Method and apparatus for decision feedback equalization

ES 2 365 730 T3

DESCRIPTION

Procedure and apparatus for a decision feedback equalization

Background

Field

The present invention relates generally to equalization of a received signal, and more specifically to hybrid decision feedback equalization.

Background

Digital information transmission typically uses a modulator that maps digital information to analog waveforms. The mapping is generally carried out in blocks of bits contained in the information sequence to be transmitted. Waveforms can differ in amplitude, phase, frequency, or a combination thereof. The information is then transmitted as the corresponding waveform. The process of mapping from the digital domain to the analog domain is called modulation.

In a wireless communication system, the modulated signal is transmitted over a radio channel. Then a receiver demodulates the received signal to extract the original digital information sequence. At the receiver, the transmitted signal is subject to linear distortions introduced by the channel, as well as external additive noise and interference. Generally, the characteristics of the channel vary in time and, therefore, are not known a priori by the receiver. Receivers compensate for distortion and interference introduced by the channel in several ways. One procedure to compensate for distortion and reduce interference in the received signal uses an equalizer. Equalization generally encompasses procedures used to reduce the effects of distortion on a communications channel. From the received signal, an equalizer generates estimates of the original digital information.

Current equalization procedures are based on assumptions related to the received signal. Generally, such assumptions are not correct in a variety of coding, modulation, and transmission scenarios, and therefore these equalizers do not work correctly under many conditions. Furthermore, current equalizers that use decision feedback frequently experience error propagation effects that increase the effect of isolated decision errors. Also, the decision feedback process involves firm decisions related to each symbol and does not consider the possibility that a symbol decision is correct. The publication “Decision feedback equalization for channels with error correcting capabilities”, by BEDNARZ ET AL., Discloses a decision feedback equalization comprising feed-in and feedback components. The publication “Mitigating error propagation effects in a decision feedback equalizeh” by REUTER ET AL., Refers to a decision feedback equalization that has the objective of mitigating the effects of error propagation caused by feedback incorrectly detected symbols.

Therefore, there is a need in the art for an equalization procedure that reduces linear distortion in a received signal under a variety of operating conditions. Furthermore, there is a need to reduce error propagation in a decision feedback equalizer. Also, there is a need to provide a measure of probability to the decision feedback process.

Brief description of the drawings

FIG. 1A is a component block diagram in a communication system.

FIG. 1B is a detailed part of the communication system like the one in FIG. 1A.

FIG. 2 is a conceptual model of a decision feedback equalizer within a communication system.

FIG. 3 is a block diagram of a decision feedback equalizer like the one in FIG. 2.

FIG. 4 is a mathematical model of a symbol level slicer.

FIG. 5 is an algorithm for optimizing filter coefficients in a decision feedback equalizer.

FIG. 6 is an adaptive least squares filtering algorithm for optimizing filter coefficients in a decision feedback equalizer.

FIG. 7 is an adaptive least squares filtering algorithm for optimizing filter coefficients in a decision feedback equalizer for a system using a periodic burst pilot.

FIG. 8A is a constellation mapping for 8 symbol phase shift keying (PSK).

FIG. 8B illustrates grating regions used for flexible slicer decisions such as those superimposed on the constellation mapping of FIG. 8B.

FIG. 9A is a constellation mapping for a binary phase shift keying (BPSK) or 2-PSK case.

FIG. 9B illustrates grid regions used for flexible slicer decisions such as those superimposed on

ES 2 365 730 T3 the constellation mapping of FIG. 9A.

FIG. 10 is a decision feedback equalizer that implements a "soft sectioning" decision process.

FIG. 11 is a process for a “soft sectioning” decision process.

FIG. 12 is a process for a “flexible sectioning” decision process that applies a Taylor series calculation.

FIG. 13 is a block diagram of a "flex switch".

FIG. 14 is a block diagram of a "flexible sectionalizer" applying a Taylor series calculation.

Detailed description

The term "by way of example" is used herein to mean "serving as an example, instance, or illustration." Any embodiment described herein as "by way of example" should not necessarily be regarded as preferred or advantageous over other embodiments.

FIG. 1A illustrates a portion of the components of a communication system 100. Other blocks and modules can be incorporated into a communication system in addition to the illustrated blocks. The bits generated by a source (not shown) are framed, encoded, and then mapped to symbols in a signaling constellation. The sequence of binary digits provided by the source is referred to as the information sequence. The information sequence is encoded by an encoder 102, which provides a sequence of bits. The output of the encoder 102 is provided to a mapping unit 104 that serves as the interface for the communication channel. The mapping unit 104 maps the encoder output sequence to symbols y (n) of a complex valued signaling constellation. Section 120 models additional transmit processing, including modulation blocks, as well as communication channel and analog receiver processing.

FIG. 1B illustrates some of the details included within section 120 of FIG. 1A. As illustrated in FIG. 1B, the complex symbols y (n) are modulated into an analog signal pulse, and the resulting complex baseband waveform is sinusoidally modulated over the in-phase and quadrature phase bifurcations of a carrier signal. The resulting analog signal is transmitted by an RF antenna (not shown) through a communication channel. A variety of modulation schemes can be implemented in this way, such as an M-ary phase shift keying (M-PSK), a quadrature amplitude modulation 2^M-aria (2^M QAM), etc.

Each modulation scheme has an associated "signaling constellation" that maps one or more bits to a single complex symbol. For example, in 4-PSK modulation, two coded bits are mapped to one of four possible complex values ​​{1, i, -1, -i}. Therefore, each complex symbol y (n) can accept four possible values. In general, for M-PSK, log2M-encoded bits are mapped to one of M possible complex values ​​arranged in the complex unit circle.

