signal S 122 is the time integral of U- V and the quantizer chooses a value to try to reduce the magnitude of this integral. The circuit therefore tries to construct V 124 so as to locally minimize Looking at the <img file="WO2007002770A2_D0002.tif" />

0049Fourier transforms of U and V we see that the circuit attempts to keep

0050small where <img file="WO2007002770A2_D0003.tif" />

0051<img file="WO2007002770A2_D0004.tif" />

0052Thus V(ώ) approximates 0(ω) for small values of ω.

0053[0044] The basic idea above can be generalized in several ways, to higher order (more than one integral), more general error functionals (combining different integrals) and multi-level quantizers, etc. A more general form is depicted in drawing 200 of Figure 2. Figure 2 includes a linear transform function module 202 and a quantizer module 204 coupled together as shown. The linear transform function module 202 receives inputs U(z) and V(z), performs linear operations, and generates output S(z). Quantizer module 204 receives S(z) as input and outputs V(z). Here

0054S(z) ^ U(Z)L₀ (z) + V(Z)L₁ (z) and

0055V(z) = S(z) + E(z)

0056where E(z) represents the quantization noise, and

0057<img file="WO2007002770A2_D0005.tif" /> where z represents unit delay as in standard z-transform.

0058[0045] The system can also be expressed in state space form

0059S₁ = CX_{1 +} DyU₁<img file="WO2007002770A2_D0006.tif" /> where the dimension of X is the order of the modulator.

0060[0046] For example, consider the system 300 shown in Figure 3. Exemplary system 300 illustrates an exemplary second order DeltaSigma modulator. System 300 includes a first adder 302, a first integrator 304, a second adder 306, a second integrator 308, and a comparator 310 coupled together as shown in Figure 3. The inputs to the first adder 302 are digital input U 310 and -V 314; the output of first adder 302 is signal 318. The input to first integrator 304 is signal 318, and the output of first integrator 304 is signal 320. The inputs to second adder 306 are signal 320 and -2 V 316. The output of second adder 306 is signal 322 which is the input to 2^nd integrator 308. The output of 2^nd integrator 308 is signal S 324 which is an input to comparator 310. The output of comparator 310 is bit stream output signal 326 and signal V. Here,

0061<img file="WO2007002770A2_D0007.tif" />

0062In this case we have

0063<img file="WO2007002770A2_D0008.tif" />

00642.2 Representation of band-pass signals.

0065[0047] A bandpass ΔΣ is possible and that the clock frequency can be a small factor (e.g., 4 or 8) times faster than the carrier frequency. The basic reason for this is that a filter can be used to ensure the in-band signal is passed while other signals are rejected and that modulation of the carrier, effectively a low-pass signal, is sampled at a high rate, high enough to also recover carrier phase. [0048] The presen t invention exploits this basic principle. In accordance with the invention, a baseband signal is converted using a ΔΣ modulator and the result is a bandpass RF signal.

0066[0049] A standard mathematical representation for RF signals is

0067<img file="WO2007002770A2_D0009.tif" /> where u(t) is the complex baseband signal and f_c is the carrier frequency. Typically the bandwidth of u(f) is much smaller than/ . For example, u(t) might have a bandwidth of 5MHz while f might be 2GHz. However, other frequencies are possible and the invention is not limited to these exemplary frequencies.

0068[0050] A passband RF signal can be converted to a binary representation using a ΔΣ modulator running at, e.g., 4 or 8 f . In many cases, it is undesirable to require such a fast sampling of the signal.

0069[0051] A simpler and more direct approach is to perform ΔΣ modulation on the baseband signal for I and Q components (real and imaginary parts) separately and then digitally modulate the combined result up to the carrier frequency. We will focus on some embodiments of the invention which use this approach beginning in Section 5.1 below.

00703 Complex ΔΣ and RF Modulation

0071[0052] A complex baseband signal is typically separated into its real and imaginary parts (I and Q). ΔΣ modulation of the two signals can be done independently. For the purposes of the present invention, however, it may be more convenient to think of a single complex ΔΣ modulator. The summation of real and imaginary parts may occur independently, as in normal complex addition. The quantizer operates on a complex signal and the output may generally be viewed as a discrete complex signal. The quantizer may be effectively time varying. In the simplest case, where the quantizer quantizes real and imaginary parts independently, the complex ΔΣ modulator used in accordance with the invention may be, and in some embodiments is, simply two real ΔΣ modulators operating synchronously and in parallel. [0053] The complex ΔΣ modulators will produce representations of complex baseband signals that ultimately will be modulated to RF frequencies. In some cases the RF representation is produced directly. Some of the techniques for doing this are central to the present invention. The structures we consider take as input a complex base-band signal and produce a two-valued real RF modulated approximation of that signal, with noise shaped to be mostly out-of-band. We will refer to such structures generally as frequency shifting ΔΣ.

0072[0054] Drawing 400 of Figure 4 illustrates the idea of a frequency shifting complex Delta-Sigma. A complex (base-band) ΔΣ 402 has an output V (baseband representation) 404 that is the discrete, complex, approximation to the input U 406. This signal 404 is used in a feedback path to measure its deviation from U 406, thereby controlling the ΔΣ 402 decisions. In the frequency shifting ΔΣ 402 the "true" output is W 408. This output W 408 represents a frequency shifted version of £/406. Often, W 4OS will be a two-valued real signal. W 408 will typically be related to V 404 in a simple way and will be derivable from V 404. Thus, all information about W 408 is available in V 404, and vice-versa.

00734 Correction for switching disturbance

0074[0055] An application being addressed by this invention is power amplification, e.g., of bandpass RF signals or other signals. The signals 501 being produced by a frequency shifting ΔΣ modulator, are used in accordance with the invention to drive a (two-state) switching amplifier 502 as depicted in drawing 500 of Figure 5. For example, the frequency shifting ΔΣ modulator producing signal 501 may be ΔΣ modulator 402 of Figure 4 and signal 501 may be signal W 408. The switching unit 502, using e.g. high power FET transistors (504, 506), serves to connect the output 507 to a power supply with two voltage levels, here indicated as +A and -A (508, 510), respectively. The switching unit 502 drives a circuit 511 including a band-pass filter 512 followed by the load 514. The switching unit (SU) 502 of the amplifier cannot be expected to accurately reproduce the waveform with which it is driven, especially in a high-frequency high-power setting.

