Joint equalization and coding for intersymbol interference channels

We present a novel scheme that combines decision feedback equalization (DFE) with high-rate error-detection coding in an efficient manner. The proposed scheme is shown to considerably outperform the conventional practice on channels with high SNR, such as those encountered in twisted-pair telephony systems. In order to analyze the performance of our method, we introduce an approximate mathematical model taking into account the error propagation phenomenon. Based on this model, upper and lower bounds on the overall probability of error are developed. These show that a simple low-redundancy error-detecting code, when properly integrated with the equalizer, can make the overall probability of error several orders of magnitude lower than that obtained with the conventional DFE, or with a DFE followed by an error-correcting code. Computer simulations of the proposed method have been performed for several channels, including the so-called high-bit-rate digital subscriber line (HDSL) test-loop 4, which is known to have a considerable amount of intersymbol interference. For all these channels, our results show that a reduction in the probability of error by more than three orders of magnitude can be obtained using codes of rate 0.96 and above. This, in turn, translates into power savings (coding gain) of 2.5 to 3 dB     

Joint coding and decision feedback equalization for broadbandwireless channels

This paper introduces a new approach for joint convolutional coding and decision feedback equalization (DPE). To minimize error propagation, the DFE uses a combination of soft decisions and delayed tentative decisions to cancel intersymbol interference (ISI). Soft decisions are obtained by passing the DFE output through a (soft) nonlinear device. This simple method is shown to perform almost as well as an optimum soft feedback approach on wireless channels with diversity. Tentative decisions from the Viterbi decoder are used to cancel ISI due to multipath with large delays, thus remedying the increasing effect of error propagation in channels with large delay spreads. We consider the use of this soft/delayed feedback DFE (S/D-DFE) technique in broadband wireless channels (with delay spreads up to several tens of the symbol period) typical in high-bitrate mobile data applications. Simulation results indicate that the proposed joint coding and S/D-DFE technique performs to within 1-2 dB [in required signal-to-noise ratio (SNR)] of an ideal coded DFE without error propagation. When combined with antenna diversity and a reduced-complexity DFE concept with adaptive feedforward tap assignment, it provides high packet throughput against Rayleigh fading, severe delay spreads, and high Doppler rates     

Combined equalization and coding using precoding

Recently developed techniques that achieve the joint objectives of increasing the signaling rate so as to use the maximum possible channel bandwidth, and then using powerful equalization techniques to cope with the resulting distortion are reviewed. These techniques generalize the Tomlinson-Harashima precoding techniques, which were proposed more than 20 years ago. The principal classes of classical equalization techniques are described, and Tomlinson-Harashima precoding is introduced. It is shown that precoding combines nicely with coded modulation and with a technique known as shaping. It is also shown that, in principle, optimized combinations of coding, shaping, and precoding can achieve nearly the channel capacity of any strictly band-limited, high-SNR Gaussian channel, and in practice can approach capacity within about 3 dB or less     

Combined equalization for uplink MC-CDMA in Rayleigh fading channels

In this letter, we propose the concept of combined equalization for uplink multicarrier code-division multiple access (MC-CDMA) and perform a theoretical analysis which shows that better single-user bounds than the classical matched-filter bounds are achieved with this new concept. Moreover, we illustrate how to properly design an uplink MC-CDMA transmitter and receiver for combined equalization, and show by Monte Carlo simulations that the improved single-user bounds are closely approached, even in the case of a fully loaded system.     

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     

Integrated MAP equalization and coding for optical-fiber-communication systems

In this paper, an integrated maximum a posteriori equalization and turbo product coding (IMAP-TPC) scheme for optical-fiber-communication systems (OFCS) is proposed. The scheme uses a probabilistic characterization of the electrical current in the presence of intersymbol interference (ISI) and noise to compensate their effects and improve the bit error rate. In the new IMAP-TPC scheme, TPC decoding is integrated with a symbol-by-symbol MAP detector. The MAP detector calculates the log-likelihood ratio of a received symbol using the conditional probability-density information and, hence, obtains a much more accurate reliability measure than the traditional measure used in the TPC decoder. The TPC was generated by serial concatenation of two Bose, Chaudhuri, and Hocquenghem codes with low overhead, which is a structure similar to a recently proposed hardware implementation of TPC decoder for optical systems. Simulation results with all-order polarization mode dispersion and amplified spontaneous emission noise demonstrate both the practicality and the effectiveness of the IMAP-TPC scheme for OFCS.     

