Filter For Impulse Response Shortening With Additional Spectral Constraints For Multicarrier Transmission

ES 2 389 626 T3

DESCRIPTION

Impulse response shortening filter, with additional spectral restrictions, for multi-carrier transmission

Background

The invention relates to time domain equalization in a discrete multi-tone (DMT) receiver.

Conventional single carrier modulation techniques translate data bits for transmission over a communication channel by varying the amplitude and / or phase of a single sinusoidal carrier. In contrast, DMT, which is also called orthogonal frequency division multiplexing (OFDM) or multi-carrier modulation (MCM), employs a large number of sinusoidal subcarriers, for example 128 or 256 subcarriers. The available bandwidth of the communication channel is divided into subchannels and each subchannel communicates a part of the data. A DMT system can employ quadrature amplitude modulation (QAM) for each of the subcarriers.

OFDM-based systems transmit blocks of information bits. The time required to transmit one of these blocks is called the symbol period. The time domain waveform that corresponds to one of these bit blocks is called a symbol.

Inter Symbol Interference (ISI) arises from the characteristics of practical communication channels and limits the rate at which information can be transmitted over them. Specifically, communication channels typically have an effective discrete time impulse response (EDIR) that is greater than a sample time in length, causing lSI. ISI is a well known phenomenon in single carrier communication systems and there are many techniques to reduce it. The process of such a reduction in lSI is called equalization. lSI is discussed, for example, in Proakis, Digital Communication, McGraw Hill, 2^to Edition, 1989.

Equalization in OFDM-based systems is achieved through a two-stage process. First, a cyclic prefix (CP) is employed at the transmitter by setting an end portion of each symbol to the beginning of the symbol. A cyclic prefix that is greater than the channel EDIR prevents one symbol from interfering with another. Additionally, it also provides a simple method of neutralizing the time domain spreading of each symbol forced by the channel. This is achieved through a simple frequency domain process in the receiver that requires a multiplication operation for each subcarrier used. The use of a cyclic prefix to reduce lSI is discussed, for example, in: Cimini, “Analysis and Simulation of a Digital Mobile Channel using Orthogonal Frequency Division Multiplexing,” IEEE Transactions on communications, pp. 665-675, July 1985; Chow, "A Discrete Multi-Tone Transceiver System for HDSL applications", IEEE Journal on Selected Areas of Communications, 9 (6): 895-908, August 1991; and "DMT Group VDSL PMD Draft Standard Proposal," Technical Report, T1E1.4 / 96-329R2, ANSI 1997.

Another problem that arises in conventional DMT systems is superimposed noise, which occurs when noise in one frequency band interferes with a signal whose subcarrier is in another frequency band. Overlapping noise is generally caused by a discrete Fourier transform (OFT) operation at the receiver. Overlapping noise is discussed, for example, in Worthen et. al., "Simulation of VDSL Test Loops", Technical Report T1E1.4 / 97-288, ANSI 1997.

In a perfectly synchronized DMT system, a signal in one frequency band does not interfere with a signal whose subcarrier is in another frequency band. However, noise from one band can interfere with other less noisy bands and make them unusable. Techniques for dealing with overlapping noise include wavelet-based solutions. However, wavelet-based solutions are, in general, computationally intensive.

Other references dealing with time domain equalization include: Chow, JS and Cioffi, JM, "A Costeffective Maximum Likelihood Receiver for Multicarrier Sytems", Proceedings of the ICC, 1992; Melsa, Peter JW, Younce, Richard C., and Rohrs, Charles E., "Optimal Impulse Response Shortening," Proceedings of the thirty-third Annual Allerton Conference on Communication, Control and Computing, 1995, pp. 431-438; Harikumar, Gopal and Marchok, Daniel, “Shortening of the Channel Impulse Response of VDSL Loops for Multicarrier Applications,” Technical report T1E1 A / 97-289, ANSI, 1997.

EP 0 768 778 A1 describes an arrangement in which an energy restriction is used in order to ensure that a solution for an optimal target response vector is not found which places all the received energy in unused frequency bands. WO 93/26096 describes a system in which a set of parameters is optimized to equalize a multi-carrier data signal using a predetermined and encoded signal.

ES 2 389 626 T3

Summary

The present invention provides a method of equalizing a communication channel according to claim 1. There is further provided an impulse response shortening filter according to claim 3 and a corresponding computer program according to claim 6.

The invention provides a filter according to claims 3-5 hereinafter referred to as the spectrally restricted pulse shortening filter (SCISF) which could be used, for example, in DMT systems. The SCISF serves two main functions.

First, SCISF reduces inter-symbol interference (ISI) by reducing the length of the effective discrete time impulse response (EDIR) of the communication channel. Conventional pulse shortening filters can have deep nulls in their frequency response. Instead, the SCISF has a filter characteristic that is essentially free of unwanted nulls that can attenuate or completely eliminate certain subcarriers.

Second, SCISF reduces overlapping noise between subchannels by attenuating noisy channels in a way that does not reduce the signal-to-noise ratio (SNR) on these channels, but reduces the power of noise that may appear on subchannel side lobes. adjacent. The SCISF performs these functions by applying a frequency constraint to the signal based on a desired spectral response.

In a general aspect, the invention features the equalization of a channel according to claim 1.

In another general aspect, the invention features an impulse response shortening filter according to claim 3.

In another aspect, the invention features a computer program according to claim 6.

The techniques described in this document are not limited to any particular hardware or software configuration. They may have applicability in any computing or processing environment that can be used for a communication system. The techniques can be implemented in hardware or software, or a combination of the two. Preferably, the techniques are implemented in computer programs that run on a digital signal processor that includes a processor and processor-readable storage medium (including volatile and non-volatile memory).

Claim 2 provides further details of the method according to claim 1.

Claims 4 and 5 provide further details of the filter according to claim 3.

Claim 7 provides further details of the computer program according to claim 6.

Brief description of the drawings

Figure 1 is a block diagram of a discrete multi-tone communication system.

Figure 2 is a graphical representation of the effective discrete time impulse response (EDIR) of a communication channel that includes transmit and receive filters.