Continuing with FIG. 1B, at the receiver, the analog waveform is down-converted, filtered, and sampled, such as at a suitable multiple of the Nyquist velocity. The resulting samples are processed by equalizer 110, which corrects for signal distortions and other noise and interference introduced by the channel, as modeled by section 120. Equalizer 110 provides estimates of the transmitted symbols y (n). The symbol estimates are then processed by a decoder to determine the original information bits, that is, the source bits that are input to the encoder 102.

The combination of a pulse filter, an IQ modulator, the channel and an analog processor in the input section of the receiver, illustrated in FIG. 1A and in FIG. 1B, is modeled by a linear filter 106 having an impulse response {hk} and a z transform H (z), where the interferences and noise introduced by the channel are modeled as additive white Gaussian noise (AWGN).

In FIG. 1B highlights that the processing section 120 includes a front-end processing unit 122 coupled to baseband filters 126 and 128 to process the in-phase component (I) and the quadrature component (Q), respectively. Each baseband filter 126, 128 is then coupled to a multiplier for multiplication with a respective carrier. The resulting waveforms are then summed at an adder node 134 and transmitted over the communications channel to the receiver. At the receiver, an analog pre-processing unit 142 receives the transmitted signal, which is processed and passed to a matched filter 144. The output of the matched filter 144 is then provided to an analog / digital (A / D) converter. 146. It should be noted that other modules can be implemented according to the design and functional criteria. The components and elements of FIG. 1A and 1B are provided for the understanding of the following discussion and are not intended to be a complete description of a communication system.

As indicated above, the transmitted symbol sequence is identified as {y (n)}. For the present analysis, it is assumed that the symbols {y (n)} are normalized to have a mean unit energy, that is, E | yn |² = 1. If the channel output is filtered and sampled at the symbol rate (which may or may not be the

ES 2 365 730 T3 of Nyquist), the channel output is given as:

^ = Σ^ΛίΧ »- *⁺% (0) k

where η is the Gaussian white noise with variance (Es / Nq) '¹. The equalizer is normally implemented as a linear filter with coefficients {f_k} and is defined by a z transform F (z). Denote and_n the equalizer output, where and_n is given as:

λ = Σ / Λ-ίΐ (1) k

<img file="ES2365730T3_D0001.tif" />

where G (z) = F (z) H (z) y = Σ / Λ-_ί. (2a) k

It should be noted that the second term within the brackets, [...] in equation (2) represents inter-symbol interference (ISI) and noise. The first term in equation (2) corresponds to the interference associated with past symbols, while the second term corresponds to the interference associated with future symbols. The first term is often referred to as "causal" ISI, while the second term is often referred to as anti-causal ISI. If the designer assumes that the passed symbols were detected correctly, the causal ISI term can be dropped. In an ideal case, if the equalizer knows the constellation symbols and_n-1, Y_n-2, K, that is, the constellation symbols transmitted before time n, when the estimate is determined and_n, the equalizer can eliminate some of the inter-symbol interference by subtracting the first term of [...] from equation (2). However, in practical systems, the equalizer only knows previously generated symbol estimates, such as and_n_ , Y_n_₂ , K. If the interference and noise are small enough, it is reasonable to expect that the symbol decisions about the estimation and_n provide the original transmitted constellation symbol and n. A device that makes such symbol decisions is referred to as a disconnector and its operation is denoted as σ (.). The receiver can then generate an estimate of the causal ISI using the slicer symbol decision sequence and subtract this estimate from the equalizer output to provide:

<img file="ES2365730T3_D0002.tif" />

<img file="ES2365730T3_D0003.tif" />

<img file="ES2365730T3_D0004.tif" />

assuming that σ (and_n__k) " Y_n__k . This is the fundamental principle of decision feedback equalization, in which the causal ISI is eliminated by causally filtering symbol decisions made by a symbol level slicer operating on the output of the equalizer.

FIG. 3 illustrates a communication system 350 using a decision feedback equalizer (DFE) 340. The communication system 350 is modeled to include an equivalent linear channel 352, which filters the symbol sequence yn. Noise and interference, η_η, are summed at an adder node 354, and the output, Xn, denotes the received signal samples after front end processing and receiver sampling. The DFE

ES 2 365 730 T3

340 processes Xn and filters Xn to generate the estimate and_n. The DFE 340 is modeled including a linear feedforward filter 356 and a linear feedback filter 358. The feedforward filter 356 has tap coefficients designated as {fk} and implements the z-F (z) transform. The DFE 340 further includes a purely causal feedback filter 358 coupled to a slicer 360 forming a feedback loop that generates an estimate of the causal ISI. In other words, the feedback filter 358 removes that part of the ISI from the current symbol estimate generated by previously detected symbols. The causal ISI estimate from the feedback filter 358 is provided to an adder node 308 which subtracts the causal ISI estimate from the output of the feedforward filter 356. The resulting output from the adder node 308 is the equalizer output Y_n. The equalizer output and_n it is also an estimate of the transmitted symbol yn and is provided to a decoder 364 to determine the original information sequence.

The slicer 360 processes the equalizer output of the adder node 308 and, in response, makes a decision regarding the original symbol yn. Then, the output of the disconnector 360 is provided to the purely causal feedback filter 358. The feed-in filter 356 is also referred to herein as a feed-in filter (FFF). Feedback filter 358 is also referred to herein as a feedback filter (FBF). In a DFE, optimizing the filter coefficients of both the feed-in filter 356 and the feedback filter 358 directly affects the performance of the equalizer. The device that performs this optimization is designed as the coefficient optimizer 362 of FIG. 3. There are several procedures available to optimize the filter coefficients. Traditionally, the FFF and FBF coefficients are optimized under the implicit assumption that the slicer symbol decisions are fully reliable and that the causal ISI, that is, past symbol interference, is completely eliminated by the FBF. Under this assumption, the FFF coefficients are optimized so that the residual noise and interference term from equation (3) has a small value. More precisely, the FFF's z transform, F (z), is optimized so that y_n of equation (3) approximates yn in the mean square sense.