0075[0056] Drawing 600 of Figure 6 illustrates the concept of DeltaSigma correction. For frequency shifting ΔΣ modulators, e.g., frequency shifting ΔΣ modulator 602 of Figure 6, the signal W or W _A 614, where W _A 614 denotes an analog form of W suitable for driving the switching unit 604, determines V 618 and the relationship between the two is relatively straightforward. Here we let M608 denote the map that gives F618 from W^.614. In Figure 6 we have illustrated the concept of ΔΣ correction for frequency shifting ΔΣ 602. The actual waveform delivered to the filter/load 606 will of course differ from W A. 606. We denote the actual

0076waveform by 616. Now, we imagine a map M 610 that takes W^ 616 to V 620, such that if <img file="WO2007002770A2_D0010.tif" /> ^^en<img file="WO2007002770A2_D0011.tif" /> T^ne ^^ea *^s ^^at by replacing V with V in the feedback path of the ΔΣ <img file="WO2007002770A2_D0012.tif" /> modulator 602, then W would represent a frequency translated version of U 612. In other words, V 620 would be a faithful base-band representation of W^. 616. The function V 620 can be assumed to be discrete-time with the same sample times as V 618 In such a case the values have been adjusted. The goal of the correction operation is to adjust the values of V 618 so as to properly produce V 620 so that, in effect, the signal W^ 616 represents the frequency shifted version of U 612. It is expected, and in many embodiments it is the case, that W^ 614 will therefore no longer be a faithful representation of a frequency shifted U 612 but will, rather, represent a compensated version, compensation being in accordance with the invention for the non-ideal behavior of the switching unit or units, e.g., transistors.

0077[0057] Non-ideal behavior in switching amplifiers has many sources. These include limited slew rate, which may differ in the two switching directions, transient impedances, current dependent voltage drop, etc. A significant fraction of these effects arise during the switch between states. The distortion introduced by these effects therefore is exacerbated at high operating frequencies.

0078[0058] In accordance with the present invention, it is possible to model the non-ideal behavior of the power delivering circuit (e.g., power transistors) under various realistic conditions to analyze the effect on the signal, and to use the results to correct the driving signal by altering the state of the frequency shifting ΔΣ modulator. In other words, it is possible to correct V to more closely resemble V. In practice, this can be complicated but is possible when using the methods and/or apparatus of the present invention. In accordance with the present invention, it is possible to correct the internal state of the ΔΣ modulator. [0059] One of the observations underlying the present invention is that a portion of the distortion of the waveform will depend on the current being delivered to the filter and load, especially during switching transitions. For band-pass RF signals the current to the load is proportional to real(u(t)e^jκ'), perhaps with some phase shift. A more detailed analysis is presented in the portion of this application under the subheading Analysis and Form of Compensation. In this discussion, u(t) is used to represent the base-band signal. In some cases, where the band-pass filter is not ideal for example, u(t) might be a filtered version of the input signal Thus, correction will be a function of recent transitions and the current base-band signal, or a filtered version of the base-band signal.

0079[0060] The switching unit is a physical device. Disturbances due to switching will decay over time. We can assume, however, that knowledge of the current and the input to the unit for some prior amount of time determines the output of the circuit to sufficient accuracy. The input to the circuit is determined by the output of the frequency shifting ΔΣ, whereas, assuming correct operation, the current is determined by the input signal. Because the bandwidth of the filter is small compared to the operating frequency, the memory of transitions is normally much smaller then the time scale over which envelope of the current to the filter can change significantly. Therefore, the correction to V to better approximate V will be a function of a state including past discrete outputs of the ΔΣ modulator and the baseband input, or its filtered version.

0080[0061] Figure 7 is a drawing 700 illustrating a correction computation module 702 which can be used in the system 800 shown in Figure 8. Figures 7 and 8 illustrate the idea of a compensated ΔΣ circuit implemented in accordance with the invention. System 800 of Figure 8 includes a complex Delta-Sigma Modulator 802 coupled to a correction computation module 702. Signal U 704 is a complex baseband signal which is input to both complex Delta-Sigma modulator 802 and correction computation module 702. Signal V 706 conveying complex decisions from Delta-Sigma, is output from Delta-Sigma Modulator 802 and used as input to correction module 702. Correction computation module 702 outputs correction signals 708, conveying correction to feedback and state values, which is input to complex delta-sigma modulator 802. In correction computation module 702, state information 707, e.g., V(t-1), V(t) is obtained from received signal 706. Input signal or a filtered version of the input signal ""^' sufficient to cϊefivi-citϊrferϊf Λs is obtained from complex baseband input signal 704. For example, information 705 is the information needed to decide the current that you want in a power amplifier for an ideal Delta-Sigma modulator. In sub-module 709, the correction computation module 702, performs a computation of correction to decision feedback, e.g., module 709 performs a parameter look-up based on state information 707 and a calculation of a parameterized function of current signal to determine a correction. Output correction signals 708 are input to the complex Delta-Sigma modulator 802. The compensator corrects the feedback term, representing the signal, to reflect the effects of the power amplifier. In general the correction will depend on some past window of ΔΣ output decisions and also the desired signal or a filtered version.

0081[0062] The compensator, e.g., correction computation module, uses and often stores, various parameters which can be learned from the operation of the amplifier. Some or all of the utilized parameters may be determined off-line in a calibration mode and/or programmed into the corrections computation module. In a general embodiment a current-dependent correction is represented as values of a function tabulated at many discrete points in a complex plane. The function is then evaluated by interpolation. A simpler alternative scheme that can be used in accordance with the invention uses a parameterized set of functions. Analysis by the inventors of the present application has shown that various low-order terms depending on the current can be sufficient, e.g. see Section 8. Other aspects of the current invention, including various frequency shifting ΔΣ schemes are designed to reduce the complexity of this calculation. We will address this issue in subsequent sections of this application.

0082[0063] In later sections of this application we show that it is reasonable to expect a term of the form au+βu to arise from current dependent correction. We will refer to this term as the proportional term. One such term requires 4 real parameters, as indicated by the complex α and β coefficients. The number of such terms required depends on the number of distinct cases. Different transitions with different relevant history constitute different cases that may require distinct parameters. Many of the modulation schemes of the invention described in the following sections aim at minimizing the number of cases for which distinct parameters are used. We will generally consider the number of such cases as we develop the various modulation schemes. 5 Frequency Shifting Δ∑

0083[0064] In this section we present various frequency shifting ΔΣ modulation schemes that can, and are, used in various embodiments of the invention.

00845.1 Direct Modulation Scheme

0085[0065] Drawing 900 of Figure 9 illustrates an example of a direct modulation scheme. Drawing 900 includes a linear transform function module 901, a quantizer Q₄ 902, a pulse shaping module 904, a multiplier module 908, a real part determination module 910 and a pulse shaping (D/ A) module 914 coupled together as shown in Figure 9. Linear transform function module 901 receives digital input U and input V, performs linear operations, and outputs signal S. Signal S is input to quantizer 902 which generates outputs Y and V. Output V is a feedback to the input of the linear transform module 901, while output Y is an input to pulse shaping module 904. One simple scheme for a frequency shifting ΔΣ modulator, that we will refer to as the direct modulation scheme of the present invention, is the following. Suppose the baseband I and Q signals are ΔΣ converted to produce +1 representations

00861 — ..., b_₁ , b₀ , b₁ ,

0087Q = ..., C_₁ , C₀ , C₁ ,

0088at a rate off J K samples per second where K is a positive integer. It is more convenient to view

0089these sequences as the functions and Q where δ, denotes a Dirac delta <img file="WO2007002770A2_D0013.tif" /><img file="WO2007002770A2_D0014.tif" /> function positioned at time t. We can think of the pair of functions as the complex function I-j^'Q, viewing this as a sequence of complex δ functions. The Fourier transform is periodic with period

0090<img file="WO2007002770A2_D0015.tif" /> [0066] Consider up-sampling by repeating each sample 4K times, e.g., using pulse shape module 904, so samples now are spaced T:=l/(4f ) seconds apart. This can be viewed as

0091convolving the function I-jQ with he Fourier transform of this function is <img file="WO2007002770A2_D0016.tif" />

0092<img file="WO2007002770A2_D0017.tif" />

0093a periodic form of the sine function that is nearly flat across the base-band.

