Decision-feedback MAP receiver for time-selective fading CDMAchannels

A decision-feedback maximum a posteriori (MAP) receiver is proposed for code-division multiple-access channels with time-selective fading. The receiver consists of a sequence-matched filter and a MAP demodulator. Output samples (more than one per symbol) from the matched filter are fed into the MAP demodulator. The MAP demodulator exploits the channel memory by delaying the decision and using a sequence of observations. This receiver also rejects multiple-access interference and estimates channel fading coefficients implicitly to give good demodulation decisions. Moreover, computer simulations are performed to evaluate the bit-error rate performance of the receiver under various channel conditions     

Designing low-complexity equalizers for wireless systems

The demand on wireless communications to provide high data rates, high mobility, and high quality of service poses more challenges for designers. To contend with deleterious channel fading effects, both the transmitter and the receiver must be designed appropriately to exploit the diversity embedded in the channels. From the perspective of receiver design, the ultimate goal is to achieve both low complexity and high performance. In this article, we first summarize the complexity and performance of low-complexity receivers, including linear equalizers and decision feedback equalizers, and then we reveal the fundamental condition when LEs and DFEs collect the same diversity as the maximum-likelihood equalizer. Recently, lattice reduction techniques were introduced to enhance the performance of low-complexity equalizers without increasing the complexity significantly. Thus, we also provide a comprehensive review of LR-aided low-complexity equalizers and analyze their performance. Furthermore, we describe the architecture and initial results of a very-large-scale-integration implementation of an LR algorithm.     

A decision feedback equalizer with time-reversal structure

This work describes the use of a receiver with a time-reversal structure for low-complexity decision feedback equalization of slowly fading dispersive indoor radio channels. Time-reversal is done by storing each block of received signal samples in a buffer and reversing the sequential order of the signal samples in time prior to equalization. As a result, the equivalent channel impulse response as seen by the equalizer is a time-reverse of the actual channel impulse response. Selective time-reversal operation, therefore, allows a decision feedback equalizer (DFE) with a small number of forward filter taps to perform equally well for both minimum-phase and maximum-phase channel characteristics. The author evaluates the theoretical performance bounds for such a receiver and quantifies the possible performance improvement for discrete multipath channels with Rayleigh fading statistics. Two extreme cases of DFE examples are considered: an infinite-length DFE; and a DFE with a single forward filter tap. Optimum burst and symbol timing recovery is addressed and several practical schemes are suggested. Simulation results are presented. The combined use of equalization and diversity reception is considered     

BLIND CHANNEL ESTIMATION IN DELAY DIVERSITY FOR FREQUENCY SELECTIVE CHANNELS1

Delay diversity is an effective transmit diversity technique to combat adverse effects of fading. Thus far, previous work in delay diversity assumed that perfect estimates of current channel fading conditions are available at the receiver and training symbols are required to estimate the channel from the transmitter to the receiver. However, increasing the number of the antennas increases the required training interval and reduces the available time with in whichdata may be transmitted. Learning the channel coefficients becomes increasingly difficult for the frequency selective channels. In this paper, with the subspace method and the delay character of delay diversity, a channel estimation method is proposed, which does not use training symbols. It addresses the transmit diversity for a frequency selective channel from a single carrier perspective in the form of a simple equivalent flat fading model. Monte Carlo simulations give the performance of channel estimation and the performance comparison of our channel-estimation-based detector with decision feedback equalization, which uses the perfect channel information.     

Receiver structures for time-varying frequency-selective fadingchannels

Several receiver structures for linearly modulated signals are proposed for time-varying frequency-selective channels. Their channel estimators explicitly model the time variation of the channel taps via polynomials. These structures are constructed from the following building blocks: (i) sliding or fixed block channel estimators; (ii) maximum likelihood sequence detectors (MLSDs) or decision feedback equalizers (DFEs); and (iii) single or multiple passes. A sliding window channel estimator uses a window of received samples to estimate the channel taps within or at the end of the window. Every symbol period, the window of samples is slid along another symbol period, and a new estimate is calculated. A fixed block channel estimator uses all received samples to estimate the channel taps throughout the packet, all at once. A single pass receiver estimates the channel and detects data once only. A multipass receiver performs channel estimation and data detection repetitively. The effect of the training symbol positions on the performance of the block multipass approach is studied. The bit error rate (BER) performance of the MLSD structures is characterized through simulation and analysis. The proposed receivers offer a range of performance/complexity tradeoffs, but all are well suited to time-varying channels. In fast fading channels, as the signal-to-noise ratio (SNR) increases, they begin to significantly outperform the per-survivor processing-based MLSD receivers which employ the least mean-squares (LMS) algorithm for channel estimation     

Letter: An Improved Decision-Feedback Receiver for CDMA IS-95 Reverse Link

In this paper, an improved decision feedback receiver is presented for the CDMA IS-95 reverse link. Two techniques are proposed to improve the receiver performance: (1) noncoherent block detection that uses multiple Walsh codes for joint detection, and (2) iterative decision feedback detection. Comparing with conventional "decision feedback receiver," a significant performance improvement is observed via the computer simulations for both AWGN and Rayleigh flat fading channels.     