Figure 3 is a graphical representation of a EDIR shortened due to a spectrally restricted pulse shortening filter (SCISF).

Figure 4 is a block diagram of a SCISF.

Figure 5 is a graphical representation of transmit signal power, signal power at the SCISF input, and noise power at the SCISF input.

Figure 6 is a graphical representation of signal power and noise at the SCISF output.

Figure 7 shows the filter response of a discrete Fourier transform for a frequency band.

Figure 8 is a graphical representation of the desired spectral response of the SCISF, G_d((o), versus actual frequency response, Θ (ω).

Figure 9 is a graphical representation of signal-to-noise ratio at the SCISF output, the DFT output with the SCISF, and the DFT output without the SCISF.

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Figure 10 is a block diagram of a system for fitting a spectrally restricted pulse shortening filter in an initial training process.

Figures 11 and 12 are block diagrams of a system for fitting a spectrally restricted pulse shortening filter in a periodic or continuous training process.

Figure 13 is a block diagram of a generalized matching system employing frequency scaling in the feedback loop.

Figure 14 is a block diagram of a system for fitting a spectrally restricted pulse shortening filter in an initial training process that includes frequency scaling in the feedback loop.

Figures 15 and 16 are block diagrams of a system for fitting a spectrally restricted pulse shortening filter in a periodic or continuous training process that includes frequency scaling in the feedback loop.

Figures 17-20 are graphical representations of simulation results for a discrete multi-tone system.

Figures 21-24 are graphical representations of simulation results for a discrete multi-tone system.

Description

As shown in Figure 1, a discrete multi-tone (DMT) communication system 10 has a transmitter 12 and a receiver 14. The transmitter 12 accepts an input data bit stream that passes through a constellation encoder 20 . Encoder 20 divides the serial input bit stream into data blocks. These data blocks are further subdivided into smaller blocks corresponding to subchannels. Each of these smaller blocks is used to calculate a complex value that represents a constellation point. Each constellation point corresponds to a subsymbol. The subsymbols are then output by the encoder. Together, the subsymbols constitute a symbol.

The subsymbols are supplied to an inverse discrete Fourier transform (IDFT) 30, which can be implemented, for example, in a digital signal processor. The IDFT 30 outputs N time samples of a symbol. The time samples are processed by a parallel-to-series converter 40 to form a single stream of time samples.

After the parallel-to-serial converter 40, a prefix adder 50 adds a cyclic prefix to the beginning of each symbol to reduce inter-symbol interference (ISI). Alternatively, the cyclic prefix can be added in the parallel to serial converter. After adding the cyclic prefix, the resulting signal passes through a digital-to-analog (D / A) converter 60 for transmission to receiver 14 via communication channel 70. An analog transmit filter 65 may be included after the D / A converter to band limit the transmitted signal.

At receiver 14, the signal passes through an analog-to-digital (A / D) converter 80 and then through a spectrally restricted pulse shortening filter (SCISF) 90. A prefix remover 100 removes cyclic prefixes from the resulting symbols and a serial-to-parallel converter 110 divides the stream of time samples into parallel signal paths that form the inputs to a discrete Fourier transform (DFT) 120. The DFT 120 converts time samples to subsymbols. A frequency domain equalization filter 130 equalizes the subsymbols. A decoder 140 converts the subsymbols into data bits and outputs the resulting data. An analog receive filter 75 may be included before the A / D converter in order to band limit the received signal.

As discussed above, a cyclic prefix is ​​added to each symbol prior to transmission over the communication channel to reduce the effects of ISI. The cyclic prefix is ​​added by copying the last v time samples from the end of a symbol and placing them at the beginning of the symbol. To eliminate lSI, the length of the cyclic prefix, ν, is chosen to be longer than the channel's effective discrete time impulse response (EDIR). However, because the cyclic prefix constitutes redundant data, increasing the length of the cyclic prefix reduces the efficiency of the communication system. For example, in a system that has N time samples per symbol and a cyclic prefix of ν time samples, the efficiency of the system will be reduced by a factor of N / (N + v). Efficiency can be maximized either by minimizing v or by maximizing N. However, increasing N increases the complexity, latency, and computational requirements of the system and at some point becomes impractical. Therefore, it is desirable to minimize v.

A spectrally restricted pulse shortening filter having an impulse response, g (n), can be employed in the receiver to minimize the length of the cyclic prefix by lowering the EDIR of the signal channel.

ES 2 389 626 T3 efficient communication, which includes the transmit and receive filters, the pulse shortening filter, and the physical transmission channel. The use of a pulse shortening filter is called time domain equalization. Decreasing the EDIR allows a shorter cyclic prefix to be used without increasing lSI.

Figure 2 is a graphical representation of the EDlR for a DMT test setup that has a communication channel that is 4500 feet long and operates at a sample rate of 11.04 MHz (test loop 4, as shown. described in "Very-high Speed ​​Digital Subscriber Lines: System Requirements", Technical Report T1E1.4 / 97-131Rl, ANSI 1998). EDlR includes the effects of a transmit filter, the communication channel, and a receive filter. Figure 3 shows the shortened impulse response by the addition of a impulse shortening filter.

The impulse shortening filter is selected so that a significant part of the joint impulse response energy of the filter and the effective communication channel, g (n) * h (n), is confined to a region that is more shorter in length than the length of the cyclic prefix. Some previous algorithms for calculating g (n) considered only the shortening of the EDIR and did not consider the spectral characteristics of the resulting impulse shortening filter. Such filters used to have deep nulls in some frequency bands, rendering some of the corresponding subchannels useless.

Since increasing the length of the cyclic prefix reduces the efficiency of the system, the receiver can dynamically calculate an optimal length for the cyclic prefix and can send that information to the transmitter. For example, the receiver can calculate a set of impulse responses for the impulse shortening filter based on a set of predetermined cyclic prefix lengths. The receiver then calculates the overall performance of the system for each particular cyclic prefix length. The length that maximizes the overall performance of the system is selected and the result of that selection is communicated to the transmitter. The transmitter then operates using the selected cyclic prefix length.