0094[0067] Now consider multiplying this function 905 by e²^. 906 using multiplier 908 to produce signal 909. At the sample points, this evaluates to the sequence ...,lj^',-l,-j,l,.... This operation translates the Fourier transform by f Hz. Talcing the real part of the result 909 using module 910 gives

0095) <img file="WO2007002770A2_D0018.tif" />

0096e.g., for K=I, we effectively get the sequence

0097in this case.

0098[0068] Finally, the result W 912 is convolved with the square function (1 on <img file="WO2007002770A2_D0019.tif" /> and 0 elsewhere), e.g., by pulse shaping D/A module 914, to yield a ±1 function W^. <img file="WO2007002770A2_D0020.tif" />

0099916. This can be viewed as a pulse shaping step. The process is illustrated in Figure 9 where we have introduced the quantizer QA 902 to denote the four quadrant quantizer that quantizes the real and imaginary parts of its argument independently to +1 and -1 according to their sign. !I^"J1 IL, I! / l<img file="WO2007002770A2_D0021.tif" />^^b of the set of transitions that occur both within a clock period and at the beginning of that period then we may take account of each of the transitions. It is reasonable to expect in this case that the memory effects in the correction can be limited to one ΔΣ clock cycle. Thus, the correction for a given cycle depends on the decision in that given cycle and the one in the preceding cycle, earlier decisions can be ignored. During each ΔΣ cycle the signal W^ is a square wave with the same frequency as the carrier. The impact of the transitions will depend on the phase and amplitude of the current relative to the position of those transitions. +1 to -1 transitions may behave differently than -1 to +1 transitions. Therefore, for the proportional terms we may require 4* 16=64 parameters to cover each of the cases. Additional parameters may be used for shifts or if higher order current dependent terms are needed. Consider for example the embodiment shown in drawing 1000 of Figure 10. Drawing 1000 of Figure 10 illustrates a real form of a direct modulation scheme. Drawing 1000 includes a linear transform function module 901, a quantizer Q4 902, a pulse shaping module 904, a Real part determination module 1001, a Imaginary part determination module 1003, a first multiplier module 1006, a second multiplier module 1012, a summing module 1018, and a pulse shaping (D/A) module 1022 coupled together as shown in Figure 10. Note that in Figure 10, the output of the pulse shaping module 904 is used as input to both the real part determination module 1001 and imaginary part determination module 1003.

0100[0070] Notice that the ΔΣ loop representing U can run at a much slower frequency than f. (K can be large). For example, if the carrier frequency is IGHz then the samples of W are at

01014Gsps (Giga samples per second). The ΔΣ loop for U could run at some fraction of this speed, e.g., 200Msps (Mega samples per second).

0102[0071] The above method can be interpreted in other ways. For example, we can effectively avoid the complex domain as follows. Let / and Q denote the up-sampled / and Q signals. We multiply / 1002 by cos(w/), 1004 using multiplier module 1006 where, of course, ω :=2πf , which at the sample points gives the sequence

0103..., 0, 1, 0, -1, 0, 1, 0, ... and we multiply 1008 by sin(ω J) 1010 using multiplier module 1012 which, at the <img file="WO2007002770A2_D0022.tif" /> sample points, gives the sequence

0104..., - 1, 0, 1, 0, - 1, 0, 1, ...

0105then the results (1014, 1016) can simply be added together using adder module 1018 to give W 1022. Figure 10 illustrates this interpretation. The ordering of operations can be changed as shown in drawing 1100 of Figure 11, Drawing 1100 illustrates a re-ordered Real form of the direct modulation scheme of Figure 10. In Figure 11 processing is performed by two pulse shaping (DfA) modules (1102, 1104) prior to subjecting the signals to summing module 1110, while in Figure 10, the signal summing is performed by summing module 1018 prior to the single pulse shaping (D/ A) module 1022. In implementation 1100 of Figure 11, output signal 1014 from multiplier 1014 is input to pulse shaping (D/A) module 1102, while the output signal 1016 from multiplier module 1008 is input to pulse shaping (D/A) module 1104. The output signal (1106, 1108) from pulse shaping D/A modules (1102, 1104), respectively are input to summing module 1110 which combines the signals and generates output signal W_A 1112. Exemplary waveforms produced by this arrangement are depicted in drawing 1200 Figure 12 illustrating exemplary signals (1102, 1014, 1008, 1106, 1108, 1112), respectively, when viewed from the top of the page to the bottom of the page.

0106[0072] A more suggestive variation in accordance with another feature of the invention is shown in drawing 1300 Figure 13. Here the up-sampling by AK and multiplication by ^^r has been placed prior to the quantizer. Linear transformation function module 1301 receives inputs U and V, performs linear operations, and outs signal S. Signal S is an input to pulse shaping module 1302. Pulse shape module 1302 outputs signal 1303 which is input to multipler module 1306. The multiplier module 1306 multiplies input signal 1303 with &lt;/^ωc^r 1304 resulting in signal 1307 which is input to quantizer ^ 1308. The symmetry of the quantizer

01071308 matches the timing so that if the output of the quantizer Q^ 1310 is multiplied by e^"^^ωc'

01081312 by multiplier module 1314 resulting in signal 1315 and then signal 1315 is down-sampled by AK by module 1316 resulting in V, then the operation is as before. Note that the operations of modules 1314 and 1316 (demodulation and down sampling) perform the inverse of modules 1302 and 1316 (up sampling and modulation). The output Y 1316 from Q₄ is already centered around ω_c. In such an embodiment, we take the real part of signal y 1316 using module 1318 and obtain signal W 1320. Signal W 1320 is subjected to pulse shaping by pulse shaping (D/A) module 1322 obtaining output signal WA 1324. Notice that the imaginary output of the quantizer is not used in such an embodiment except in the feedback path. We can remove it also from the feedback path provided we adjust the down-sampling appropriately. This shows that it is viable to have a real quantizer operating within the ΔΣ loop in accordance with some embodiments of the invention.

01095.1.1 Implementation with Delays

0110[0073] The direct modulation scheme may seem to require an output clock at frequency Af _c, or at least an invertible square clock at frequency Tf . However, we can implement the above scheme, with a square- wave clock running at/\ by providing the a clock having four equally spaced phases, and by selecting between them using the complex output of the quantizer. Drawing 1400 of Figure 14 illustrates a circuit implemented in accordance with this feature of the invention that uses this idea. Drawing 1400 illustrates an exemplary four phase carrier clock implementation of a direct modulation scheme in accordance with various embodiments of the invention. Digital input U and feedback input Fare used as input by linear transform function module 1401, which performs linear operations and outputs signal S to the input of quantizer Q₄ 1414. A clock having four equally spaced phases (1402, 1404, 1406, 1408) is provided. Complex output 71410 of quantizer Q₄ 1414 is used by multiplexer module 1416 to select between the four phases of the clock outputting signal WA 1418. A selection is applied for a duration of K carrier cycles. In various embodiments, the switching rate of the mux 1416 is slower than the clock rate.

