Reduced-complexity equalization techniques for broadband wirelesschannels

This paper presents reduced-complexity equalization techniques for broadband wireless communications, both outdoors (fixed or mobile wireless asynchronous transfer mode (ATM) networks) and indoors [high-speed local-area networks (LANs)]. The two basic equalization techniques investigated are decision-feedback equalization (FE) and delayed decision-feedback sequence estimation (DDFSE). We consider the use of these techniques in highly dispersive channels, where the impulse response can last up to 100 symbol periods. The challenge is in minimizing the complexity as well as providing fast equalizer start-up for transmissions of short packets. We propose two techniques which, taken together, provide an answer to this challenge. One is an open-loop timing recovery approach (for both DFE and DDFSE) which can be executed prior to equalization; the other is a modified DFE structure for precanceling postcursors without requiring training of the feedback filter. Simulation results are presented to demonstrate the feasibility of the proposed techniques for both indoor and outdoor multipath channel models. The proposed open-loop timing recovery technique plays a crucial role in maximizing the performance of DFE and DDFSE with short feedforward spans (the feedforward section of DDFSE is a Viterbi sequence estimator). A feedforward span of only five is quite sufficient for channels with symbol rate-delay spread products approaching 100. The modified DFE structure speeds up the training process for these channels by 10-20 times, compared to the conventional structure without postcursor precancellation. The proposed techniques offer the possibility of practical equalization for broadband wireless systems     

Linear LLR approximation for iterative decoding on wireless channels

On a fading channel with no channel state information at the receiver, true log-likelihood ratios (LLR) are complicated functions of the channel output. It is assumed in the literature that the power of the additive noise is known and the expected value of the fading gain is used in a linear function of the channel output to find approximate LLRs. This approach, however, is not optimal in the sense of bit error rate performance. In this paper, we introduce a measure of accuracy for the approximate LLRs based on their probability density function and we show that this measure provides a very convenient tool for finding good approximate LLRs. Assuming that the power of the additive noise is known, and using the proposed measure, we find a linear LLR approximation whose performance is extremely close to that of the true LLR calculation on an uncorrelated Rayleigh fading channel. These results are then extended to the case that the noise power is also unknown and a performance almost identical to the previous case is obtained.     

New results about analysis and design of TCM for ISI channels andcombined equalization/decoding

New upper bounds for the performance of the optimum combined symbol-by-symbol (SbS) Abend-Fritchman-like equalizer and decoder are presented, and a related criterion for the actual design of good trellis-coded-modulated (TCM) schemes effectively matched to the distortion introduced by the intersymbol interference (ISI)-corrupted transmission channel is developed. The actual application of the proposed design criterion is also addressed     

Linear turbo equalization for parallel ISI channels

We propose a method for exploiting transmit diversity using parallel independent intersymbol interference channels together with an iterative equalizing receiver. Linear iterative turbo equalization (LITE) employs an interleaver in the transmitter and passes a priori information on the transmitted symbols between multiple soft-input/soft-output minimum mean-square error linear equalizers in the receiver. We describe the LITE algorithm, present simulations for both stationary and fading channels, and develop a framework for analyzing the evolution of the a priori information as the algorithm iterates.     

Joint MF combining and turbo equalization for wireless communications over ISI channels with diversity reception

A new method called joint Matched Filter (MF) combining and turbo equalization is proposed for wireless communications over Inter-Symbol Interference (ISI) channels with diversity reception. This method takes diversity combining and equalization as integrity and need just one turbo equalizer for all diversity branches. Computer simulations prove that our method can take advantage of turbo equalization and diversity reception to combat fading of wireless channels.     

MLSE equalization and decoding for multipath-fading channels

The performance of a receiver using a combined MLSE (maximum likelihood sequence estimation) equalizer/decoder and D-diversity reception is analyzed for multipath Rayleigh fading channels. An upper bound on the (decoded) bit error probability is derived. Comparisons to simulation results show that this upper bound is quite tight when the system has a high signal-to-noise ratio or when diversity reception is used. The upper bound involves an infinite series that must be truncated at a point where the remainder can be safely assumed to be small. An algorithm based on a one-directional stack algorithm is proposed for this calculation because it makes efficient use of computer memory     

FIR channel-shortening equalizers for MIMO ISI channels

Finite-length delay-optimized multi-input multi-output (MIMO) equalizers that optimally shorten the impulse response memory of frequency-selective MIMO channels are derived. The MIMO equalizers are designed to minimize the average energy of the error sequence between the equalized MIMO channel impulse response and an MIMO target impulse response (TIR) with shorter memory. Two criteria for optimizing the MIMO TIR are analyzed and compared. The presented analytical framework encompasses a multitude of previously-studied finite-length equalization techniques     

Layered MAP algorithm for MIMO ISI channels

The layered maximum a posteriori （L-MAP） algorithm has been proposed to detect signals under frequency selective fading multiple input multiple output （MIMO） channels. Compared to the optimum MAP detector, the L-MAP algorithm can efficiently identify signal bits, and the complexity grows linearly with the number of input antennas. The basic idea of L-MAP is to operate on each input sub-stream with an optimum MAP sequential detector separately by assuming the other streams are Gaussian noise. The soft output can also be forwarded to outer channel decoder for iterative decoding. Simulation results show that the proposed method can converge with a small number of iterations under different channel conditions and outperforms other sub-optimum detectors for rank-deficient channels.     