To avoid a possible attenuation of frequency bands, it is further required that the spectral response of the pulse shortening filter has a spectral response that | G (ra) | meet a specified spectral constraint. A spectral constraint of the form | Θ (ω) Η (ω) |> τ, where τ is a threshold, is sufficient to avoid nulls in the frequency response of the impulse shortening filter. However, it is possible to calculate a spectral constraint or a desired spectral response, | Gd (o) |, that provides additional performance improvements, such as reduction of overlapping noise between subchannels. A spectrally restricted pulse filter is configured to have a spectral response that approximates the desired spectral response.

As shown in Figure 4, the spectrally restricted pulse shortening filter (SCISF) 90 may be implemented as a time-domain digital filter, which has a digital filter structure 92 with multiple taps 94 or filter coefficient inputs for adjust filter response. The coefficients can be calculated and supplied to the taps by a digital signal processor (DSP). Alternatively, the SCISF can be implemented entirely in software, that is, within a DSP.

A desired spectral response can be applied to a received signal using a filter that is separate from the pulse shortening or time domain equalization (TEQ) filter. For example, an analog filter can be placed before the A / D converter. However, the adjustability of such a filter would be limited. As a further example, a digital filter could be added before the TEQ filter. Both of these configurations have the disadvantage that the TEQ filter can distort the desired spectral characteristics of the added filter. A filter could also be placed after the TEQ filter, which would reduce the overlapping noise, but could reduce the pulse shortening provided by the TEQ filter. Consequently, the SCISF integrates the TEQ function (ie, pulse shortening) with the desired spectral response in a single filter.

In summary, the filter characteristic, g (n), of the SCISF satisfies two conditions. First, the effective length of the convolution of the filter characteristic with the impulse response of the communication channel, g (n) * h (n), is less than a target length. Second, the cost function (error function) between the desired spectral response, Gd (o), and the actual filter spectral response, Θ (ω), is minimized.

The desired spectral response is an ideal filter characteristic that is selected to maximize the overall throughput of data bits in the subchannels of a DMT system by reducing the impact of noise. There are many sources of noise in a DMT communication system, such as near end crossover (NEXT), radio frequency interference (RFI), and noise generated in the communication channel (white noise). As shown in Figures 5 and 6, the spectral density of noise is generally non-uniform across the frequency band of the communication system. This non-uniformity contributes to the overlapping noise problem, in which noise in one frequency band interferes with a signal in another frequency band.

In general, overlapping noise is caused by filter side lobes in a DFT. Figure 7 shows the filter response of a DFT for a frequency band or interval (ie, interval 128). The first side lobes (96) are only 13 dB below the main lobe (98). Therefore, the noise located outside the range 128, but within the first side lobe of the range 128, that is, approximately halfway

ES 2 389 626 T3 between Ranges 126 and 127, would appear in Range 128 with an attenuation of only 13 dB. Consequently, noisy subchannels in a DMT system can degrade the performance of the quiet subchannels.

The desired spectral response is essentially a spectral restriction that attenuates noisy channels more than non-noisy channels. Signal and noise on noisy channels are reduced Equally, so attenuation does not affect the signal-to-noise ratio on these channels. However, since the absolute noise level in the noisy channels is reduced, there is less noise available to enter the side lobes of the non-noisy channels. Therefore, the problem of overlapping noise is minimized.

To determine the desired spectral response, the noise power spectral density (noise PSD) at the receiver must be known. The noise PSD can be determined, for example, by performing a perlodogram on the received data. This measurement is more complicated if a transmitter is transmitting, since the transmitted signal must be separated from the noise measurement. The noise PSD is determined by: (I) segmenting the received constellation of subcarriers after the DFT to determine the closest valid constellation point; (¡I) determining an error signal based on the difference between the received constellation point and the valid constellation point; (II) performing an IDFT on the error signal; and (¡v) the generation of a perlodogram (without applying a window function) from the error signals. The noise PSD can then be determined from the perlodogram.

An example of a noise PSD characteristic for a DMT communication system is shown in Figure 5 (test loop 4, as described in "Very High Speed ​​Digital Subscriber Lines: System Requirements", Technical Report T1E1. 4 / 97-131R1, ANSI 1998). The transmit signal power is measured at the output of the transmit filter in the transmitter. The graphical representations shown in Figure 5 of the signal and noise PSD are measured at the input of the A / D converter in the receiver, which is before the SCISF.

A digital signal processor (DSP) uses a measured noise PSD to calculate a desired spectral response, G_d(ro), using the algorithm described below. Alternatively, the Inverse of the noise PSD can be used as a proxy for the desired spectral response. A spectral response, G (ro), is then determined for the SCISF that minimizes the error between the spectral response of the SCISF and the desired spectral response. A set of filter coefficients can then be generated to configure the SCISF with respect to the given characteristic. These calculations can be performed periodically to tune the performance of the communication system. Frequency domain equalization coefficients and symbol timing can also be adjusted based on these calculations.

Figure 8 is a graphical representation of the desired SCISF spectral response, Gd (ro), versus the actual frequency response, G (ro). The difference between the responses is only a few dB. Figure 6 shows the signal and noise PSD at the SCISF output.

Figure 9 shows the dramatic effect of SCISF on system performance. Without the SCISF (i.e. using a filter that provides only Impulse shortening), the signal to noise ratio (SNR) drops significantly at the Fourler transform output (i.e. FFT or DFT) to less than 7 dB . This decrease is due, in large part, to the overlapping noise caused by the side lobes of the Fourler transform. In contrast, with the SCISF, the SNR, at the output of the Fourler transform, tracks the SNR at the output of the SCISF by a few dB. In general, SCISF provides an improvement in SNR.

The desired spectral response of the SCISF, Gd (ro), and the actual frequency response, G (ro), are derived from an energy constraint for the SCISF, that is, the desired spectral response must locate the energy of the response to the Effective boost within a desired frequency band. The energy constraint is combined with a desired spectral response based on the measured noise power spectral density. The resulting cost function (or error function) is then minimized to obtain a practical filter characteristic for the SCISF. This process is presented in detail below.