In practice, the FFF and FBF are frequently implemented by finite impulse response (FIR) filters and, during an initial training / preamble / adaptation period, the FFF and FBF are "trained" on pilot symbols assuming a perfect performance of the disconnector, that is, σ (and_n) = and_n. This is accomplished by bypassing the slicer and feeding locally generated (and therefore correct) pilot symbols, rather than sliced ​​pilot symbol decisions (hence possibly wrong), into the FBF. A plurality of algorithms can be implemented for the optimization of filter coefficients during the training period, including adaptive algorithms, such as the algorithm of least squares (LMS), the recursive algorithm of least squares (RLS), direct matrix inversion, as well as others. Once the training period is over, slicer 360 is ready and sliced ​​data symbols are fed back through the FBF.

Conventional DFE optimization algorithms introduce a plurality of possible problems. For systems using robust coding, disconnector decisions typically have a high Symbol Error Rate (SER). For example, a SER of 25% or higher is typical for a system that uses a medium-size constellation, such as 16-QAM, and a low-speed turbo code, such as 1/3 speed, when operating on the 1% packet error rate point. On the other hand, the FFF and FBF coefficients of the DFE are conventionally optimized under the incorrect assumption that the disconnector decisions are fully reliable.

Furthermore, the coefficients of FFF and FBF are optimized assuming that the causal ISI is completely eliminated. As a result, the anticausal ISI is reduced at the expense of a higher causal ISI. Conventional DFE optimization algorithms, as regards the equations provided in this document (specifically, equations (1) - (3)), provide gk values ​​that tend to be large for k> 0 but small for k < 0. However, when the SER of the disconnector is not negligible, the wrong symbol decisions infect the FBF and are therefore incorrectly subtracted. When the gk values ​​for k> 0 are large, the residual interference is amplified, possibly resulting in additional slicer errors in later symbols. This phenomenon is called as error propagation.

Attempts to mitigate error propagation include refeeding striped pilot symbols during training, as opposed to training the FFF and FBF by refeeding locally generated pilot samples (thus correct). Striped pilot symbols are occasionally errored, causing the FFF and FBF to adjust accordingly. This procedure is not without its problems. Striped pilot symbols and striped data symbols can incur very different error rates since pilot symbols are normally transmitted over BPSK, i.e. 2-PSK, (or other smaller constellation), but the Data symbols are typically transmitted through a larger constellation. As a result, the SER of the pilot symbols and the data symbols can be very different. In this case, since the coefficients of FFF and FBF are optimized based on the sectioned pilot symbols, the effect of those coefficients on the processing of the data symbols results in suboptimal performance.

ES 2 365 730 T3

These problems are solved by optimizing the coefficients of FFF and FBF to take into account the errors caused by the slicer 360 of FIG. 3. In other words, the coefficient optimizer 362 is modified to recognize that the causal ISI may not be completely eliminated due to slicer errors. This approach is different from the previous procedures which implicitly assume that the slicer is error free and therefore that the causal ISI is completely removed.

The theory behind one embodiment is to model the operation of the sectionalizer using an independent and identically distributed "channel" (iid), labeled Q (~ | ~). The channel is assumed to be independent of the noisy process designated as {η_η} in equation (0) and from the transmitted symbol sequence designated as {yn}. This channel is fully characterized by its conditional density Q (y | ~) where y and y denote the output of the slicer and the actual transmitted symbol, respectively. Such a channel is assumed to be the cause of the symbol errors in the FBF. In practice, symbol errors occur in bursts, as a slicer error in the current symbol means that subsequent symbols may have a higher chance of being sliced ​​incorrectly. In the simplified disconnector model considered in this document, the disconnector errors are assumed to be iid

FIG. 2 illustrates a conceptual model 300 of a communication system with a decision feedback equalizer. Symbols transmitted through communication channel 302 modeled by transfer function H (z) are corrupted by additive noise at summing node 304. The resulting signal is filtered by FFF 306. An estimate of the original transmitted symbol is generated subtracting an error term at adder node 308. The estimate of the original transmitted symbol is available to the decoder 316. The error term is generated by a causal feedback filter 310, with the transfer function B (z), which filters the outputs of the "channel" Q (~ | ~ ) 314. The error term generated by the feedback filter 310 represents an estimate of the causal ISI present at the output of the FFF 306. The "channel" Q (y | y) mimics the statistical behavior of the slicer 360 of FIG. 3, that is, the statistical relationship between the input and the output of channel 314 is identical to the statistical relationship between the transmitted symbol and_n and the corresponding output and_n = σ (and_n) of disconnector 360.

The coefficient optimizer 320 is responsible for optimizing the filter coefficients for the FFF 306 and the FBF 310. It should be noted that the main difference between FIG. 3 and FIG. 2 is the replacement of the disconnector 360 by the conceptual model of “channel” Q (y | y) 314.