01115.2 More General Forms and Offset Clocks

0112[0074] Another variation on the frequency shifting ΔΣ is depicted in drawing 1500 of Figure 15 where we have also indicated different clock domains. Drawing 1500 illustrates an alternate frequency shifting DeltaSigma form including a 1^st stage 1502 having a clock period T₁ followed by a second stage 1504 having a clock period T]/K. The second stage 1504 is followed by a pulse shaping (D/A) 1506. [0075] The first stage 1502 includes a linear transform function module 1502, a first multiplier 1503, a quantizer Q₂ 1508 and a second multiplier 1505. Linear transform function module 1501 receives digital input U and feedback input V, performs linear operations, and generates output signal S. Output signal S and e^jwst are inputs to multiplier module 1503 which outputs a signal to quantizer 1508. Output signal Y from quantizer 1508 is an input to the second stage 1504. An output from quantizer 1508 and e^"jwst are inputs to multiplier module 1505 resulting in output signal V.

0113[0076] Note that in the Figure 15 embodiment, we have used quantizer Q^ 1508. This quantizer 1508 produces ±1 depending on the sign of the real part of its argument. Since the output Y 1509 of the quantizer 1508 is real we do not need to select the real part and the f_aCtø_r j_s ^placed with cos In second stage 1504, input signal Y <img file="WO2007002770A2_D0023.tif" /><img file="WO2007002770A2_D0024.tif" />

01141509 is processed by pulse shaping module 1511 generating signal 1513, which is multiplied with cos((ω -ω )f). 1502 by multiplier module 1515 generating signal W \5\l which is output from the second stage 1504. The pulse shaping module 1506 processes signal W \5\l and generates signal W_A 1519.

0115[0077] We remark in passing that the first stage 1502, with clock period T_j , has an equivalent form as illustrated in equivalent first stage 1602 of Figure 16. First stage 1602 includes a multiplier module 1603, a linear transform function module 1601 and a quantizer Q₂ 1608 coupled together as shown in Figure 16. Digital input signal U and e^iwst are inputs to multiplier module 1603 which outputs one of the inputs to the linear transform function module 1601. The other input to the linear transform function module 1601 is an output of quantizer 1608.

0116[0078] Here the input!!/ is modulated up to ω _ by module 1603 and, in the transfer

0117functions LQ and L^, z is replaced with effectively rotating the unit circle in the z <img file="WO2007002770A2_D0025.tif" /> domain to center on ω^,. Equivalence holds regardless of the quantizer, i.e., not just for Q^

0118[0080] The frequency ω „ represents a partial shifting of frequency. Even negative values for ω are conceivable, but we will focus on positive values. Various possible choices for the 'parameters will now be discussed. Let us start by setting ω =αω „ where α is a fraction. The sample times in the first loop are multiples of T-, . For convenience of implementation we might

0119choose T₁ so that e^jωΛkΑ) e {l,j -l -j}. We can achieve this if fj_λ = of J₁ is a multiple of <img file="WO2007002770A2_D0026.tif" /> (odd multiples preferably). For example let us set it to so <img file="WO2007002770A2_D0027.tif" />

0120<img file="WO2007002770A2_D0028.tif" />

0121We observe that the quantizer £?2 alternates between quantizing the real and imaginary part. By construction the output of the quantizer Y approximates the input signal shifted to center frequency ω . In other words, approximates U. <img file="WO2007002770A2_D0029.tif" />

0122[0081] Similarly, in order to ensure that W^ is a two-valued function, we choose

0123<img file="WO2007002770A2_D0030.tif" />

0124so that, in the faster processing, we have

0125<img file="WO2007002770A2_D0031.tif" />

0126(where A; is an arbitrary integer). We therefore obtain the relation

0127<img file="WO2007002770A2_D0032.tif" /> which yields α= <img file="WO2007002770A2_D0033.tif" />

0128[0082] Finally, we pulse shape with a square pulse of width to give a ±1 function <img file="WO2007002770A2_D0034.tif" />

0129^WA- [0083] Notice that an equivalent implementation, and this was the underlying motivation, is to simply take the output 7 and use it to modulate a square wave clock of

0130frequency ^~z — . The scheme of the present invention is depicted in drawing 1700 of Figure 17.

0131Drawing 1700 includes a linear transform function module 1701, a first multiplier 1702, a quantizer Qj 1703, a second multiplier 1704, a clock 1705, and a clock boundary modulation module 1606, coupled together as shown in Figure 17. Linear transform function module 1701 receives as input U(z) and V(z), performs linear operations and generates output signal S(z) . Output signal S(z) and e?^wst are inputs to multiplier module 1603 which outputs a signal to quantizer Q₂ 1703. Quantizer Q₂ 1703 quantizes into 2 quantities, e.g., such as with BPSK quantization. Output Y(z) 1705 from quantizer 1703 is a control input to module 1706, which decides whether or not to invert the clock input as a function of the control input signal 1705. Module 1706 receives input clock 1705 and outputs WA. Module 1706, performs flipping of the clock, as determined, on clock boundaries. Thus signal W_A either matches the clock or is an inverted version of the clock at any given time.

0132[0084] One advantage of this method of the invention, besides the fact that it can be implemented with a single clock of frequency lower than/., is that it can significantly reduce the number of parameters needed for correction. There are two possible waveforms in each cycle rather than four. The number of proportional parameters needed is therefore reduced by a factor of four from the previous case (still assuming single symbol memory).

0133[0085] In such an embodiment we can still use a symmetric clock (or a clock at twice the frequency) to avoid additional correction terms.

01345.3 Zero-One Signals

0135[0086] So far we have limited our discussion to systems and embodiments that produce +1 signals. Here we will consider signals that use instead 1 and 0. Such embodiments will be seen to have several advantages with regard to correction.

0136[0087] Let us consider the very simple variation of the invention shown in Figure 18 and let us assume that the clock speed is high, on the order of the carrier frequency. Figure 18 may be a special case of a Figure 17 embodiment. Drawing 1800 of Figure 18 includes a linear transform function module 1802, a first multipler module 1802, a quantizer Q∑ 1803, and a second multiplier module 1804, coupled together as shown. Linera transform function module 1801 receives input signal U(z) and feedback signal V(z) as inputs, performs linear operations using function LQ(Z) and Li(z), combines results and outputs signal S(z). Multiplier module 1802 receives S(z) and e^⁰¹ as input and outputs a signal which input to quantizer Q2 1803. Quantizer Q2 outputs signal Y(z). The output from quantizer Q₂ 1803 is also input to second multiplier module 1804, which multiples the output from the quantizer 1803 with e^"jwct obtaining V(z) Let the quantizer 1803 by asymmetrical, producing only the real values 0 and 1. Some region around the point (1,0) gets quantized to 1, all other points quantize to 0. Ideally, the output Y is a 1,0 discrete signal that approximates the real part of the desired signal in the band of interest.