Zero forcing and minimum mean-square-error equalization formultiuser detection in code-division multiple-access channels

In code-division multiple-access (CDMA) systems transmitting over time-varying multipath channels, both intersymbol interference (ISI) and multiple-access interference (MAI) arise. The conventional suboptimum receiver consisting of a bank of matched filters is often inefficient because interference is treated as noise. The optimum multiuser detector is too complex to be implemented at present. Four suboptimum detection techniques based on zero forcing (ZF) and minimum mean-square-error (MMSE) equalization with and without decision feedback (DF) are presented and compared. They combat both ISI and MAI. The computational complexity of all four equalizers is essentially the same. All four equalizers are independent of the size of the data symbol alphabet. It is shown that the performance of the MMSE equalizers is better than that of the corresponding ZF equalizers. Furthermore, the performance of the equalizers with DF is better than that of the corresponding equalizers without DF. The impairing effect of error propagation on the equalizers with DF is reduced by channel sorting     

Comparison of DFE and MLSE Receiver Performance on HF Channels

Data communication at rates near or above 2 kbits/s on 3 kHz-baadwidth HF radio channels is subject to impairment from severe linear dispersion, rapid channel time variation, and severe fading. In this investigation, recorded 2.4 kbit/s QPSK signals received from HF channels were processed to extract a time-varying estimate of the channel impulse response. From the estimated channel impulse responses, performance-related parameters were computed for ideal matched filter reception, maximum-likelihood sequence-estimation (MLSE), and decision feedback equalization (DFE). The results indicated that the simpler DFE receiver suffered only a small theoretical performance degradation relative to the more complex MLSE receiver. Other HF channel impulse response statistics were also obtained to shed light on equalization and filter adaptation techniques.     

Performance Improvement of IS-95 CDMA Uplink Using Decision Feedback and Sub-Optimal Viterbi Decoding

This paper presents a methodology designed to improve the effectiveness of a non-iterative decision feedback (DF) receiver/decoder for IS-95 Code Division Multiple Access (CDMA) uplink in additive white Gaussian noise (AWGN) and Rayleigh fading. The effectiveness of the DF receiver/decoder is linked to the interleaver specification and the decoding delay of the convolutional decoder. Using sub-optimal convolutional decoding the average decoding delay is reduced resulting in more effective decision feedback decoding (DFD). Simulation results of average decoding delay, bit error rate (BER) and frame error rate (FER) are presented for coherent and noncoherent detection of unfaded single-path and Rayleigh fading multipath signals. Instead of the usual performance degradation these results show that the DF receiver/decoder benefits from some forms of sub-optimal Viterbi decoding. The additional performance gain can further improve the quality of service and/or capacity of a cellular IS-95 system.     

Unification of MLSE receivers and extension to time-varyingchannels

Forney (1972) and Ungerboeck (1974) have each developed maximum-likelihood sequence estimation (MLSE) receivers for intersymbol interference (ISI) channels. The Forney receiver uses a whitened matched filter, followed by a sequence estimation algorithm using the Euclidean distance metric. The Ungerboeck receiver uses a matched filter, followed by a sequence estimation algorithm using a modified metric. A unified development of both receivers is given, in which each receiver is derived from the other. By deriving the Ungerboeck receiver from the Forney receiver, we show that the whitening operation is cancelled in the Euclidean distance metric, leaving the modified metric. In addition, the Ungerboeck receiver is extended to the case of a time-varying known channel. When the channel is unknown, decision-directed channel estimation is assumed, which requires channel prediction to account for the decision delay. It is shown that the Ungerboeck receiver requires additional channel prediction, degrading performance due to prediction uncertainty. To solve this problem, two alternative receiver forms are developed which do not require additional prediction, though the computational complexity is increased. Performance and complexity of the receiver forms are compared for the IS-136 digital cellular time-division multiple-access (TDMA) standard     

Digital Transmission Performance on Fading Dispersive Diversity Channels

The reception and detection of a single digit under known channel conditions are investigated. The probability of error for an optimum one-shot receiver instantaneously matched to the channel state is averaged over an ensemble of dispersive diversity channels. The average probability of error as a function of energy to noise ratio is found to be solely dependent on the ratio of rms dispersion width to data symbol width. For these dispersive channels an implicit diversity effect is qualitatively explained in terms of eigenvalues that depend on the ensemble statistic. The one-shot receiver performance provides a bound for practical receivers. In a comparison with a decision feedback equalizer, it is shown that on moderately dispersive channels the equalizer nearly achieves optimum one-shot performance. Since an adaptive version of this equalizer exists, this means data transmission on slowly fading channels is possible at rates above the natural rate suggested by the channel dispersion spread without bandwidth expansion and with small intersymbol interference penalty. The use of one-shot receiver performance curves can also be used as estimates of equalizer performance in situations where computation of the latter is impractical.     