As mentioned above, the sectionalizer is modeled in FIG. 2 selecting the "channel" Q (y | y) to model the statistical behavior of a real disconnector while ignoring the statistical dependence in time of the disconnector errors. Since the actual sectionalizer operates on the equalizer output, the relevant marginal statistics imply residual interference. Let SINR represent the signal-to-interference plus noise ratio at the equalizer output, that is, at the output of summing node 308 of FIG. 2. Suppose that the residual interference and noise at the equalizer output can be modeled as a complex Gaussian random variable Z of zero mean with independent real and imaginary parts, each with variance σ², in which:

2 (SINR)

The marginal statistics are provided by the equivalent channel Q (y \ y), where:

g (y | y) = Pr {tf (y + z) = y}, (7) where σ () denotes a minimum distance sectioning function given as:

tf (y) = arg (8) and eK ¹ and Z in equation (7) is the zero-mean complex Gaussian random variable that models the residual interference with properties described above. FIG. 4 illustrates the Q (y | y) channel modeled according to the assumptions and equations provided above. Specifically, the mathematical description of Q (y | y) 314 of FIG. 2 is illustrated as system 380. The input to the disconnector 384 is denoted as y and is modeled as the transmitted symbol y, corrupted by additive noise and interference. Noise and interference are modeled by the complex Gaussian random variable Z. The sectionalizer 384 implements a minimum distance sectioning function as described in equation (8), resulting in a

ES 2 365 730 T3 switch output marked as y. The joint statistics relating y and y constitute the complete mathematical description of the model for the "channel" Q (y | y). The construction of the Q (y | y) channel illustrated in FIG. 4 is novel and differs from previous procedures in that the Z noise can have a non-zero variance. The above procedures implicitly assume that Z is identically equal to zero. Therefore, this model for the slicer is assumed to generate decision errors, as opposed to previous procedures which assume that the slicer is error free.

Returning to FIG. 2, denote fQ and óq the coefficients of FFF and FBF selected to minimize the root mean square error between the transmitted symbol yn (the input of channel 302) and the symbol estimate y_n (the output of adder node 308). In other words, the coefficients f_Q and b_Q they are "Wiener MMSE optimal" coefficients. For reasons that will be clarified later in this document, these coefficients are referred to as Wiener hybrid DFE coefficients ”. The coefficients fQ and óq can be determined by a standard Wiener-Hopf optimization and are defined by the following equation:

<img file="ES2365730T3_D0005.tif" />

r_F

PqR-F'B

PqRf, B r_b

<td> - -1</td><td>~ Pf ~</td>

<td></td><td> 0</td>

f (4) in which Rf denotes the covariance of the contents of the FFF, Rb denotes the covariance of the contents of the FBF, Rf, b denotes the cross covariance of the contents of the FFF and the FBF, and pf denotes the cross covariance between the contents of the FFF and the transmitted symbol. These covariances and cross covariances depend on the linear channel 302 described by H (z). Assuming that the symbols of Y, that is, the transmission constellation, are used with equal probability, then pq is defined as:

Pq = ¿i ΣΣ [5 © l &lt;2 (y | y) (5)

FI yer yey where / Y / denotes the cardinality of Y, that is, the number of possible symbols in the transmit constellation. Therefore, for a Q (^Y | y) given and a channel with z transform H (z), the coefficients fQ and óq of MMSE are determined by applying equation (4) and equation (5).

It should be remembered that Q (y | y) was defined according to equation (6) and equation (7) estimating a SINR value at the equalizer output. Therefore, the application of equation (4) and equation (5) gives rise to the coefficients fQ and óq of MMSE. When these values ​​for the FFF and FBF coefficients are used in the FFF 306 and FBF 310 of FIG. 2, the resulting SINR at the equalizer output may be different from the SINR value you originally estimated. Therefore, the estimated SINR value may or may not be consistent. However, a coherent SINR value can be obtained, and therefore a coherent set of coefficients f_Q and b_Q of MMSE, iterating, that is, using the SINR value just obtained to define a new “channel” Q (^Y | y), finding a new set of corresponding MMSE coefficients, etc. This iterative process can be represented schematically as follows:

<img file="ES2365730T3_D0006.tif" />

In particular, an iterative algorithm can be used to calculate Weiner's hybrid DFE. The algorithm of the present embodiment is illustrated in FIG. 5. Process 400 begins by setting n = 0 in step 402 and selecting SINR⁰ arbitrarily. The process continues to determine SINRⁿ and calculating p (SINRⁿ) applying equations (5), (6) and (7) in step 404. The filter coefficients fn, bn, are calculated in step 406 using equation (4). According to the present embodiment, the process calculates SINR^{n + 1} = SINR (fn, b_n, WITHOUT Rⁿ) in step 408. It should be noted that SINR (f, b, x) denotes the SINR at the equalizer output with the coefficients f of FFF, the coefficients b of FBF, and a sectionalizer channel Q (. |.) with SINR x. The sectionalizer channel is defined by equation (6) and equation (7). If the process converges at decision block 410, processing continues to step 412 to set the filter coefficients. If the process has not converged, the processing returns to step 404.

It should be noted that, as described in the iterative algorithm of FIG. 5, the value of SINR⁰ can be chosen arbitrarily. The two extremes, SINR⁰ = 0, SINR⁰ = a>, correspond to starting with a totally unreliable disconnector or with a perfect disconnector, respectively.

It should be noted that p represents the correlation between the disconnector output and the actual transmitted symbol and, as

ES 2 365 730 T3 such, p is a function of the equalizer output SINR. If the equalizer output has a high noise level, the correlation is small. In this case, the slicer symbol decisions are very unreliable and an accurate estimate of the causal ISI is not possible. As expected, in this case, the algorithm of FIG. 5 converges on coefficients of FFF and FBF that closely resemble those of a linear equalizer, that is, one in which the coefficients of FBF are limited to zero. On the other hand, when the output of the equalizer has a practically non-existent noise level, the correlation p of the sectionalizer tends to approach one. In this case, the algorithm of FIG. 5 converges on FFF and FBF coefficients that closely resemble those of an “ideal” DFE, that is, a DFE with a fully reliable disconnect. Between these extremes, the algorithm of FIG. 5 converges on coefficients of FFF and FBF that are a "hybrid" of these two limit extremes. This "hybridization" is achieved automatically by the iterative algorithm. For this reason, the FFF and FBF coefficients obtained in this way are referred to as hybrid DFE coefficients.