0137[0088] Let plq be a fraction in lowest terms. Consider a clock that has q cycles for every p cycles of the carrier. Each cycle of the clock traverses φ radians of the carrier where gφ=p2π or §=(p/q)2π. Thus, the sample times are p/(qf )Z so

0138<img file="WO2007002770A2_D0035.tif" />

0139taking q possible values. Thus Fis a 0,1 sequence and approximates t/in the <img file="WO2007002770A2_D0036.tif" /> baseband. We pulse shape Y by using a square wave of width and it can be implemented by <img file="WO2007002770A2_D0037.tif" /> gating (allowing a pulse or not) a clock of frequency <img file="WO2007002770A2_D0038.tif" />

0140[0089] If q=5 for example, a quantizer might be chosen as indicated in Figure 19 where a 72 degree cone covers the region where a 1 is selected, a region around the origin being excluded. The cone could be chosen wider, e.g. 90 degrees, to simplify implementation and to encourage selection of multiple points in q cycles. Figure 19 is a drawing 1900 illustrating an exemplary possible decision region for q=5. Drawing 1900 illustrates the complex plane with vertical axis 1901 representing the Imaginary axis and horizontal axis 1903 representing the Real axis. Point (1,0) 1907 is shown, and area 1905 gets quantized to I₅ all other points in the plane quantize to 0. ^"'" <img file="WO2007002770A2_D0039.tif" /> circuit the effect of the decision is not seen until two clocks later. Thus, ifp does not equal 1 or q-\ modulo q then it is very unlikely that a 1 will be picked two cycles in a row (and it could be enforced). Thus, each 1 is likely to be followed by a zero. Correction in this case can be nearly memoryless or possibly memoryless, which can be an advantage over some other embodiments.

0141[0091] It is feasible to slow down the ΔΣ clock in such a scheme. For example an architecture such as shown in Figure 15 in which Q_j is replaced with a 0-1 quantizer is possible, but it reduces to repetition in the second stage. Indeed, set (ϋ_s=a(ϋ_c and set the clock period Tγ such that <img file="WO2007002770A2_D0040.tif" /> Then

0142(\-a)f_cTJK = l. so

0143\ ~ a

0144^■ = Kq / 2 a ox a=ll(l+Kql2).

0145[0092] Figure 19 shows a possible decision region for q=5.

0146[0093] Since the driving signal is only 0 and 1 and all phase information is carried in pulse position, correction requirements are tremendously reduced. If all Is are followed by at least one 0, then switching effects can be expected to be memoryless, assuming appropriate pulse shaping. Asymmetry in up and down transitions is irrelevant since this just affects the pulse shape and a single form maybe used. As long as the clock is accurate, the corrections can be limited to current dependent ones. Moreover, in such an embodiment since there is a single pulse shape, a single correction function can be used.

01476 Striding ΔΣ .

0148[0094] It can be advantageous for noise shaping to run a ΔΣ loop at a high clock rate, much higher than the Nyquist rate of the signal. In many embodiments, for the input sampling it is usually sufficient to sample at some smaller multiple of the Nyquist frequency, e.g. 16 times, <img file="WO2007002770A2_D0041.tif" /> domain are sufficiently far away. Subsequent to that, the signal can be up-sampled by repetition by a factor of K say to the clock rate of the ΔΣ. This means, however, that the input to the ΔΣ is predictable for those K- 1 repetitions. Given the state XQ of the ΔΣ and the input UQ the states up until Xg are determined. Instead of running the ΔΣ loop for these cycles, we can, and in various embodiment do, stride directly to the state Xg- and produce the K outputs for the steps. In such implementations we are free to generalize in several ways. We can, and in some embodiments do, choose the outputs differently, non-causally for example, and update the state accordingly. The decision rules for sequences can be more complicated then in single step ΔΣ. In a high order ΔΣ, for example, we could first choose sequences so as to minimize the error in the first integral and then, among viable choices, minimize the error in the second, and so on. Different functionals can also be used. For example we have multi-dimensional representations of possible sequences, in some embodiments, indicating their impact on the state of the ΔΣ, and then several functionals of the current state and input are used to select the sequence. Moreover, in at least some but not necessarily all such embodiments, the delays inherent in standard ΔΣ can be partially eliminated.

0149[0095] The output in various embodiments gets mapped to a two-level function and the state update is effectively performed at the higher clock rate.

0150[0096] Let us here give a simple example of an application of the striding concept using the frequency shifting ΔΣ modulator presented in Section 5.3. Let the striding ΔΣ step with a clock of period p/f , i.e. p periods of the carrier. During that period the bit clock in this example runs through exactly q cycles. At each possible sample point the ΔΣ may select to transmit a given pulse waveform, the timing of the pulse giving rise to a distinct phase offset with respect to the carrier of a multiple of 2π/q modulo 2π. Assuming for the moment that only zero or one pulse can be selected in each q cycle period, the modulation is approximately equivalent to choosing a qth root of unity point in baseband, or the origin. Choosing one of the q+l possibilities. In a single striding update, we recognize that it involves q clock cycles and, depending on the point chosen, the state will be appropriately updated.

0151[0097] We could also, e.g., allow pairs of adjacent (in phase) pulses to be chosen. In the constellation, such pairs can be represented by the sum of the corresponding points. If /modulo^1' yyf riVtfWeffWtses which are adjacent in phase are not adjacent in time. In this case, one might reasonably expect that the correction process could be essentially memoryless, reducing its complexity. Figure 20 shows possible constellations for q-5 and p=2 with and without allowed pairs. Drawing 2000 of Figure 20 shows an exemplary six point constellation facilitating pairs of adjacent pulses to be chosen. Drawing 2002 of Figure 20 shows an exemplary 11 point constellation without allowed pairs.

0152[0098] Notice how with a striding ΔΣ we can impose constraints on used waveforms. This can be exploited to a greater extent taking advantage of very fast digital circuits. Suppose for example, a clock that is 8 times the carrier frequency is available. We can use a pulse, triggered by the clock, as our driving signal. In addition, however, we allow the pulse to last either 1, 2, or 3 cycles long. The allowed pulses are therefore of three types, along with time shifts. Let us assume that striding ΔΣ is clocked at the carrier frequency. In each clock cycle it chooses the length of the pulse, 0, 1, 2, or 3, and, assuming 0 is not chosen, its starting point. This is similar to picking a point from the constellation shown in Figure 21. Drawing 2100 of Figure 21 shows an exemplary constellation that may be used if a clock that is 8 times the carrier frequency is available.

0153[0099] Each layer of points may require a fixed correction for differences in pulse shaping, but this would be one complex parameter per additional level beyond the first (two in this example), since phase symmetry holds. For current dependent correction, each type of pulse can use its corresponding set of parameters, (three in this example).