Combined turbo detection and decoding for unknown ISI channels

We present two decoding structures which combine turbo detection and decoding, allowing communication in the presence of intersymbol interference (ISI). The first one treats the ISI as another constituent decoder which participates in the exchange of extrinsic information, and performs slightly worse than the second structure, which combines the trellis representing each one of the constituent encoders with the ISI trellis. We show that for both methods, it is possible to obtain good performance, even when no a priori information about the ISI channel is available to the decoder.     

Layered space-time equalization for wireless MIMO systems

We investigate layered space-time equalization (LSTE) architectures for multiple-input multiple-output (MIMO) frequency-selective channels. At each stage or layer of detection, a MIMO delayed decision feedback sequence estimator (MIMO-DDFSE) is used to tentatively detect a group of selected data streams, among which a subgroup of data streams are output and are canceled from the received signals. With the proposed architectures, the numbers of the tentatively detected data streams and output data streams can be different at different LSTE stages, while the MIMO-DDFSE can also reduce to the special cases of multiple-input single-output decision feedback equalizer (MISO-DFE), MISO-DDFSE, and MIMO-DFE, allowing tradeoffs between performance and complexity. We also derive the equalizer coefficients, discuss timing recovery, and consider channel estimation. Simulation results demonstrate the performance of the proposed LSTE structures and the tradeoffs between performance and complexity of the multistage structure and the single-stage version. We also demonstrate the impact of imperfect channel estimation, imperfect interference cancellation, the number of receive antennas, filter length, and oversampling on performance.     

Adaptive turbo reduced-rank equalization for MIMO channels

An adaptive iterative (turbo) decision-feedback equalizer (DFE) for channels with intersymbol interference (ISI) is presented. The filters are computed directly from the soft decisions and received data to minimize a least-squares (LS) cost function. Numerical results show that this method gives a substantial improvement in performance relative to a turbo DFE computed from an exact channel estimate, assuming perfect feedback. Adaptive reduced-rank estimation methods are also presented, based on the multistage Wiener filter (MSWF). The adaptive reduced-rank turbo DFE for single-input/single-output channels is extended to multiple-input/multiple-output (MIMO) channels with ISI and multiple receive antennas. Numerical results show that for MIMO channels with limited training, the reduced-rank turbo DFE can perform significantly better than the full-rank turbo DFE.     

Sampling-based soft equalization for frequency-selective MIMO channels

We consider the problem of channel equalization in broadband wireless multiple-input multiple-output (MIMO) systems over frequency-selective fading channels, based on the sequential Monte Carlo (SMC) sampling techniques for Bayesian inference. Built on the technique of importance sampling, the stochastic sampler generates weighted random MIMO symbol samples and uses resampling to rejuvenate the sample streams; whereas the deterministic sampler, a heuristic modification of the stochastic counterpart, recursively performs exploration and selection steps in a greedy manner in both space and time domains. Such a space-time sampling scheme is very effective in combating both intersymbol interference and cochannel interference caused by frequency-selective channel and multiple transmit and receiver antennas. The proposed sampling-based MIMO equalizers significantly outperform the decision-feedback MIMO equalizers with comparable computational complexity. More importantly, being soft-input soft-output in nature, these sampling-based MIMO equalizers can be employed as the first-stage soft demodulator in a turbo receiver for coded broadband MIMO systems. Such a turbo receiver successively improves the receiver performance through iterative equalization, channel re-estimation, and channel decoding. Finally, computer simulation results are provided to demonstrate the performance of the proposed sampling-based soft MIMO equalizers in both uncoded and turbo coded systems.     

On the performance of turbo equalization for precoded ISI channels

In this paper, we present a semi‐analytical approach for analyzing the serial concatenation (SCC) of a high rate convolutional code and a precoded intersymbol interference (ISI) channel. The significance of the proposed approach is that it can be used to identify, for a given outer high rate code and fixed ISI channel, the precoder that results in the lowest error rate floor. In estimating the bit error performance in the floor region, we use analytical techniques developed for trellis codes to compute the overall system minimum squared Euclidean distance, and then use a semi‐analytical approach to find the corresponding multiplicity. We also demonstrate via simulations that the proposed technique may be extended to fading ISI channels with favorable results. We give examples that support our analysis. Copyright © 2006 John Wiley & Sons, Ltd.     

MIMOHSDPA系统中一种导频抵消迭代码片均衡算法

MIMO HSDPA(High Speed Downlink PacketAccess)系统采用多天线技术,传统的LMMSE码片均衡算法计算复杂度较高,为降低运算量,本文将SMW定理引入LMMSE算法中,并引入导频抵消模块,提出了一种PC-ILMMSE算法.理论分析与仿真结果表明,新算法的性能优于传统的LMMSE,而运算量大大降低.     