In the following derivation, all vectors are column vectors by default. Vectors are indicated by bold lowercase letters (for example, t). Size m_t of a vector t, is written The components of a vector are indicated by lowercase letters, for example, t (m_t) = [í₀... í jj⁷”. The convolution of the length m_t + / 77h - 1 of the vectors t (m_t) and h (/ 77h) t * h is indicated. The Toeplltz matrix of a vector is written

VT (”mn)^{X =} * ^x\ mn) The discrete time Fourler transform (DTFT) of a vector t can be represented as:

W'T'rZ⁷'· (L)

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The channel EDIR and the SCISF Impulse response are expressed as h (/ 77h) and Q (m_g), respectively. The cyclic prefix has a length of m_c per symbol. The energy of the response to the effective Impulse must be located on a contiguous ruler of target length mi, where mi <m_c, while satisfying a spectral constraint. The energy criterion to be satisfied by the SCISF can be written as:

for some 0 <m <m_g + / T? H-2 and some 0 <a <I. Defining the set S^m as the response to the SCISF Impulse must belong to S^m for some m.

Suppose that ωι, ..., with is the location of the subcarriers in the frequency domain. The spectral restriction can be applied by selecting ge S^m, so that the cost function

0g) = is minimized for the desired spectral response Gd (ro).

Normally, this optimization would have to be repeated for all possible m to select the response to the Filter Impulse, g, that achieves the lowest possible value of J. However, as discussed below, the optimization can be limited to a few well chosen values ​​of m.

The determination of the response to the filter impulse can be carried out in two phases. First, the desired magnitude frequency response G is obtained_d(ro) of the Impulse shortening filter g over the Intervals used by the DMT system. Second, J is optimized over S^m for a specific value of m.

To determine the desired spectral response Gd (ro), it is necessary to use expressions for the signal-to-noise ratios observed in the various frequency ranges at the DFT output at the receiver. The DMT system has M tones (subcarriers), of which N are used (those of M-¡a / 1 +), and the communication channel has an analog frequency response H_c(F). The observed analog noise power spectral density at the input of the A / D receiver is S „(t). Before conversion in the A / D converter, the received analog signal can be filtered by an anti-lapse filter with transfer function H_to(F). The EDIR in the absence of the Impulse shortening filter is h (n). After the A / D converter, the signal is fed to the Impulse shortening filter with a Impulse response of g (n). The Impulse shortening filter ensures that (h (n) * g (r¡)) has a length shorter than the cyclic prefix. G (ro) is the discrete time Fourier transform of g (n). Under these conditions, the expected signal energy ¡i (k) observed in Interval k at the output of the receiver DFT of length 2M is given by:

<img file="ES2389626T3_D0001.tif" />

where C1 is a constant, 1 / T the sampling frequency and Dk the transmitted power in Interval k. The noise power η (Κ) in Interval k is:

<img file="ES2389626T3_D0002.tif" />

where C2 is another constant and * indicates the convolution. Assuming that the noise in the bands corresponding to unused tones is sufficiently attenuated by the anti-lapse filter, η (Κ) is approximately equal to:

<img file="ES2389626T3_D0003.tif" />

ES 2 389 626 T3 (8) where a (n) is defined as:

ΓΜ

M,

M1 ... M2 are the tones used and C₃ another constant. Defining x to be the vector of frequency magnitudes to be solved as:

<img file="ES2389626T3_D0004.tif" />

&lt;9) the SNR in the interval k can be seen as being in the form, where bk are scalars and * are vectors.

To determine the desired spectral response, choose x to maximize the overall bit throughput. Approximating the capacity of the interval k by means of jsNRjk), ®l optimal spectral profile is obtained by minimizing the cost function F, where:

(10)

This minimization is done in:

(ll) and can be performed by any one of a variety of restricted optimization strategies, as discussed in Bertsekas, Nonlnear Programming, Athena Sclentlflc, Belmont, MA, 1995. A median filter can be applied to the output of the optimization algorithm to smooth the resulting desired spectral response.

Suppose to be written as í &amp; iWj,

B =

The energy restriction in equation (3) can (12)

Matrix A has a complete column rank, since it corresponds to a complete convolution, so

RjJA'A R.JB'b q = Rj⁵h „° s that can be Inverted. Suppose^to ~. Defining^Ί , where is the square root of the positive definite matrix the stated energy constraint can be written in terms of q as:

_P-O.5 „q^rq (13)

The next stage is to reduce dimensionality, that is, the number of variables to look for in the optimization process. For example, in a video digital subscriber line (VDSL) application, a pulse clipping filter that has several hundred taps may be required. Searching in such a large variable space is difficult and impractical. In turn, the optimization is performed by looking for a cleverly chosen lower-dimensional subset of the variable space. This simplification in the optimization process can be done without significant reduction in the performance of the communication system.

The reduction in dimensionality is accomplished through a transformation of variables. Suppose^rs^r^ Suppose _{it is} |_to singular value decomposition of C, where Σ is a

ES 2 389 626 T3 diagonal matrix whose element (I, ¡) -th is o¡ and where the o¡ is arranged in descending order, If o¡ &lt;a, there is no viable solution corresponding to the delay m. If o¡&gt; a, suppose

ΓΣ

L

2lJ '(14) where Ui has a size (m_g, md) and Σι has a size (/ 77 ^, / 77 ^) for some md. These equations define the dimension of the range space of the matrix Ui, on which the search is confined. The dimension md can be chosen either to include all oj greater than some threshold β, β &lt;cr, or md can be a fixed number. Simulations indicate that md can be less than m_g by more than an order of magnitude without significantly affecting the performance of the communication system.