0154[00100] A striding ΔΣ can be run at a slower clock. In the above example, it can make a decision every K cycles of the carrier. We could think of this as choosing from the constellation K times. To simplify the implementation we can implement one choice with repetition. We might allow from 1 to K repetitions. This is similar to using a larger constellation which includes the current one and each point scaled by factor of 2, 3,..., K. For value of the first integral, this is equivalent. For each first integral value, however, we can freely choose which cycles receive the pulses (assuming less than K) in order to minimize higher order error terms.

0155[00101] We have mentioned several times that various schemes have the advantage of memorylessness in the correction. For striding ΔΣ this can, and in some but not necessarily all embodiments is, enforced. For example, in the above scheme where we repeat a pulse, even if "^'"' '""' <img file="WO2007002770A2_D0042.tif" /> it is possible that at boundaries, between decision regions, pulses could be close enough together to interact, introducing the use of memory in implementing the correction. In some embodiments a striding ΔΣ simply uses a small buffer region, e.g., a certain period in which no pulses are allowed, at the end of its decision period thereby allowing for memoryless correction.

0156[00102] A striding ΔΣ can mimic multi-bit or multi-level ΔΣ. There are some differences with regard to higher order integrals. One could, however, choose a sequence for each constellation point so that the overall behavior is similar to a multi-bit ΔΣ. In such embodiments, performance advantages of using a multilevel ΔΣ would accrue. Even better performance might then be possible by choosing among other sequences that equate to the same constellation point under first order considerations.

0157[00103] It will be apparent that the striding ΔΣ concept applies equally well to real ΔΣ and also to ΔΣ that are not necessarily frequency shifting.

01587 Calibration

0159[00104] The proposed methods may, and in some embodiments do, involve the evaluation of certain parameters representing non-ideal behavior of the switching amplifier, e.g., under actual conditions of use. These parameters may vary over time due to, e.g., thermal drift. Thus, on-line calibration of the parameters can be useful and is performed in some but not necessarily all embodiments.

0160[00105] Figure 22 is a drawing 2200 of exemplary receiver based calibration used in various embodiments. Drawing 2200 includes a complex Delta-Sigma Modulator module 2202, a power amplifier 2204, a receiver chain 2206, a parameter estimation module 2208, an a correction computation module 2210 coupled together as shown in Figure 22. The parameter estimation module 2208 and receiver module 2206 are part of a calibration module 2201. The receiver module 2206, in the illustrated embodiment, includes a demodulator 2207. However, in other embodiments the demodulator 2207 may be omitted from the receiver circuitry. Input signal U is an input to both the complex Delta-Sigma Modulator 2202 and correction computation module 2210. Signal WA is an output of the complex Delta-Sigma Modulator module 2202 and is an input to the power amplifier 2204 and correction computation module IF L <img file="WO2007002770A2_D0043.tif" /> a signal which is transmitted from the device and fed back into receiver chain 2206. The power amplifier 2204 has a characteristic physical behavior which is modeled in accordance with various embodiments. The output of the power amplifier is coupled to the input of the receiver module 2206 and also to an additional element, e.g., antenna, which is not shown. In some embodiments, a connection to the antenna is used as the source of the signal being supplied to the receiver 2206. In some but not necessarily all embodiments, a load and/or filter, not shown, may be coupled between the power amplifier output and the receiver module 2206. The receiver module output signal is an input to the parameter estimation module 2208. The output of the parameter estimation module 2208 is an input to the correction computation module 2210. When used in a communications device, the receiver module 2206 used to support device calibration through processing of the signal being generated, e.g., for transmission, may be in addition to a receiver in the communications device used for processing signals received by the device from a wireless communications channel.

0161[00106] Receiver chain 2206 obtains noise free or nearly noise free reception, in some embodiments, by obtaining the input signal used for parameter estimation by tapping off the power amplifier output used as the antenna signal. Thus, air link associated noise, which would otherwise be an additional error source impacting calibration, does not degrade the parameter estimation. Parameter estimation module 2208 looks at the signal from the receiver chain 2206 and estimates one or more parameters, e.g., parameters which are utilized by correction computation module 2210. In various embodiments, null pilot signals are advantageously utilized. For example, in an exemplary OFDM wireless communications systems, null pilot tone signals, are intentionally placed on some predetermined tone-symbols in a recurring channel structure. If zero is not observed on a null pilot measurement, the observed value may be attributed to some sort of calibration error. The value of the measured signal, where a null was expected can be advantageously used in estimating modeling parameters.

0162[00107] Consider that correction computation module 2210 is module 702 of Figure 7, the parameter estimation of module 2208 may be, and sometimes is, used to update the processing of module 709, e.g., updating a parameter look up table, storing a new parameter look-up table, adjusting parameters in a mapping function, etc. Thus parameter estimation module 2208 facilitates dynamic recalibration of correction computation module 2210. Thus the correction computation module 2210 can be adjusted to more accurately reflect a power amplifier's current characteristics. In various embodiments, the updating to the correction computation module <img file="WO2007002770A2_D0044.tif" /> estimation module 2208, is performed at a slower rate than the corrections, e.g., corrections to feedback and state values, are communicated to the complex delta-sigma modulator module by the correction computation module 2210 and/or used by the delta-sigma modulator 2202.

01638 Analysis and Form of Compensation

0164[00108] In this section we present some analysis of current dependent correction expected from switching amplifier circuits.

0165[00109] Let us first consider modeling the circuit using a time varying Thevenin equivalent circuit 2300, see Figure 23. Exemplary time varying Thevenin equivalent circuit 2300 includes a time varying voltage V(t) 2302 in series with a resistance R(t) 2304.

0166[00110] Drawing 2400 shows an exemplary drawing including a time- varying voltage V(t) 2402, a resistance R(ή 2404, a filter 2406 and a load 2408 connected in series. For simplicity at this point let us assume that the circuit has a representation using the Thevenin equivalent as a time- varying voltage V(f) 2302 and resistance R(t) 2304. This is expected to be valid for e.g., FET transistors operating in the triode region. Let us also assume that the filter 2406 is an ideal band-pass filter: constant gain in the passband with no delay.

0167[00111] Let us consider the impact of R(t) during a single clock cycle. Let Iψ(t) be the indicator function of that cycle. We are interested in the function

0168(I _w (OR(O)I_n (O where I_β(t) denotes the instantaneous current entering the filter. Over the support of I_jψ(t) the

0169current is proportional to real(W°V) with, possibly a phase shift that we will ignore. Here u is the input signal or a suitably filtered version at that point in time and represents the envelope of the current passing through the filter and load. Extending this function over all time (for convenience) the Fourier transform is given by,

0170F[IR) = u,δ_ω + u'δ__ω In general, F(I_WR) is a relatively complex object. We are interested, for purposes of discussion, in its contribution to the pass-band. Since the time support oilψR is very short, the Fourier transform is relatively smooth. We shall approximate by treating the value of the transform as a constant over any interval of size equal to the pass-band. Then, in the pass band (for ωω_c) we see that

0171F(I_wRI_R)(ω) ==^■ F(IwR)(Q)X + J⁷(IwB)(2ω_c)x* := au + βu^* .