Feedback equalization for fading dispersive channels

Data transmission through a slowly fading dispersive channel is considered. A receiver that linearly operates on both the received signal and reconstructed data is postulated. Assuming an absence of decision errors, the receiver is optimized for a minimum-mean-square-error criterion. Transfer functions are determined and superiority over nonfeedback receivers is indicated. The feedback receiver can be realized in a slowly varying unknown environment by means of an adaptive technique that requires neither test signals nor statistical estimation. The receiver will eliminate timing jitter and Doppler shifts. In addition, the receiver provides a time-diversity effect, as the receiver probability of error averaged over the fading statistics is lower in the presence of dispersion than in its absence.     

Compound strategies of coding, equalization, and space diversityfor wide-band TDMA indoor wireless channels

Compound strategies of equalization and space diversity in the form of an optimum baseband combiner are attractive for wideband time division multiple access (TDMA) portable communication radio links in order to combat dispersive fading and cochannel interference. The authors investigate the performance of such a scheme in conjunction with convolutional coding and soft-decision Viterbi decoding via a semianalytical technique based on the method of moments. Such an approach avoids a Gaussian characterization of interference and yields results for both ideal interleaving and no interleaving. With dual space diversity, three taps per forward filter, and a data rate of 10 Mb/s, it is shown that, although a third space diversity branch remains preferable in terms of performance, channel coding can be a viable alternative, particularly in terms of outage rate, to increasing the space diversity order, even in the absence of interleaving, provided the signal-to-interference ratio is sufficiently high     

Simple equalization of time-varying channels for OFDM

We present a block minimum mean-squared error (MMSE) equalizer for orthogonal frequency-division multiplexing (OFDM) systems over time-varying multipath channels. The equalization algorithm exploits the band structure of the frequency-domain channel matrix by means of a band LDL/sup H/ factorization. The complexity of the proposed algorithm is linear in the number of subcarriers and turns out to be smaller with respect to a serial MMSE equalizer characterized by a similar 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.     

Time-varying FIR equalization for doubly selective channels

We propose a time-varying (TV) finite impulse response (FIR) equalizer for doubly selective (time- and frequency-selective) channels. We use a basis expansion model (BEM) to approximate the doubly selective channel and to design the TV FIR equalizer. This allows us to turn a complicated equalization problem into an equivalent simpler equalization problem, containing only the BEM coefficients of both the doubly selective channel and the TV FIR equalizer. The minimum mean-square error (MMSE) as well as the zero-forcing (ZF) solutions are considered. Comparisons with the block linear equalizer (BLE) are made. The TV FIR equalization we propose here unifies and extends many previously proposed serial equalization approaches. In contrast to the BLE, the proposed TV FIR equalizer allows a flexible tradeoff between complexity and performance. Moreover, through computer simulations, we show that the performance of the proposed MMSE TV FIR equalizer comes close to the performance of the ZF and MMSE BLE, at a point where the design as well as the implementation complexity are much lower.     

一种较低复杂度的UWB信道自适应均衡技术

针对多用户UWB信道存在的符号间干扰和用户间干扰问题,提出了一种用于DS-UWB/TH-UWB接收机的较少复杂度的自适应均衡技术及相应算法,并与传统算法在复杂性和性能方面进行了比较。研究结果表明所提出的算法在运算量上远小于单独使用RLS算法,在输出误差的收敛上远快于单独使用LMS算法。     

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.     

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.     