The dimensionality reduction is achieved through an additional transformation of variables: q = Iv. The established energy restriction now becomes:

jv € r^j : ^V itlvlp - ι / ϊ, ν SO

05) using the identity ufcu, = s,

The cost function is then expressed in terms of v. For a particular v, the corresponding g comes - π^_0·⁵ι given by ^{g) V}, which leads to:

fi _and-&gt; 'Γ'³¹ ... Ί (16)

OA FAR j U, A reál f D} θ A uhíie í Z?) □ ¡

Suppose. Suppose - and ”. D and D are real matrices of size (N, m_d). Let's suppose^R-ⁿ' ¹ ”And ~ ⁿ ~ N _be |_ace f¡ |_ace j_and and respectively, Then:

TT r „JdD„ dp_n έ d »„ di _n where ' . These definitions result in:

(17)

<img file="ES2389626T3_D0005.tif" />

The projection P_v(y) of any ye R^md in V is defined as (18) (19)

P_r(y) = argminjjy - v | f (20)

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To develop an algorithm to optimize the cost function J_or on V, an expression must be derived for P_v(and). There is no closed form expression for this projection operator; however, there is a very efficient algorithm to calculate it. SI ye V, P_v(and)⁼and. If not, the projection on V is the same as the projection on its limit, defined by:

<img file="ES2389626T3_D0006.tif" />

(2t)

The latter can be accomplished using LaGrange multipliers as follows. Defining a modified cost function S as:

5 (v) J lly - vlP + μ ^ όίΜΙ¹ - ν^ΓΣ, ν (22)

The equation ^Vs (^v)= ⁰ must be solved in the limit of V. This reduces to the following simultaneous equations:

(22)

[(1 + / ίβ) Ι- μΣι] ν = 0 (23) aH^Í"V^rZ, v = 0 (24)

Solving for v in terms of μ from (23) and substituting in (24), the following equation is obtained for μ.

<img file="ES2389626T3_D0007.tif" />

(25)

Equation (25) can be written as a pollnomic equation of order 2m_d in μ. The pollnomic equation must be solved for the real and positive roots, which can be done using one of a variety of efficient algorithms for finding the root in the literature. One of the real, positive roots must be chosen by enumeration so that, when substituted into the expression for v, it leads to ¡l^{and V}!.

Since the gradient and the Hessian matrix of the cost function J_or and V projection operator are available, optimization can be done very efficiently. For example, the penallzaclones method can be used, as described in Bertsekas, Nonlnear Programming, Athena Scientific, Belmont, MA, 1995, or an Iterative strategy consisting of gradient descent followed by V projection. Both techniques they have been tested and work well.

The SCISF can be configured, determining the filter coefficients during a training or adaptation period. The SCISF filters the output {yk} of the A / D receiver 80. The coefficients are selected using an algorithm that minimizes the squared error between a reference sequence {Uk} generated by the receiver and the output of the SCISF {ük}. The SCISF can be a Finite Impulse Response (FIR) filter or an Infinite Impulse Response (IIR) filter. The SCISF can be trained after activation of the communication system or periodically during system operation to compensate for variations in the channel noise profile.

Training can be done using a variation of one of the classic adaptive algorithms, such as least mean squares (LMS). Normalized LMS, or recursive least squares (RLS). For example, the following algorithm is a version of the normalized LMS algorithm in which óo, ..., ów ya ?, are the FIR and IIR parts of a SCISF that has an Impulse response, g. The transform of z G (z) is:

The adaptation of the coefficients a, and b, is defined in the following equations, in which al (k) and bl (k) are the values ​​of these coefficients during the k-th iteration. The parameter μ is a default constant with a value of 0.4.

ES 2 389 626 T3

<td colspan="2"></td><td rowspan="2"> (27)</td>

<td></td><td>Jl</td>

<td>to,</td><td>W]</td><td> (28)</td>

<td>β, = [^αιΜ. ·&gt;^toi</td><td> ,(*)]</td><td> (23)</td>

<td>^di = bw.-.....</td><td>.Λ- »!</td><td> (30)</td>

<td>= t Ai. ··</td><td>Ak]</td><td> (31)</td>

<td>-OR,</td><td></td><td> (32)</td>

<td>^eCfi⁺TO -</td><td>t 3</td><td> (33)</td>

In a first example, the SCISF coefficients are determined during an Initial training period after activation of the communication system using the LMS algorithm described above. A predetermined sequence of bits is entered x_k to transmitter 12. The bit sequence results in a sequence of real numbers {xj at the input of the D / A 60. As shown in Figures 1 and 10, the transmitted signal is filtered and corrupted by noise by the transmission channel 70, resulting in a received sequence {&gt;%} at the output of the A / D 80 at receiver 14. The SCISF 90 filters and transforms the received sequence {y *} into a sequence of f í} f í } Exit ^{1 11}. The output sequence^{1 11} is compared (in a signal comparator 205) with the predetermined sequence x_k, which is stored in memory 210 in the receiver. The comparison results in a

ÍÁ 1 error signal that is input to the LMS algorithm processor 215 along with the sequence ¹

The training process determines coefficients for the SCISF so that the output matches the predetermined sequence {x / &lt;} as much as possible in a least squares sense, that is, the mean square error between the output and the sequence is minimized. default. During the training process, the SCISF coefficients converge to values ​​that allow the SCISF to reduce ISI and additive noise. The resulting SCISF matches Pi (®) in the frequency domain in a least squares sense, where:

(35)

In the above equation, S_x(®) is the power spectral density at the input of the D / A 60 transmitter, S „(®) is the power spectral density of the additive noise at the output of the A / D 80, and Η (ω) is the response frequency response to the effective discrete time impulse (EOIR) of transmit channel 70, transmit filter 65, and receive filter 75 measured between the input of the D / A transmitter 60 and the output of the A / D receiver 80.

With the completion of the Initial SCISF training, the SCISF coefficients are set and the receiver frequency domain equalizer (FEQ 130) is trained using standard techniques for DMT receptors. Following FEQ training, the SCISF can be periodically trained or adapted during the operation of the communication system. Since it is not efficient to repeatedly transmit a predetermined sequence of bits during operation of the communication system, the periodic training process uses transmitted communication data to generate the reference and output sequences, as described below.

During communication system operation, a sequence of communication data bits is input x_TOto transmitter 12 (see Figure 1). The sequence of data bits results in a sequence of real numbers {x / &lt;} at the input of the D / A 60. As shown in Figures 1 and 11, the transmitted signal is filtered and corrupted by noise by the transmit channel 70, resulting in a received sequence {y *} at the output of the A / D 80 at receiver 14. The SCISF 90 filters and transforms the received sequence {y *} into an output sequence

ES 2 389 626 T3

The received sequence {/ r} is also input at a delay 305 and then to a secondary SCISF 300 having the same coefficients as the primary SCISF 90 after initial training. Such a configuration allows regular training to be carried out without affecting the operation of the communication system. The secondary SCISF 300 is trained periodically or continuously using an algorithm similar to that used for initial training. The new coefficients from the secondary SCISF 300 are periodically copied to the primary SCISF 90.