Fast adaptive equalization/diversity combining for time-varyingdispersive channels

We examine adaptive equalization and diversity combining methods for fast Rayleigh-fading frequency selective channels. We assume a block adaptive receiver in which the receiver coefficients are obtained from feedforward channel estimation. For the feedforward channel estimation, we propose a novel reduced dimension channel estimation procedure, where the number of unknown parameters are reduced using a priori information of the transmit shaping filter's impulse response. Fewer unknown parameters require a shorter training sequence. We obtain least-squares, maximum-likelihood, and maximum a posteriori (MAP) estimators for the reduced dimension channel estimation problem. For symbol detection, we propose the use of a matched filtered diversity combining decision feedback equalizer (DFE) instead of a straightforward diversity combining DFE. The matched filter form has lower computational complexity and provides a well-conditioned matrix inversion. To cope with fast time-varying channels, we introduce a new DFE coefficient computation algorithm which is obtained by incorporating the channel variation during the decision delay into the minimum mean square error (MMSE) criterion. We refer to this as the non-Toeplitz DFE (NT-DFE). We also show the feasibility of a suboptimal receiver which has a lower complexity than a recursive least squares adaptation, with performance close to the optimal NT-DFE     

An MLSE receiver using channel classification for Rayleigh fadingchannels

We propose a channel classification method that identifies the delay path profile of Rayleigh fading channels, which can be used in conjunction with conventional maximum-likelihood sequence estimation (MLSE) receivers. The proposed method determines the appropriate number of delay taps for the MLSE trellis, based on a decision variable obtained from multiple traffic bursts. By formulating the decision variable using the F-distribution, we derive exact expressions for misclassification probability. A new MLSE receiver structure that utilizes the channel classification method is described, and bit error rate (BER) simulation results are presented to demonstrate the performance improvement. The particular application which is discussed is the IS-136 TDMA standard     

Approximate ML Decision-Feedback Block Equalizer for Doubly Selective Fading Channels

To effectively suppress intersymbol interference (ISI) at low complexity, in this paper, we propose an approximate maximum-likelihood decision-feedback block equalizer (A-ML-DFBE) for doubly selective (frequency- and time-selective) fading channels. The proposed equalizer design makes efficient use of the special time-domain representation of multipath channels through a matched filter, a sliding window, a Gaussian approximation, and a decision feedback. The A-ML-DFBE has the following features: 1) It achieves a performance that is close that to that of maximum-likelihood sequence estimation (MLSE) and significantly outperforms minimum mean square error (MMSE)-based detectors. 2) It has substantially lower complexity than conventional equalizers. 3) It easily realizes complexity and performance tradeoff by adjusting the length of the sliding window. 4) It has a simple and fixed-length feedback filter. The symbol error rate (SER) is derived to characterize the behavior of the A-ML-DFBE and can also be used to find the key parameters of the proposed equalizer. In addition, we further prove that the A-ML-DFBE obtains full multipath diversity.      

Adaptive MAPSD algorithms for symbol and timing recovery of mobileradio TDMA signals

Dual-mode adaptive algorithms with rapid convergence properties are presented for the equalization of frequency selective fading channels and the recovery of time-division multiple access (TDMA) mobile radio signals. The dual-mode structure consists of an auxiliary adaptive filter that estimates the channel during the training cycle. The converged filter weights are used to initialize a parallel bank of filters that are adapted blindly during the data cycle. When the symbol timing is known, this filter bank generates error residuals that are used to perform approximate maximum a posteriori symbol detection (MAPSD) and provide reliable decisions of the transmitted signal. For channels with timing jitter, joint estimation of the channel parameters and the symbol timing using an extended Kalman filter algorithm is proposed. Various methods are described to reduce the computational complexity of the MAP detector, usually at the cost of some performance degradation. Also, a blind MAPSD algorithm for combining signals from spatially diverse receivers is derived. This diversity MAPSD (DMAPSD) algorithm, which can be easily modified for the dual-mode TDMA application, maintains a global set of MAP metrics even while blindly tracking the individual spatial channels using local error estimates. The performance of these single-channel and diversity MAPSD dual-mode algorithms are studied via computer simulations for various channel models, including a mobile radio channel simulator for the IS-54 digital cellular TDMA standard     