Space-time turbo equalization in frequency-selective MIMO channels

A computationally efficient space-time turbo equalization algorithm is derived for frequency-selective multiple-input-multiple-output (MIMO) channels. The algorithm is an extension of the iterative equalization algorithm by Reynolds and Wang (see Signal Processing, vol.81, no.5, p.989-995, 2001) for frequency-selective fading channels and of iterative multiuser detection for code-division multiple-access (CDMA) systems by Wang and Poor (see IEEE Trans. Commun., vol.47, p.1046-1061, 1999). The proposed algorithm is implemented as a MIMO detector consisting of a soft-input-soft-output (SISO) linear MMSE detector followed by SISO channel decoders for the multiple users. The detector first forms a soft replica of each composite interfering signal using the log likelihood ratio (LLR), fed back from the SISO channel decoders, of the transmitted coded symbols and subtracts it from the received signal vector. Linear adaptive filtering then takes place to suppress the interference residuals: filter taps are adjusted based on the minimum mean square error (MMSE) criterion. The LLR is then calculated for adaptive filter output. This process is repeated in an iterative fashion to enhance signal-detection performance. This paper also discusses the performance sensitivity of the proposed algorithm to channel-estimation error. A channel-estimation scheme is introduced that works with the iterative MIMO equalization process to reduce estimation errors.     

Reduced-complexity decoding algorithm for low-density parity-checkcodes

A new reduced-complexity decoding algorithm for low-density parity-check codes that operates entirely in the log-likelihood domain is presented. The computationally expensive check-node updates of the sum-product algorithm are simplified by using a difference-metric approach on a two-state trellis and by employing the dual-max approximation. The dual-max approximation is further improved by using a correction factor that allows the performance to approach that of full sum-product decoding     

Blind equalization for an application of unitary space-time modulation in ISI channels

Transmit diversity schemes have gained attention due to the promise of increased capacity and improved performance. Among these schemes, unitary space-time modulation and differentially encoded unitary space-time modulation allow for simple noncoherent decoding for flat-fading channels. In this paper, a new blind equalization algorithm for these transmission schemes in intersymbol interference (ISI) channels is proposed. A matrix-type constant modulus algorithm that exploits the unitary structure of the space-time codes is developed. The equalizer is paired with a noncoherent decoder, resulting in a completely blind, low-complexity method for decoding in the presence of ISI. A noiseless convergence analysis is conducted and verified via simulation in both noiseless and noisy cases. The performance of the overall system is evaluated via simulation and semi-analytically, and the achieved performance is between that of the ideal zero-forcing and the minimum-mean squared-error equalizers.     

Capacity-approaching turbo coding and iterative decoding for relay channels

In this paper, we design turbo-based coding schemes for relay systems together with iterative decoding algorithms. In the proposed schemes, the source node sends coded information bits to both the relay and the destination nodes, while the relay simultaneously forwards its estimate for the previous coded block to the destination after decoding and re-encoding. The destination observes a superposition of the codewords and uses an iterative decoding algorithm to estimate the transmitted messages. Different from the block-by-block decoding techniques used in the literature, this decoding scheme operates over all the transmitted blocks jointly. Various encoding and decoding approaches are proposed for both single-input single-output and multi-input multi-output systems over several different channel models. Capacity bounds and information-rate bounds with binary inputs are also provided, and it is shown that the performance of the proposed practical scheme is typically about 1.0-1.5 dB away from the theoretical limits, and a remarkable advantage can be achieved over the direct and multihop transmission alternatives.     

CHANNEL ESTIMATION FOR ITERATIVE DECODING OVER FADING CHANNELS

A method of coherent detection and channel estimation for punctured convolutional coded binary Quadrature Amplitude Modulation (QAM) signals transmitted over a frequency-flat Rayleigh fading channels used for a digital radio broadcasting transmission is presented.Some known symbols are inserted in the encoded data stream to enhance the channel estimation process.The puilot symbols are used to replace the existing parity symbols so no bandwidth expansion is required.An iterative algorithm that uses decoding information as well as the information contained in the known symbols is used to improve the channel parameter estimate.The scheme complexity grows exponentially with the channel estimation filter length,The performance of the system is compared for a normalized fading rate with both perfect coherent detection(Corresponding to a perfect knowledge of the fading process and noise variance)and differential detection of Differential Amplitude Phase Shift Keying (DAPSK).The tradeoff between simplicity of implementation and bit-error-rate performance of different techniques is also compared.     

MIMO MAP equalization and turbo decoding in interleaved space-time coded systems

Decoding of space-time codes in frequency-selective fading channels is considered. The approach is based on iterative soft-in soft-out equalization and decoding. It is applicable to space-time coded systems that deploy symbol/bit interleavers. We focus on the equalization stage by extending the Ungerboeck equalizer formulation to a multiple-input multiple-output time-variant channel. The resulting structure comprises a bank of matched filters, followed by an a posteriori probabilities calculator that runs the Bahl-Cocke-Jelinek-Raviv/maximum a posteriori algorithm with an appropriate metric. Simulation results are reported for space-time bit-interleaved codes designed over the enhanced data rates for GSM evolution (EDGE) air interface.