In an initial training process, the output sequence 'of the secondary SCISF 300 (in a signal comparator 205) would be compared to a predetermined sequence xr stored in memory. However, as discussed above, a data communication bit sequence is used as a reference sequence for training instead of a predetermined sequence. As such, the receiver must have a way to generate a reference signal to compare with the output of the SCISF.

To calculate the reference sequence, the receiver essentially duplicates the transmitter's encoding and modulation processes using the output of decoder 140. Because initial training has already been done, the output of SCISF 90 largely matches the predetermined sequence. {xr} and ISI and additive noise are minimized. Thus, the data output of the decoder 140 largely matches the transmitted sequence of communication data bits xr. The data bits are input to an encoder 320, an IDFT 330, a parallel-to-serial converter 340, and a transmitter-like prefix adder 350. The output sequence {xr} from this string is input to the LMS algorithm processor 215 and used as a reference sequence in the training algorithm.

The output sequence of the secondary SCISF 300 is compared (in a signal comparator 205) with the reference sequence {XR}, which is output by the coding / modulation chain (320, 330, 340 and 350). As noted above, the received sequence {y / &lt;} goes through a delay 305 before being input to the secondary SCISF 300. The delay 305 compensates for the processing delay in the demodulation / decoding chain and the coding / modulation chain. The comparison results in an error signal e_k which is input to the LMS algorithm processor 215: The training process determines the coefficients for the SCISF 300 (!

secondary so that the output ¹ * 'matches the reference sequence {xr} as much as possible in a least squares sense, that is, the mean square error between the output and the reference sequence is minimized. Periodically, the coefficients are copied from the secondary SCISF 300 to the primary SCISF 90.

In another example as shown in Figure 12, periodic training can be performed with a single SCISF 90. In this configuration, the A / D 80 outputs a received sequence {j / r} on receiver 14. SCISF 90 filters and transforms the received sequence {j / r} into an output sequence i * '*). The received sequence {j / r} is also input at delay 305. After the received sequence {j / r} passes through SCISF 90, a data switch 360 is changed from position A to position B, allowing the delayed received sequence to make a second pass through SCISF 90. An output switch 370 can also be opened so that data is not output during the training process. Furthermore, the SCISF coefficients are controlled by the LMS algorithm during the training process.

A reference sequence is calculated as in the configuration of FIG. 11. The data bits are input to an encoder 320, an IDFT 330, a parallel-to-serial converter 340, and a prefix adder 350. The resulting reference sequence {xr} is input to the LMS algorithm processor.

The output sequence ¹ The second pass through SCISF 90 is compared (in signal comparator 205) to the reference sequence. As noted above, the received sequence Q / r} passes through a delay 305 before entering the SCISF 90 for the second pass. The delay 305 compensates for the processing delay in the demodulation / decoding chain and the coding / modulation chain. The comparison results in an error signal e_k which is input to LMS algorithm processor 215. The training process determines the coefficients for the SCISF 90 so that the output^{1 11} match the reference sequence {xr} as much as possible in a least squares sense, that is, the mean square error between the output and the reference sequence is minimized.

The SCISF 90 coefficients are then updated with respect to the coefficients determined in the training process.

In a second exemplary embodiment, the SCISF coefficients 90 are chosen so that the frequency response of the SCISF matches a desired spectral response Gd (ro) that seeks to minimize the effects of overlapping noise and maximize overall bit throughput. of the system. The desired spectral response Gd (®) is determined based on the signal-to-noise ratios observed in the various frequency ranges of the DFT 120 at the receiver.

ES 2 389 626 T3

For example, an OFDM system may have M tones, of which N (mi to mw) are used. The system operates on a channel with analog frequency response H_c(F). Referring again to FIG. 1, the analog noise power spectral density at the input of the A / D receiver 80 is S „(f). Prior to the A / D receiver 80, the received analog signal can be filtered by an anti-lapse filter (i.e., receive filter 75) that has a transfer function H_to(F). The response to the Efficient Discrete Time Impulse (EDIR) of the transmission channel of the OFDM system (Including the transmit filter 65 and the receive filter 75) is h (n). The output of the A / D 80 is input to a SCISF 90 that has a response to Impulse g (n). G (ro) is the spectral response that corresponds to g (n).

The expected signal energy μ (Κ) observed in the frequency interval k at the output of the DFT 120, which has a length of NM, is:

<img file="ES2389626T3_D0008.tif" />

(36) where Ci is a constant, 1 / T is the sampling frequency and Dk is the transmitted power in the frequency interval k. The noise power r \ (k) in the interval k is:

M-Cji,

<img file="ES2389626T3_D0009.tif" />

(37) where C₂ is a constant and * Indicates a convolution of the discrete Fourler transforms. IF the noise, in the bands occupied by unused tones, is sufficiently attenuated by the anti-lapse filter (receive filter 75), r \ (k) is approximately:

where τ (η) is defined as:

are the tones used, and C₃ is a constant. A vector of magnitudes of frequency g is defined as:

<img file="ES2389626T3_D0010.tif" />

The SNR in the frequency interval k is

<img file="ES2389626T3_D0011.tif" />

(40) for scalars rk and vectors Sk. The scalars rk are defined by:

(41) and Sk (/), the / -th component of Sk is defined by:

<img file="ES2389626T3_D0012.tif" />

(42)

To determine an expression for g that maximizes the overall bit throughput of the system, the capacity of each frequency interval k is approximated by log (1+ SNR / &lt;). Therefore, the optimal spectral profile is determined by minimizing the cost function F, where:

ES 2 389 626 T3

<img file="ES2389626T3_D0013.tif" />

(43) _D . G, = | G (zr7M_t

Since ¹from Gr, like:

/ A /) 'the calculation of the cost function is carried out on all positive values ​​g_to„= ArgminF (g) (44) where:

G = {ge Λ *: | [g || = l, G₍ 20.1 &lt;í &lt;tv} (45)