Bidirectional iterative ISI canceller for high-rate DSSS/CCK communications

This paper proposes a new RAKE receiver incorporated with a bidirectional iterative intersymbol interference (ISI) canceller in order to reinforce multipath robustness of high-rate direct-sequence spread-spectrum complementary code keying (DSSS/CCK) systems. The proposed RAKE receiver first combines multipath signal components through a channel matched filter (CMF) and removes postcursor-ISI by employing a codeword decision feedback equalizer (DFE). Then, a CCK codeword detector tentatively determines the current CCK codeword symbol and reuses it to subtract precursor-ISI from the previous symbol. Therefore, the ultimate symbol decision is made using the delayed signal with both postcursor-ISI and precursor-ISI cancelled. The detection performance can be more improved through an iterative refinement processing between the postcursor and the precursor components. Simulation results exhibit a significantly improved error rate performance of the proposed receiver compared with that of the legacy RAKE receiver employing only a postcursor DFE. The additional cost for realization of the proposed receiver is one symbol decision delay and reuse complexity of the DFE and the codeword detector.     

Optimizing the transmit power for slow fading channels

We consider the design of power-adaptive systems for minimizing the average bit-error rate over flat fading channels. Channel state information, obtained through estimation at the receiver, is sent to the transmitter over a feedback channel, where it is used to optimally adapt the transmit power. We consider finite-state optimal policies to reflect the limitations of the feedback channel. We develop an iterative algorithm that determines the optimal finite-state power control policy given the probability density function (PDF) of the fading. Next, we present a discretized formulation of the problem and obtain a suboptimal solution via standard dynamic programming techniques. The discretization of the problem enables us to obtain a suboptimal policy for arbitrary fading channels for which the analytic expression of the fading probability density function is not available. Simulation results are used to draw conclusions regarding the effects of limited feedback channel capacity, delay and number of states on the bit-error rate performance of the proposed policies under slow and moderate fading conditions     

OFDM power loading using limited feedback

Orthogonal frequency division multiplexing (OFDM) is a practical broadband signaling technique for use in multipath fading channels. Over the past ten years, research has shown that power loading, where the power allocations on the OFDM frequency tones are jointly optimized, can improve error rate or capacity performance. The implementation of power loading, however, is dependent on the presence of complete forward link channel knowledge at the transmitter. In systems using frequency division duplexing (FDD), this assumption is unrealistic. In this paper, we propose power loading for OFDM symbols using a limited number of feedback bits sent from the receiver to the transmitter. The power loading vector is designed at the receiver, which is assumed to have perfect knowledge of the forward link channel, and conveyed back to the transmitter over a limited rate feedback channel. To allow for the vector to be represented by a small number of bits, the power loading vector is restricted to lie in a finite set, or codebook, of power loading vectors. This codebook is designed offline and known a priori to both the transmitter and receiver. We present two power allocation selection algorithms that optimize the probability of symbol error and capacity, respectively. Simulation results show that the proposed limited feedback techniques provide performance close to full channel knowledge power loading.     

Joint Data and Kalman Estimation for Rayleigh Fading Channels

Channel estimation is an essential part of many detection techniques proposed for data transmission over fading channels. For the frequency selective Rayleigh fading channel an autoregressive moving average representation is proposed based on the fading model parameters. The parameters of this representation are determined based on the fading channel characteristics, making it possible to employ the Kalman filter as the best estimator for the channel impulse response. For IS-136 formatted data transmission the Kalman filter is employed with the Viterbi algorithm in a Per-Survivor Processing (PSP) fashion and the ove rall bit error rate performance is shown to be superior to that of detection techniques using the RLS and LMS estimators. To allow more than one channel estimation per symbol interval, Per-Branch Processing (PBP) method is introduced as a general case of PSP and its effect on performance is evaluated. The sensitivity of performance to parameters such as fading model order and vehicle speed is also studied.     

An adaptive receiver for the time- and frequency-selective fadingchannel

An adaptive receiver is presented in this paper for the reception of linearly modulated signals transmitted over a time- and frequency-selective fading channel. The channel is modeled as a truncated power series which represents the dispersive fading channel as a sum of three elementary flat-fading channels. The proposed receiver consists of a sequence estimator with a parallel channel estimator. The channel estimator recovers the instantaneous fading processes associated with each elementary channel and filters them to generate one-step predictions of each fading process. Some implementation difficulties and solutions are also discussed. Computer simulations using quadrature phase-shift keying (QPSK) and channels with moderate delay spreads and fade rates have been used to evaluate the performance of the receiver. The results show that our technique has potential in channels with delay spread of about 20%, signal-to-noise ratio (SNR) greater than 15 dB, and applications requiring bit-error rates (BER's) less than 10^-2