The embodiment (s) described so far require an explicit knowledge of the H (z) channel in order to generate the various covariances and cross covariances of equation (4). Then, the Wiener hybrid FFF and FBF coefficients are determined by solving equation (4) for Q, bQ. However, in practice, the receiver does not normally know H (z), so an alternative procedure to determine the Weiner hybrid DFE coefficients for the FFF and FBF is desirable. An alternative embodiment, referred to as the adaptive hybrid DFE, does not require explicit knowledge of the H (z) channel. First, the mean square error (MSE) is defined as:

MSE = E |> „- yr (9) = ^ y_n-fX, -biZ.₊^ where Xn are the FFF contents at time n, Zn are the FBF contents assuming error-free feedback, and An are feedback symbol errors introduced by the "channel" Q (y | y). Since the errors introduced by Q (y | y) are assumed to be iid and independent, equation (9) can be written as:

MSE = E \ y „-fX, -bz„ |² + bE (A „Á) b (9a) = E |_Y, -fx.-b «z4²₊M^2£JV-y ||² where Eq denotes the expectation ”with respect to Q (y | y). Using the fact that the transmission constellation is normalized to the unit energy and to the definition of pQ in equation (5), it is obtained that:

<img file="ES2365730T3_D0007.tif" />

<img file="ES2365730T3_D0008.tif" />

where

V - ΓΤϊΣ Σι * I '&lt;2 (y | y) Combining equation (9b) with equation (9a), we obtain:

MSí-xIj.-f'x.-b'z.l '+ a + V- ^ eW.

It should be noted that || b ||² that appears in equation (9c) can be interpreted as the energy in the FBF coefficients. Equation (9c) is the starting point to obtain a plurality of adaptive algorithms. For example, to obtain an adaptive algorithm based on the recursive least squares (RLS) procedure, a new cost function is defined by substituting the statistical expectation for a sample mean over, for example, n = 1, ..., N . Standard techniques are then applied to obtain a recursive optimizer for this cost function. One embodiment implements an RLS optimizer of a cost function defined as follows:

ES 2 365 730 T3

<img file="ES2365730T3_D0009.tif" />

in which:

<img file="ES2365730T3_D0010.tif" />

It should be noted that aQ¡ | b || it may be referred to as a "modified energy measure of feedback filter coefficients" or as an "error correction term". RLS optimization can be carried out on the pilot symbols present in the transmission.

Least squares algorithm: Another embodiment that optimizes equation (9c) is based on the least squares algorithm (LMS). The least squares (LMS) algorithm recursively adjusts the FFF and FBF coefficients of the hybrid DFE to minimize the MSE defined in equation (9c). For a fixed channel Q (~ | y), least squares (LMS) algorithm updates are given as:

<img file="ES2365730T3_D0011.tif" />

<img file="ES2365730T3_D0012.tif" />

in which the MSE is the one defined in equation (9c), μ is the step size of LMS and E denotes the reduction of the statistical expectation in the definition of equation (9c). Calculating the partial derivatives gives as a result:

^ n + ln + A- ^ n ^ n>

b_{n + 1} = (1 ~ μ (1 + Λ_ΰ²-2 P_Q)) b „+ / £„ &lt;;

= (1 - // ¾) b „+ // Z, X ^ = y_n-Cx_n-b „^wz „.

(11) (12) (12a) (13)

When μ is chosen with a suitably small value, the sequence of iterations defined from equation (11) to equation (13) is stable and converges on the set of coefficients that solve equation (4). It should be noted that this sequence of iterations does not require explicitly estimating the covariances and cross covariances of equation (4).

FIG. 6 illustrates an LMS algorithm according to one embodiment. Algorithm 500 begins with the selection of a SINR value⁰ initialization in step 502. Furthermore, the index k is initialized as k = 0. In step 504 the value of SINR is estimated^k and is calculated or determined to (SINR^k) from a precomputed look-up table (LUT). Equations (11) to (13) provided above are calculated iteratively, based on the pilot symbols of the transmission, until a convergence criterion is met in step 506. The result of such iteration determines the values ​​for ( F_k, b_k). In step 508, the process estimates SINR^{k + 1}, which is the SINR at the equalizer output when the coefficients of FFF and FBF are (fk, bk). The estimation can be done using the pilot symbols in the transmission. Then the process increments the index k. At the convergence of SINR^k at decision node 510, the process continues to step 512 to apply the filter coefficients. If not, processing returns to step 504.

Periodic Pilot Burst Algorithm: According to another embodiment, a communication system incorporates periodically transmitted pilot bursts that are used by receivers to adjust filter coefficients in the receivers equalizer. Such an adjustment is often referred to as "equalizer training." An example of such a system is a system that supports a high data transfer rate (HDR) as defined in the "TIA / EIA-IS-856 CDMA2000 High Rate Packet Data Air Interface Specification" standard. -856). In an HDR system 96 pilot symbols are transmitted every 0.833 ms. Each group of 96 pilot symbols is referred to as a "pilot burst". Between pilot bursts, the HDR system transmits symbols of

ES 2 365 730 T3 data intended for recipients. FIG. 7 illustrates an algorithm for applying an LMS-based hybrid DFE in such a system. Algorithm 600 initially sets SINR⁰ to 0 or a ω in step 602. The initial choice of SINR is not specified and may not be critical, although for faster convergence it may be preferred to set SINR⁰ to ω. The index k is also initialized and set equal to 0. In step 604, the algorithm determines SINR^k and calculates u (SINR^k) or determines the required value by querying a precomputed lookup table. The initial values ​​for f and b are set as f₀ = 0 and b₀ = 0 in step 606. During the (k + 1) -th pilot burst, the process iterates from equation (11) to (13) for all pieces of information in the pilot burst, step 608. In the Current HDR example, algorithm 600 iterates for all 96 chips of the pilot burst and the final values ​​of f and b are saved. In step 610, the process estimates SINR^{k + 1} using all 96 chips from the previous pilot burst. During the data portion following the (k + 1) pilot burst, the stored values ​​of f and b are loaded into the FFF and FBF, and the data symbols are equalized by standard decision feedback. In step 614, the process calculates the value of a (SINR^{k + 1}) and increments k. The process continues to implement the algorithm during demodulation operations.