A variety of restricted optimization strategies can be used to solve the above equations for

9opt Once the optimal impulse response g is determined_{opt and} the desired spectral response G_d(ro) (which can be expressed as G_d(xm¡ / M) for a system having M tones), a training process is used to tailor the SCISF 90 so that its response to Impulse g matches the desired spectral response. As shown in Figure 13, the training process can be generalized as a replay system. A reference sequence xr is introduced to the system. This corresponds to introducing a predetermined reference bit sequence to a transmitter. The reference sequence passes through a transmit channel 410 having a frequency response H (f) (Including the physical transmit channel and the transmit and receive filters). The additive noise η_Α of the transmission channel is represented in this general model as an external input 420 to the system. The resulting signal y * is input to a filter 430 having a frequency response G (t), for example, a SCISF. The output of filter 430 is then passed to a matching processor 440, which calculates an error signal based on feedback loop 450 and adapts the filter accordingly. The adaptation processor can use, for example, the LMS algorithm described above.

The xr reference sequence is also input to the feedback loop 450, which passes the xr reference sequence through a frequency characteristic Q (t) scaling filter 460. The frequency characteristic Q (t) of the scaling filter 460 (which can be expressed as a set of frequency domain scaling factors Qr) is determined so that the SCISF is tailored to the desired spectral response. The output of the scaling filter 460 is used as a reference for the calculation of the error signal in the matching processor 440, as described above.

Using the general feedback system shown in Figure 13, a SCISF having a response to Impulse g can be trained to minimize the error 'ϊ + δΟ. The resulting filter coincides with P2 &lt;®) in the frequency domain in a sense of minima. squares, where:

(46)

S_x(®) is the power spectral density at the input of the system. Η (ω) is the frequency response of the response to the effective discrete time impulse (EDIR) of the transmitting channel, S₇(®) is the power spectral density of the additive noise, and Q (ro) is the spectral response of the scaling filter 460 that has a response to Impulse q.

The solution for g_opt in the above equations specifies only the magnitude of the spectral response of the SCISF. IF the SCISF is an FIR filter, a linear phase characteristic can be used. IF the length of the SCISF is n_g, the desired values ​​of G (ro) for the Frequency Intervals of Interest are:

(47)

Qr values ​​are defined by:

ES 2 389 626 T3 + S ^ (jrtk / Μ))

The Qr values ​​can be calculated during an initial training period and can be updated periodically during the operation of the communication system.

As shown in Figures 14-16, the general feedback training process can be used to perform initial training of a SCISF followed by periodic training analogous to the process described above with respect to Figures 10-12. One difference between the techniques is that a scaled reference signal (** &lt;?) * Is used instead of a non-scaled reference x_k.

Referring to FIG. 14, to perform initial training, a predetermined sequence of bits xr is input to the transmitter. The transmitted signal is filtered and corrupted by noise by the transmit channel, resulting in a received sequence {j / r} at the output of the A / D 80 at the receiver. The SCISF 90 filters and transforms the received sequence {j / r} into an output sequence¹ 'L The output sequence' ¹¹ is compared (in a comparator (x * i).

205 signals) with a scaled reference sequence

The scaled reference sequence is calculated from a copy of the predetermined sequence Xr that is stored in memory 210 in the receiver. As a first stage, the predetermined sequence is input to a serial-to-parallel converter 510 and a DFT 515. The resulting frequency domain signal is input to a scaling filter 520 that applies the set of frequency domain scaling factors Qr that makes the SCISF match the desired spectral response, as discussed above. . The scaled signal is input to an inverse discrete Fourier transform 330, a parallel-to-series converter 340, and a cyclic prefix adder 350, resulting in a scaled reference sequence (χ * Λ Íí l (-^v* '/) i. Comparison of the output sequence¹ with the scaled reference sequence results in an error signal and_TOwhich is input to the LMS algorithm processor 215 along with the sequence

Alternatively, a frequency domain reference (for example, a predetermined bit sequence that has been processed by a signal-to-parallel converter and DFT) can be stored in memory in the receiver, eliminating the need for a signal converter. to parallel and the discrete Fourier transform in the feedback loop.

After initial training, the SCISF is trained periodically during the operation of the communication system. A sequence of communication data bits Xr is input to the transmitter. Referring to FIG. 15, the transmitted signal is filtered and noise corrupted by the transmit channel, resulting in a received sequence {yR} at the output of the A / D 80 at the receiver. The SCISF 90 filters and transforms the f¿ ·) received sequence {y_TO} in an output sequence ¹

The received sequence {yR} is also input to a delay 305 and then to a secondary SCISF 300 having the same coefficients as the primary SCISF 90 after initial training. The secondary SCISF 300 provides fi!

an output sequence ¹ *&gt;, which is compared to a reference sequence during the periodic training process. Such a configuration allows periodic training to be carried out without affecting the operation of the communication system. The secondary SCISF 300 is trained periodically or continuously using an algorithm similar to that used for initial training. The new coefficients from the secondary SCISF 300 are periodically copied to the primary SCISF 90.

To calculate the reference sequence, the data output from decoder 140 is input to an encoder 320. The resulting frequency domain signal is input to a scaling filter 520 that applies the set of domain scaling factors. frequency Qr that makes the SCISF adapt to the desired spectral response, as discussed above. The scaled signal is input into an inverse discrete Fourier transform 330, a parallel-to-series converter 340, and a cyclic prefix adder 350, resulting in a scaled reference sequence

Comparing the f ί l (x * &lt;?) ,.

output sequence ¹ with the scaled reference sequence results in an error signal and_k which is input to the LMS algorithm processor 215. The training process determines the fe 1 coefficients for the secondary SCISF 300 so that the output¹ matches the reference sequence (x * Λ.

scaled as much as possible in a least squares sense, that is, the mean square error between the output and the reference sequence is minimized. Periodically, the coefficients of the SCISF

ES 2 389 626 T3

300 secondary are copied to the primary SCISF 90.