0172Note that the possible phase shift in the current, ignored above, can be incorporated into the complex constants α and β. In the Fourier domain, the disturbance signal caused by IψR(t) is essentially constant across the band of interest. Thus, we are lead to the important observation: The effect transient impedance can be modeled with an equivalent complex impulse. The height of the impulse is proportional to the current signal but also depends on the phase. See drawing 2400 of Figure 24.

0173[00112] Consideration of FET transistor behavior (transient operation in non-triode regions) indicate that besides the above correction it may also be useful to use a correction which is quadratic in x. Constant terms also appear due to offsets etc. in voltages and devices, although many of the frequency shifting ΔΣ schemes obviate or minimize the use of such terms. Thus, the correction will typically have the form

01747l + au + 0U^* + 72«r_e + 73«L + 74«im«re + ...

0175where γ • are complex parameters, with higher order terms being introduced if desired. The complex coefficients may be learned or identified for each device and for each distinct transient case. They might also vary slowly over time. They capture the relevant imperfections in the devices and their effects on the delivered signal. In the most general case one might conceive of an arbitrary complex function of current for a correction term. The function could be identified and tabulated at many points in the complex plane and otherwise evaluated using interpolation.

0176[00113] The value of R(ή discussed above, as well as other disturbances, can be expected to depend on the transitions that have been made in the driving circuit. The effects will decay in tfnϊe, 'buFpemi-ifis n^'ol'iMhirrone clock cycle. In such a case, some memory of previous transitions is used to characterize the disturbance.

0177[00114] Once a correction e_t is computed it should be incorporated into the state of the ΔΣ. Where the term V_f appears in the current state it should effectively be replaced by V_t+e_f. In the case of striding ΔΣ, for example, a correction term may arise for each step strided over, the combined effect would be incorporated into the state. In many cases the corrections for sequences produced by striding ΔΣ could be pre-computed and stored. Updating of the stored values maybe be limited to when the parameters associated to corrections had changed significantly.

EXEMPLARY EMBODIMENTS:

0179[00115] As discussed above, the methods and apparatus of the invention are not limited to RF applications. Various audio amplifier features and embodiments will now be discussed. Audio amplifiers should faithfully reproduce signals in the range of 20Hz to 20,000Hz covering a range that includes a factor of 1000. A frequency shifting ΔΣ, used in various RF embodiments described above, is not used in some audio applications. However, the basic ideas of correcting and calibrating for non-ideal behavior of the amplifier in the context where a ΔΣ modulator discussed above in the context of RF applications still apply and are used in various audio embodiments.

0180[00116] One advantage of the audio amplification case, which is a lower frequency setting than the RF case, is that the absolute peak in frequency is relatively low compared to digital speeds at which may currently available digital circuits can operate. Thus, significant processing and sophisticated modeling of the correction are possible.

0181[00117] Assuming that the transient switching impedance is purely resistive, we observe that an important quantity to know is the current entering the filter. In general, properties of the instantaneous current are may be relevant to the correction. At audio frequencies it is possible to simply measure the current on a fast time scale and use this value directly to compute the correction term. This is done in some but not necessarily all embodiments. [00118] Provided the current measurement is sufficiently accurate, which it is in some embodiments, and sampled quickly enough, e.g., at a multiple 2, 4, 8 or more times the highest audio frequency signal being amplified, we could even correct for subtle components of the transient disturbance by allowing use of more complex correction models, such as ARMA models. This is done in some, but not necessarily all audio embodiments of the present invention.

0182[00119] Figure 25 illustrates a communications system 10 implemented in accordance with the invention. In the system 10, multiple wireless terminals, e.g., mobile nodes such as mobile terminals, shown as mobile nodes MN 1 (14) through MN N (16) communicate with the base station 12 through the use of communication signals 13, 15. Each mobile node may correspond to a different mobile user and are therefore sometimes referred to as user terminals. The signals 13, 15 may be, e.g., OFDM signals. The base station 12 and mobile nodes 14, 15 each implement the method of the present invention. Thus, signals 13, 15 include signals of the type discussed above, which are transmitted in accordance with the invention. Various embodiments include a plurality of base stations coupled together via a backhaul network.

0183[00120] Figure 26 illustrates an exemplary base station, e.g., access node 12, implemented in accordance with the invention. Base station 12 may also be referred to as an access router. The base station 12 includes antennas 3203, 3205 and receiver and transmitter modules 3202, 3204, respectively. The receiver module 3202 includes a demodulator 3231 and decoder 3233 while the transmitter module 3204 includes an encoder 3235. The transmitter also includes a power amplifier module 3237, e.g. a D or S type switching power amplifier module, a Delta- Sigma modulator module 3239, a correction computation module module 3241, and a calibration module 3243. The calibration module 3243 includes, in some embodiments, a receiver module 3245 and a parimeter estimation module 3247. The correction compuation module 3241 may be the same as or similar to the correction computation module 2210 of Figure 22. In addition, the calibration module 3243 may be the same as or simalar to the calibration module 2201 shown in Figure 22. The components of the transmitter may be coupled together as shown in Fig. 22 with an output of the encoder 3235 suppling an input signal to the delta sigma modulator module 3239. The receiver 3202 and transmitter 3204 are coupled by a bus 3230 to an I/O interface 3208, processor (e.g., CPU) 3206 and memory 3210. The I/O interface 3208 couples the base station 312 to the Internet and/or to other network nodes. The memory 3210 includes routines, which when executed by the processor 3206, cause the base ^"" <img file="WO2007002770A2_D0045.tif" /> with the invention. Memory includes communications routines 3223 used for controlling the base station 12 to perform various communications operations and implement various communications protocols. The memory 3210 also includes a base station control routine 3225 used to control the base station 12 to implement the steps of the method of the present invention. The base station control routine 3225 includes a scheduling module 3226 used to control transmission scheduling and/or communication resource allocation. Thus, module 3226 may serve as a scheduler. Memory 3210 also includes information used by communications routines 3223, and control routine 3225. The information 3212 includes an entry for each active mobile station user 3213, 3213' which lists the active sessions being conducted by the user and includes information identifying the mobile station (MT) being used by a user to conduct the sessions.

0184[00121] Servers and/or host devices may be implemented using circuitry which is the same as, or similar to, the circuitry of the exemplary access router shown in Figure 26 but with interfaces and/or control routines suited to the particular server/host device's requirements. The control routines and/or hardware in such servers and/or hosts cause the devices to implement the above described methods.