The algorithm of FIG. 7 is adaptive for channels that vary slowly over time, since the SINR is not expected to^k near steady state and therefore u (SINR^k) vary too much over the convergence time of the LMS algorithm.

Flexible disconnector: As described above, error propagation greatly limits the use of DFE in communication systems that use channel coding. Since the causal ISI is canceled by feeding back decisions on individual symbols, a single isolated decision error can result in a flurry of subsequent decision errors, greatly increasing the residual interference at the equalizer output. If the channel code is faulty, the probability of a symbol decision error is not negligible (typically on the order of 25 percent) and error propagation can have severe effects on the performance of the DFE. One way to avoid the effects of such error propagation is to recognize that the typical minimum distance slicer does not achieve a level of confidence for symbol decisions. In other words, the decisions of a conventional slicer do not provide any measure of the accuracy or correctness of the symbol decisions. If a decision is known to have questionable precision, it is better to avoid canceling that symbol contribution to the final part of the post-cursor rather than risk worsening residual interference by subtracting an incorrect decision. In other words, low precision symbol decisions should not be included in the feedback loop that cancels the causal ISI.

An example of a slicer that incorporates a level of confidence in the decision process will be referred to herein as a "soft slicer". A flexible disconnector is described by a mathematical model like the one explained below. First, suppose that the input symbol to the disconnector is given as:

y = y + n (14) where y is the transmitted symbol belonging to the constellation Ψ, and n consists of residual noise and inter-symbol interference. Suppose that y is uniformly distributed across Ψ such that all points in the constellation are transmitted with the same probability. Let L (y, y) be a loss function that measures the loss generated when a disconnector decides^~and when the transmitted symbol is y. An optimal sectionalizer σ: yy, where “optimal” refers to a sectionalizer that minimizes the expected loss, is given by Bayes's rule:

<img file="ES2365730T3_D0013.tif" />

<img file="ES2365730T3_D0014.tif" />

For the minimum error probability loss function (MEP), given as:

[oy = y ΙΑ? *?

(16) the expected loss results in:

<img file="ES2365730T3_D0015.tif" />

ES 2 365 730 T3 and therefore:

(18)

Furthermore, assuming that the interference n is a Gaussian random variable with zero mean and variance σ², then:

σ (Υ) = arg min yeT

<img file="ES2365730T3_D0016.tif" />

(19) independent of σ². This is a traditional "minimum distance" slicer and, while Bayes' rule optimal for the loss function in equation (16), the slicer can lead to error propagation for the reasons described above. An alternative disconnector design considers the quadratic loss function:

(20) which, unlike the MEP loss function, penalizes larger errors to a greater extent than smaller errors. From equation (15) we obtain:

a (ñ = arg ™_ψ ψ - 5f | r} = £ ^ | y] and the conditional mean is equal to:

(21)

<img file="ES2365730T3_D0017.tif" />

(22)

An important observation is that, unlike the sectionalizer in equation (19), the sectionalizer in equation _? . ¹ (22) requires an estimate of the interference and the noise variance σ (for example, σ = ----------). It should also be noted that the sectioner of equation (22) corresponds to the centroid of the posterior distribution in the constellation symbols, that is, the centroid of the term in brackets [...] of equation (22). Therefore, if σ² has a high value, the assumption of a uniform anterior distribution or a symmetric constellation implies a nearly uniform posterior distribution, and therefore the centroid is almost zero. On the other hand, when σ² has a small value, the posterior distribution has its mass concentrated on the actual transmitted symbol and its neighboring constellation points; therefore, the centroid is close to the transmitted symbol. The education sectionalizer (22) is therefore referred to as a "flexible sectionalizer".

The flexible disconnect can be used in the adaptive hybrid DFE with minimal modification. The coefficients of FFF and FBF are chosen to optimize the following definition of MSE:

(23) where ρ_α~ ε_α[Γγ} similar to equation (5), and λ²ο is defined as:

(24th)

ES 2 365 730 T3

-Mri²} (24b)

The "channel" Q (~ | y) is defined as:

(25) where σ (.) Represents the flexible slicer defined in equation (22) and Z is the complex Gaussian noise defined in exactly the same way as in equation (7). Following a development analogous to the optimization scheme based on the LMS algorithm, equations (11), (12) and (13) remain unchanged, except for the fact that oq = 1 + Xq - 2pQ is calculated based on the equations (24a) and (24b) and the flexible equalizer defined in equation (25). As before, the leakage factor (1 - 2pQ + λ² q) depends on SINR and can be determined by a look-up table.

The LMS-based algorithm described above does not require any additional changes. During the pilot / training portion of the slot, adaptation takes place as before; during the data portion of the slot, the conditional mean slicer is used in place of the minimum distance "firm" slicer.