Sliding-block coding for input-restricted channels

Work on coding arbitrary sequences into a constrained system of sequences (called a sofic system) is presented. Such systems model the input constraints for input-restricted channels (e.g., run-length limits and spectral constraints for the magnetic recording channel). In this context it is important that the code be noncatastrophic to ensure that the decoder has limited error propagation. A constructive proof is given of the existence of finite-state invertible noncatastrophic codes from arbitrary n-ary sequences to a sofic system S at constant rate p:q provided only that Shannon's condition (p/q)⩽(h/log n) is satisfied, where h is the entropy of the system S. If strict inequality holds or if equality holds and S satisfies a natural condition called `almost of finite type' (which includes the systems used in practice), a stronger result is obtained, namely, the decoders can be made `state-independent' sliding-block. This generalizes previous results. An example is also given to show that the stronger result does not hold for general sofic systems     

Quotient coding for fading channels

Multiplicative Rayleigh fading is a frequent problem in wireless communications. If the channel is relatively benign and fading is not severe, one may obtain higher bit rates for an equivalent bandwidth by using M-ary QAM modulation (MQAM). A variation, used to combat channel fading while still retaining MQAM, is differential MQAM (i.e., DQAM). The term differential refers to the phase which is coded exactly as in DPSK, however, the amplitude is still subject to distortion by the fading channel. In this paper, we propose a technique called quotient coding, which is designed to remove channel effects from the symbol amplitude as well as its phase. In particular, we shall apply it to MQAM resulting in modulation which we term QQAM. In contrast to DQAM, QQAM is just as effective at suppressing the effects of channel fading with respect to the entire symbol as DPSK is for the phase alone. In fact, the scaling of the amplitude at the receiver is entirely irrelevant to QQAM     

Coding and equalization for PPM on wireless infrared channels

We analyze the performance of trellis-coded pulse-position modulation with block decision-feedback equalization (BDFE) and parallel decision-feedback decoding (PDFD) on indoor, wireless infrared channels. We show that the reduced complexities of BDFE and PDFD as compared to maximum-likelihood sequence detection allow for better codes whose increased coding gain more than compensates for the penalty due to suboptimal detection. We quantify these net gains in performance over a range of dispersive channels, indicating where BDFE and PDFD provide the best performance. Finally, we present Monte Carlo simulation results to verify our analysis     

Superposition coding for side-information channels

We present simple, practical codes designed for the binary and Gaussian dirty-paper channels. We show that the dirty-paper decoding problem can be transformed into an equivalent multiple-access decoding problem, for which we apply superposition coding. Our concept is a generalization of the nested lattices approach of Zamir, Shamai, and Erez. In a theoretical setting, our constructions are capable of achieving capacity using random component codes and maximum-likelihood decoding. We also present practical implementations of the constructions, and simulation results for both dirty-paper channels. Our results for the Gaussian dirty-paper channel are on par with the best known results for nested lattices. We discuss the binary dirty- tape channel, for which we present a simple, effective coding technique. Finally, we propose a framework for extending our approach to general Gel'fand-Pinsker channels.     

Convolutional coding for finite-state channels

We propose new decoders for decoding convolutional codes over finite-state channels. These decoders are sequential and utilize the information about the channel state sequence contained in the channel output sequence. The performance of these decoders is evaluated by simulation and compared to the performance of memoryless decoders with and without interleaving. Our results show that the performance of these decoders is good whenever the channel statistics are such that the joint estimate of the channel state sequence and the channel input sequence is good, as, for example, when the channel is bursty. In these cases using even a partial search decoder such as the Fano decoder over the appropriate trellis is nearly optimal. However, when the information between the output sequence and the sequence of channel slates and inputs diminishes, the memoryless decoder with interleaving outperforms even the optimal decoder which knows the channel state     

Monte carlo equalization for nonlinear dispersive satellite channels

Satellite channels are generally nonlinear and dispersive in nature, due to amplifiers being driven close to saturation. These effects can cause significant degradations when they are not taken into account at either the receiver (equalization) or at the transmitter (pre-distortion). State-of-the-art equalizers rely on the forward-backward algorithm and yield excellent performance. However, they have unreasonable complexity and storage requirements, especially for highly dispersive channels and/or large constellations. In this paper, we derive an equalization strategy for nonlinear channels based on Monte Carlo methods. We present a detailed performance, complexity and storage analysis. A significant performance gain compared to the linear equalizer is reported, and the proposed technique results in a significant reduction in both complexity and storage, compared to the forward-backward equalizer.