Alternatively, as shown in Figure 16, periodic training can be performed with a single SCISF 90. In this configuration, the A / D 80 outputs a received sequence {y *} at the receiver. The SCISF 90 filters and

U ') transforms the received sequence {&gt;%} into an output sequence ¹ . The received sequence {y *} is also input at a delay. After the received sequence {yk} passes through the SCISF 90, a data switch 360 is switched from position A to position B, allowing the delayed received sequence to make a second pass through the SCISF 90. It may also an output switch 370 is opened so that data is not output during the training process. Furthermore, the SCISF coefficients are controlled by the LMS algorithm during the training process.

A reference sequence is computed as in the configuration of Figure 15. The data output from decoder 140 is input to an encoder 320. The resulting frequency domain signal is input to a scaling filter 520 that applies the set. of Qr frequency domain scaling factors that make the SCISF match the desired spectral response, as discussed above. The scaled signal is fed into a discrete Inverse Fourier transform 330, a parallel-to-serle converter 340, and a cyclic prefix adder 350, resulting in a scaled reference sequence.

The scaled reference sequence is entered into the LMS algorithm processor.

f í

The output sequence ⁽ ‘¹ The second pass through the SCISF 90 is compared (in the signal comparator 205) 6 * 4) t to the reference sequence. As noted above, the received sequence {yj passes through a delay 305 before being Introduced to SCISF 90 for the second step. Delay 305 compensates for the processing delay in the demodulation / decoding chain and the coding / modulation chain. The comparison results in an error signal e * which is input to the LMS algorithm processor 215. The training process determines coefficients for the SCISF 90 so that the output^{1 11} matches the (* * scaled reference sequence as much as possible in a least squares sense, that is, the mean square error between the output and the reference sequence is minimized. The coefficients of the SCISF 90 are then updated with respect to the coefficients determined in the training process.

In a third exemplary embodiment, the system dynamically selects the length of the cyclic prefix (CP) to maximize overall data throughput for a communication channel having a particular noise profile. As discussed above, a CP is added to each symbol prior to transmission over the communication channel to reduce the effects of ISI. However, because the CP constitutes redundant data, increasing the length of the CP reduces the efficiency of the communication system. Therefore, to maximize efficiency, the length of the CP should be as short as the noise characteristics of the communication channel allow.

For a DMT communication system with M tones, the maximum sample rate W (samples / second) for a particular channel depends, in part, on the available bandwidth and hardware limitations. The sample rate includes communication data and CP bits. For a CP length of n_c, the maximum symbol rate (which includes communication data, but not the CP) is W / (2M + n_c).

Before determining the optimal CP length, the SCISF must be initially trained with respect to the channel. However, it is not necessary for a communication system to have an SCISF to use the CP optimization algorithm. It is observed that the SCISF coefficients determined during the training process do not depend on the length of CP. The capacity of the subchannel can be approximated as log (1 + SNR¡) bits per second, so that the number of bits per symbol is Z¡log (1 + SA / R¡). For a CP length of n_c, the maximum bit rate is expressed as a function of the cyclic prefix as:

(49)

The optimal CP length is determined by calculating the maximum bit rate for a set of candidate CP length values ​​and finding the length that maximizes B_to(n_c).

The signal-to-noise ratio SNR¡ of each subchannel is determined by measuring the received signal and the noise power and calculating the ratio of both. The noise power y¡; for the Terrible interval, it can be measured by transmitting a data communication sequence and calculating the average of the squares of the errors measured in the output

ES 2 389 626 T3 of the receiver DFT. The total received power (signal and noise) 8, for the ith interval can be measured by calculating the average of the squares of the receiver DFT outputs. The signal-to-noise ratio is determined from the expression: 8¡ / y¡ = 1 + SNR ,. Since the signal-to-noise ratio is determined at the receiver, the calculated bit rate B_to(n_c) must be transmitted back to the transmitter. The transmitter compares the bit rate with the calculated values ​​for other candidate CP lengths and selects the length n_c CP with the highest maximum bit rate B_to(n_c).

Figures 17-24 show performance simulations for test systems based on system parameters and test loops described in VDSL Alliance SDMT VDSL Draft Standard Proposal, Technical report, ANSI, 1998; and Very-high-speed digital subscriber Unes; System requlrements, T1E1.4 / 97 · 131R1, Technical report, ANSI, 1997. The results are for a VDSL system working on test loops 2 and 6 with a length of 4500 feet in the upstream direction. The system has a sampling frequency of 11.04 MHz. Noise is generated by a near-end crossover from interfering ADSL and interfering HDSL and white noise at a level of 140 dBm. The SCISF used in the simulations is a length 15 FIR. A version of the standard LMS algorithm is used to train the SCISF during the initial training period using a predetermined transmitted sequence.

Figures 17-20 show simulated system performance for a communication system that has the parameters defined for Test Loop 2, which is 4500 feet long. Figure 17 shows the channel frequency response with and without a SCISF. The SCISF provides a much more uniform frequency response across the frequency band of interest and significantly improves the signal-to-noise ratio (SNR) in the higher frequency ranges. Figure 18 is a graphical representation of the error signal (ioiog | jc_t-x_t|) j_ORrante _andP_rubbing of training. The error decreases rapidly during the first few iterations and almost converges after only 20-30 iterations. Figure 19 is a graphical representation of transmitted power spectral density, received power spectral density, and additive noise power spectral density over the subchannels used at the output of the A / D receiver. Figure 20 is a graphical representation of SNR at the input to the A / D receiver, which is the maximum achievable SNR. The graph also shows the SNR at the receiver DFT output without a SCISF and the SNR at the receiver DFT outputs using a matched SCISF.

Figures 21-24 show simulated system performance for a communication system that has the parameters defined for test loop 6, which is 4500 feet long. Figure 21 shows the channel frequency response with and without a SCISF. Figure 22 is a graphical representation of the error signal (I0log | +, - x_t|) j_urant_ee| training process. Figure 23 is a graphical representation of transmitted power spectral density, received power spectral density, and additive noise power spectral density over the subchannels used at the output of the A / D receiver. Figure 24 is a graphical representation of SNR at the input to the A / D receiver. The graph also shows the SNR at the receiver DFT output without a SCISF and the SNR at the receiver DFT outputs using a matched SCISF.

Embodiments of the invention are defined by the scope of the following claims.