The calculations required in the flexible sectionalizer, specifically equation (22), can be very complicated for some practical implementations. An example simplifies the switch design to limit the switch output accepting at most N values. Equivalently, this means limiting the disconnector input to accept at most N values. In other words, the Y slicer input is quantized to one of N points using a quantizer defined by: q _: γ _{ {γ, ..., Y_N}. So, for k = 1, ..., N, a (Y) is calculated as:

a (Y) = Qk, if Q (Y) = Yk (26) where:

<img file="ES2365730T3_D0018.tif" />

(27)

The operation of the quantized slicer can be summarized as: 1) quantizing Y to one of N possible values; and 2) use this value and knowledge of the SINR as indices in a look-up table to determine Y = σ (Υ). Since the complexity in this design lies in stage 1), a further simplification would be to limit

Y_p...,Y_N so that they were arranged in a uniform grid and then quantizing Y by separately quantifying their real part and their imaginary part using the nearest neighbor criterion. Such a slicer function can be implemented with simple logic, that is, first calculating the closest set of neighbors based on the actual coordinate of Y, and then calculating the closest neighbor of this subset based on the imaginary coordinate of Y. Also, the lookup table can be imprecise in SINR, with 1dB jumps being sufficient for most implementations. For example, given lookup tables of {σ *} for SINR = 5 dB and SINR = 6 dB, appropriate values ​​of σ * for an intermediate SINR value of, say, 5.4 dB, can be determined by suitably interpolating between the two LUT. In other words, appropriate σ * values ​​in the intermediate SINR values ​​can be generated in the slicer device, thereby reducing the necessary memory / storage requirements.

As an illustration of the application of a flexible switch to a hybrid DFE (HDFE), consider FIGS. 8A and 8B. FIG. 8A illustrates an 8-PSK constellation, where 8 complex symbols represent the 3 coded bits correlated for modulation. As illustrated, the circles represent the constellation points used for modulation at the transmitter. The “x” marks indicate the samples received at the receiver and include noise and interference introduced during transmission. It should be noted that the received samples do not necessarily match the actual constellation symbols. In this case, the receiver decides which constellation symbol was actually sent. Typically, the received points are concentrated around the actual transmitted constellation symbols.

One procedure to determine the transmitted symbol from the received samples is to divide the map by

ES 2 365 730 T3 constellations in pieces of cake, as illustrated in FIG. 8B. Here, the constellation map is divided into 8 pieces 702, 704, 706, 708, 710, 712, 714 and 716. The pieces are determined, for example, according to a minimum distance metric, which uses Euclid's distance or separation. between two constellation points to select a border. There is a problem when the received sample is roughly equidistant (that is, roughly on the border) between two constellation points. In this case, if the decision process selected the wrong constellation symbol, this error would propagate in the feedback loop of a DFE. To avoid such errors and the associated amplification of a DFE, a flexible slicer is applied that provides a value not necessarily in a constellation symbol. The flexible slicer implicitly determines a confidence level from the received samples. The level of confidence provides the system with guidelines for evaluating the sample. If the confidence level is low, that is, an error is likely, the sample is not highlighted in the feedback portion of the equalizer. If the confidence level is high, the sample is considered reliable and therefore a suitable symbol estimate derived from it can be used in the feedback portion of the equalizer.

FIG. 9A illustrates a 2-PSK constellation map. It should be noted that decisions made based on the minimum distance from a constellation symbol can result in errors for received samples such as those marked by the "x". The application of a flexible slicer according to one embodiment divides the constellation map into rectangles, as illustrated in FIG. 9B. As shown, rectangles, such as rectangle 720, are semi-infinite in the y direction, and not all rectangles encompass constellation symbols. When the slicer input sample is within one of the semi-infinite rectangles, a conditional mean value is assigned. Effectively, all the points within the rectangle are mapped to a common value. This value represents the conditional mean of the transmitted symbol, since the slicer input sample is within the rectangle of interest. The mapping of each rectangle to a corresponding conditional mean value is a function of the signal-to-interference plus noise ratio (SINR). For example, a given rectangle can be mapped to σ for SINR at a first level, eg SINR = 4dB. The same rectangle can be mapped to σ 'for SINR at a second level, eg SINR = 5dB. The mapping and associated conditional mean values ​​are stored in look-up tables for easy retrieval. An alternative embodiment calculates the conditional mean value according to a predetermined algorithm. It should be noted that a square or rectangular grid is easily implemented and can be extended to more complex constellations.

FIG. 10 illustrates an equalizer 800 using a flexible disconnector. The equalizer 800 includes an FFF 802 coupled to an adder node 804. The FFF 802 is controlled by an adaptive equalization algorithm 808. The adaptive control unit 808 operates in response to a SINR estimation unit 816. In an alternative embodiment , the estimation unit SINR 816 can be implemented as an estimation unit MSE. The SINR estimation unit 816 provides a SINR estimation to a look-up table (LUT) 810. The SINR estimation is used in conjunction with the values ​​stored in the LUT 810 to determine aQ (SINR) = 1 + Xq² 2pq defined according to equations (24a), (24b) and (25). The adaptive equalization algorithm 808 uses the value of aQ generated from the LUT 810 to update the coefficients of the FFF 802 and FBF 806, iterating in equations (11), (12) and (13). It should be remembered that equations (11), (12) and (13) are based on the LMS algorithm and that they are designed to optimize the MSE cost function defined in equation (23). In an alternative example, the adaptive equalization algorithm 808 may implement another adaptive filtering algorithm, such as RLS, to optimize the MSE cost function defined in equation (23). The FBF 806 provides an estimate of the causal ISI present at the output of the FFF 802. The output of the FBF 806 is coupled to the adder node 804, where it is subtracted from the output of the FFF 802. The output of the summing node 804, that is, the estimate of the transmitted symbol, is then provided to a decoder 820, the SINR / MSE estimation unit 816, and the flexible sectionalizer 812. The flexible sectionalizer 812 receives the SINR / MSE estimate from the SINR / MSE estimation unit 816, it generates an additional estimate of the transmitted symbol and provides this additional symbol estimate for filtering in the FBF 806.