0185[00122] Figure 27 illustrates an exemplary wireless terminal, e.g., a mobile node, 14 implemented in accordance with the present invention. The mobile node 14 may be used as a mobile terminal (MT). The mobile node 14 includes receiver and transmitter antennas 3303, 3305 which are coupled to receiver and transmitter modules 3302, 3304, respectively. The receiver module 3302 includes a demodulator 3331 and decoder 3333 while the transmitter module 3304 includes an encoder 3335. In some embodiments, transmitter 3304 may also include modules which are the same as or similar to power amplifier module 3237, delta sigma modulator module 3239, correction module 3241, and/or calibration module 243. In the illustrated embodiment, the transmitter module 3304 includes an encoder 3235, power amplifer module 3337, delta sigma modulator module 3339, correction computation module 3341 and a calibration mdoule 3343. The calibration modoule 3343 includes a receiver module 3345 which may include a demodulator and a parameter estimation module 3347 used for generating correction parameters. The correction computation module may be the same as or similar to correction computation module 2210 while the calibration module 3343 may be the same as or similar to the calibration module 2201 shown in Figure 22. The receiver and transmitter modules 3302, 3304 are coupled by a bus 3330 to a memory 3310. Processor 3306, under <img file="WO2007002770A2_D0046.tif" /> in memory 3310 causes the mobile node to operate in accordance with the methods of the present invention. In order to control mobile node operation memory includes communications routine 3323, and wireless terminal control routine 3325. The wireless terminal control routine 3325 is responsible for insuring that the mobile node operates in accordance with the methods of the present invention and performs the steps to implement methods of the present invention. The memory 3310 also includes user/device/session /resource information 3312 which may be accessed and used to implement the methods of the present invention and/or data structures used to implement the invention.

0186[00123] Figure 28 is a drawing of a flowchart 2800 of an exemplary method of operating a device including a delta sigma modulator and a correction computation module in accordance with various embodiments. The exemplary method may be used in amplifying signals through the use of a delta sigma modulator which supports a plurality of discrete signal output levels and a correction computation module. For example, the exemplary method is, in some embodiments, used in a communications device such as a base station or wireless terminal, the communications device including a delta sigma modulator, a correction computation module for determining corrections to be applied to the delta-sigma modulator, and a switching amplifier stage.

0187[00124] Operation starts in step 2802, where the device is powered on and initialized. Operation proceeds from start step 2802 to step 2804. In step 2804, the device operates the delta sigma modulator to generate an output signal. Operation proceeds from step 2804 to step 2806. In step 2806, the device stores in memory the delta sigma modulator output signal value. The stored delta sigma modulation output signal value from step 2806 can be used subsequently in generating a correction signal. Operation proceeds from step 2806 to step 2808.

0188[00125] In step 2808 the correction computation module is operated to generate a correction signal as a function of a current input signal to the delta sigma modulator and the output of the delta sigma modulator. In some embodiments, generating said correction signal includes computing delta sigma modulation correction feedback from an estimate of a current envelope of a current entering a filter and load module. In some such embodiments, said estimate of a current is a linear function of the complex input to said delta sigma modulator. In some such embodiments, the method further comprises the step of supplying the estimate of a current as an input to the delta sigma modulator. [001261 Operation proceeds from step 2808 to step 2810. In step 2810, the delta sigma module is operated to generate an output signal as a function of the current input signal to the delta sigma modulator and a correction signal generated from a previous output of the delta sigma modulator.

0189[00127] In some embodiments, the delta sigma modulator is complex and the correction signal is complex. In some such embodiments, generating a correction signal includes generating a real correction signal component as a function of both a real input signal component and an imaginary input signal component of the complex input to the complex delta sigma modulator and generating an imaginary correction signal component as a function of both said real input signal component and said imaginary signal component of the complex input to the complex delta sigma modulator.

0190[00128] Operation proceeds from step 2810 to step 2812, where the device stores in memory the delta sigma modulator output signal value from step 2810. The stored delta sigma modulation output signal value from step 2812 can be used subsequently in generating correction signals.

0191[00129] Operation proceeds from step 2812 to step 2814. In step 2814, the device operates a switching amplifier coupled to the output of the delta sigma modulator to amplify the delta sigma output by switching between two states. Operation proceeds from step 2814 to step 2816. In step 2816, the output of the switching amplifier is subjected to a filtering and loading operation. In some embodiments, subjecting the output of said switching amplifier to a filtering and loading operation includes passing the output of said switching amplifier through a filter and load module which includes a filter and load coupled together. In some embodiments, the filtering and loading operation includes performing a bandpass filtering operation.

0192[00130] Operation proceeds from step 2816 to step 2818. In step 2818, the device performs a receiver operation on the amplified signal output by the switching amplifier, and then in step 2820, the device estimates at least one parameter, to be used by said correction computation module in generating correction feedback, from a signal produced by said receiver operation. <img file="WO2007002770A2_D0047.tif" /> 2802 to step 2822. In step 2822, the device operates clocking circuitry to control the correction computation module. In some such embodiments, operating the clocking circuitry to control the correction computation module includes controlling the correction module to produce a complex correction value at the same rate as an update rate of the delta sigma modulator.

0193[00132] The techniques of the present invention may be implemented using software, hardware and/or a combination of software and hardware. The present invention is directed to apparatus, e.g., mobile nodes such as mobile terminals, base stations, communications system which implement the present invention. It is also directed to methods, e.g., method of controlling and/or operating mobile nodes, base stations and/or communications systems, e.g., hosts, in accordance with the present invention. The present invention is also directed to machine readable medium, e.g., ROM, RAM, CDs, hard discs, etc., which include machine readable instructions for controlling a machine to implement one or more steps in accordance with the present invention.

0194[00133] In various embodiments nodes described herein are implemented using one or more modules to perform the steps corresponding to one or moz-e methods of the present invention, for example, signal processing, symbol generation, transmission steps, calibration, signal modeling, error measurement, correction computations, correction adjustments, state updating, delta sigma modulator control, and/or power amplifier control, etc. Thus, in some embodiments various features of the present invention are implemented using modules. Such modules may be implemented using software, hardware or a combination of software and hardware. Many of the above described methods or method steps can be implemented using machine executable instructions, such as software, included in a machine readable medium such as a memory device, e.g., RAM, floppy disk, etc. to control a machine, e.g., general purpose computer with or without additional hardware, to implement all or portions of the above described methods, e.g., in one or more nodes. Accordingly, among other things, the present invention is directed to a machine-readable medium including machine executable instructions for causing a machine, e.g., processor and associated hardware, to perform one or more of the steps of the above-described method(s).

0195[00134] While described in the context of an OFDM system, at least some of the methods and apparatus of the present invention, are applicable to a wide range of communications systems including many non-OFDM and/or non-cellular systems. Some of the methods and apparatus of the present invention are applicable to various applications which use power amplifiers, e.g., including RF and audio applications.

0196[00135] Numerous additional variations on the methods and apparatus of the present invention described above will be apparent to those skilled in the art in view of the above description of the invention. Such variations are to be considered within the scope of the invention. The methods and apparatus of the present invention may be, and in various embodiments are, used with CDMA, orthogonal frequency division multiplexing (OFDM), and/or various other types of communications techniques which may be used to provide wireless communications links between access nodes and mobile nodes. In some embodiments the access nodes are implemented as base stations which establish communications links with mobile nodes using OFDM and/or CDMA. In various embodiments the mobile nodes are implemented as notebook computers, personal data assistants (PDAs), or other portable devices including receiver/transmitter circuits and logic and/or routines, for implementing the methods of the present invention.