FIG. 11 is a flow diagram of a flexible sectionalizer process incorporating a flexible sectionalizer in accordance with one embodiment. The process first determines a region, such as a grid square or rectangle on the constellation map, corresponding to a quantization of the slicer input sample and, in step 902. The SINR value is determined in step 904. In step 906, the process selects an appropriate mapping based on the SINR value. According to one example, different parts of a memory storage device store different look-up tables. Tables are accessed based on the SINR value. At step 908 a conditional mean value is determined from the appropriate mapping and this is the output of the slicer.

Another example of a flexible slicer applies a grid of squares to the constellation map and uses a Taylor expansion to generate a more accurate conditional mean value. In this embodiment, multiple smaller look-up table storage values ​​correspond to each SINR value. The process

920 illustrated in FIG. 12. The region of the flex switch input y is determined in step 921. In step 922 a value of SINR is determined. The value of SINR is used to determine appropriate mappings σ₁(·) And σ2 (·) in step 924. The region of step 920 is mapped to a value σ ^), where i corresponds to the region.

ES 2 365 730 T3

Then, in step 922 a second coherent mapping is carried out with the value of SINR and the region of step 920 to obtain σ₂(^). A conditional mean value is approximated in step 928 as σ₁(y ^) + (y _ ^) σ₂(Y). The σ · ι (.) And σ mappings₂(.) are closely related to the zero-th and first derivatives of σ (.) defined in equation (22).

FIG. 13 illustrates a flexible switch 954 in accordance with one example. A SINR estimator 952 receives one or more symbol estimates and provides a SINR estimate value SINR (n). The SINR (n) can be quantized in an optional quantizer 956 and is provided to memory storage 960, such as a LUT. A symbol estimate corresponding to the flexible slicer input is also provided to a quantizer 956, where the symbol estimate is quantized and the quantized value is used in conjunction with the SINR estimate to determine a corresponding value stored in memory storage 960. . It should be noted that in one embodiment, the information is stored in rows and columns, where the rows correspond to SINR values ​​and the columns correspond to symbol values. However, alternative embodiments can store the information in one of several ways, where the information is retrieved based on a SINR value and a symbol value. The values ​​stored in memory storage 960 may be the conditional mean of an actual constellation symbol, given the soft slicer input estimate, as defined in equations (22), (26), and (27). FIG. 14 illustrates a flexible sectionalizer 980 in accordance with an alternate embodiment that implements a Taylor series calculation. As illustrated, one or more received symbols are provided to a SINR estimator 982, and in addition, a symbol estimate, corresponding to the flexible sectionalizer input, is provided directly to the flexible sectionalizer 980. It should be noted that the received symbols they are corrupted by the transmission channel and are therefore also referred to in this document as received samples. The SINR estimator 982 provides a SINR (n) estimate of the SINR to the flexible slicer 980. The SINR (n) can be provided to an optional quantizer 986. The SINR (n), quantized or not, is provided to two storage units memory, A 988 and B 990. The flexible slicer input symbol estimate is provided to a quantizer 984 whose output is also provided to memory storage units A 988 and B 990. The memory storage units A 988 and B 990 store information used to calculate the conditional mean values ​​of the actual constellation symbol, given the flexible slicer input symbol estimate. Such values ​​can be the zero-th and first derivatives of the conditional mean of the actual constellation symbol, given the flexible slicer input symbol estimate, as given in equations (22), (26), and ( 27). The value of SINR (n) and the quantized symbol value are used to identify the corresponding values ​​in storage memory A 988 and B 990. A summing unit 992 is used to implement the Taylor series calculation. The flexible slicer input symbol estimate as well as the quantized value are provided to the summing unit 992. In addition, the values ​​stored in memory storage units A 988 and B 990 are also provided to the summing unit 992. The summing unit 992 uses the inputs to calculate an output that is a conditional mean estimate of the actual constellation symbol. Although the present invention has been described in relation to a wireless communication system, such a system is provided merely as an example. The concepts described in this document can be applied to a plurality of communication systems including, but not limited to, a wired communication system, such as an implementation in a wired modem, etc. The present invention can be applied to a high speed data transfer communication system and allows optimizing the resources and capacity of a data communication system by increasing the sensitivity of the receivers and increasing the speed of data communication. Those skilled in the art will understand that information and signals can be represented using any of a variety of different technologies and techniques. For example, the data, instructions, commands, information, signals, bits, symbols and pieces of information that may have been referred to throughout the foregoing description may be represented by voltages, currents, electromagnetic waves, particles or magnetic fields, optical particles or fields, or any combination thereof.

Those skilled in the art will further appreciate that the various illustrative logic blocks, modules, circuits, and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, as computer software, or as combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps have been generically described above with respect to their functionality. Whether such functionality is implemented in hardware or software depends on the particular application and the design limitations imposed on the overall system. Those skilled in the art may implement the described functionality in different ways for each particular application, but such implementation decisions should not be construed as a departure from the scope of the present invention.

The various illustrative logic blocks, modules, and circuits described in connection with the embodiments disclosed herein may be implemented or carried out with a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit ( ASIC), a field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described in this document. A general purpose processor can be a microprocessor but,

As an alternative, the processor can be any conventional state machine, microcontroller, controller or processor. A processor can also be implemented as a combination of computing devices, for example, a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors together with a dSp core or any other such configuration.

The steps of a procedure or algorithm described in relation to the embodiments disclosed in this document can be performed directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module can reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such that the processor can read information from, and write information to, the storage medium. Alternatively, the storage medium can be an integral part of the processor. The processor and storage medium can reside in an ASIC. The ASIC can reside in a user terminal. Alternatively, the processor and storage medium can reside as discrete components in a user terminal.

The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications of these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the scope of the invention defined in the appended claims.