Soft-decision demodulation design for COVQ over white, colored, andISI Gaussian channels

In this work, the design of a q-bit (scalar and vector) soft-decision demodulator for Gaussian channels with binary phase-shift keying modulation is investigated. The demodulator is used in conjunction with a soft-decision channel-optimized vector quantization (COVQ) system. The COVQ is constructed for an expanded (q>1) discrete channel consisting of the concatenation of the modulator, the Gaussian channel, and the demodulator. It is found that as the demodulator resolution q increases, the capacity of the expanded channel increases, resulting in an improvement of the COVQ performance. Consequently, the soft-decision demodulator is designed to maximize the capacity of the expanded channel. Three Gaussian channel models are considered as follows: (1) additive white Gaussian noise channels; (2) additive colored Gaussian noise channels; and (3) Gaussian channels with intersymbol interference. Comparisons are made with (a) hard-decision COVQ systems, (b) COVQ systems which utilize interleaving, and (c) an unquantized (q=∞) soft-decision decoder proposed by Skoglund and Hedelin (1999). It is shown that substantial improvements can be achieved over COVQ systems which utilize hard decision demodulation and/or channel interleaving. The performance of the proposed COVQ system is comparable with the system by Skoglund and Hedelin-though its computational complexity is substantially less     

Soft-decision COVQ for turbo-coded AWGN and Rayleigh fadingchannels

A robust soft-decision channel-optimized vector quantization (COVQ) scheme for turbo coded additive white Gaussian noise (AWGN) and Rayleigh fading channels is proposed, The log likelihood ratio (LLR) generated by the turbo decoder is exploited via the use of a q-bit scalar soft-decision demodulator. The concatenation of the turbo encoder, modulator, AWGN channel or Rayleigh fading channel, turbo decoder, and q-bit soft-decision demodulator is modeled as an expanded discrete memoryless channel (DMC). A COVQ scheme for this expanded discrete channel is designed. Numerical results indicate substantial performance improvements over traditional tandem coding systems, COVQ schemes designed for hard-decision demodulated turbo coded channels (q=1), as well as performance gains over a recent soft decoding COVQ scheme by Ho (see IEEE Commun. Lett., vol.3, p.208-10, 1999)     

COVQ for MAP hard-decision demodulated channels

We design a channel optimized vector quantizer (COVQ) for symbol-by-symbol maximum a posteriori (MAP) hard-decision demodulated channels. The main objective is to exploit the non-uniformity of the indices representing the quantized source via the MAP decoder and iteratively optimize the overall discrete channel (at the symbol level) jointly with the quantizer. We consider memoryless Gaussian and Gauss-Markov sources transmitted over a binary phase-shift keying modulated Rayleigh fading channel. Our scheme has less encoding computational and storage complexity (particularly for noisy channel conditions) than both conventional and soft-decision COVQ systems, which use hard-decision and soft-decision maximum likelihood demodulation, respectively. Furthermore, it provides a notable signal-to-distortion ratio gain over the former system, and in some cases it matches or outperforms the latter one.     

Multilevel block codes for Rayleigh-fading channels

New multilevel block codes for Rayleigh-fading channels are presented. At high signal-to-noise ratios (SNRs), the proposed block codes can achieve better bit error performance over TCM codes, optimum for fading channels, with comparable decoder complexity and bandwidth efficiency. The code construction is based on variant length binary component block codes. As component codes for the 8-PSK multilevel block construction, the authors propose two modified forms of Reed-Muller codes giving a good trade-off between the decoder complexity and the effective code rates. Code design criteria are derived from the error performance analysis. Multistage decoding shows very slight degradation of bit error performance relative to the maximum likelihood algorithm     

Low-complexity bit-interleaved coded DAPSK for Rayleigh-fading channels

We analyze the achievable performance of bit-interleaved coded differential amplitude and phase-shift keying (DAPSK) systems over frequency nonselective Rayleigh-fading channels with suboptimal differential detection assuming an ideal bit interleaving. The suboptimal differential detection in this work refers to the bit metric calculation based only on the difference between two consecutive symbols, in contrast to more complex maximum-likelihood (ML)-based differential detection, which makes use of all the observed consecutive symbols for its metric calculation in channel decoding. As benchmarks of coded system performance, we analyze the average mutual information (AMI) and cutoff rate of this system. Exact probability density functions of the suboptimal differential detector outputs are derived for this purpose. Comparative studies suggest that the performance loss of the suboptimal approach is in fact noticeable. Therefore, we also develop a low-complexity receiver structure in the framework of suboptimal differential detection that can approach the performance of ML-based system by suitably incorporating the amplitude statistics of received symbols. The theoretical framework developed in this paper is also confirmed by simulations using convolutional and turbo codes.     

Quantization loss for convolutional decoding in Rayleigh-fading channels

This article presents a theoretical analysis (based on tight upper bounds on the error probability) of quantization loss with integer metrics used for convolutional decoding in the Rayleigh-fading channel. Optimum configurations with respect to the generalized cutoff rate criterion are established for 2-bit, 3-bit and 4-bit quantizers, and corresponding losses with both de facto industry-standard 1/2-rate and associated punctured 3/4-rate codes are evaluated. Assuming optimized thresholds, 4-bit metrics are shown to incur only a small quantization loss. However, results also indicate that the loss is sensitive to suboptimum threshold spacing.     

MLSE for correlated diversity sources and unknown time-varyingfrequency-selective Rayleigh-fading channels

Yu and Pasupathy (see ibid., vol.43, p. 1534-44, 1995) derived a maximum-likelihood sequence estimation (MLSE) receiver structure for unknown time varying frequency-selective Rayleigh-fading channels and uncorrelated diversity sources. This receiver design is extended to the case of correlated diversity sources. Correlated diversity sources typically arise with space diversity, where constraints on antenna volume require that diversity antennae be placed too closely together. Analytic and simulated bit-error rate (BER) curves are presented for receivers which exploit and ignore the correlation. In the former case, we find a small BER improvement that reduces with decreasing correlation. However, for a fixed receiver complexity, superior performance is achieved when the correlation is ignored     

Predictive downlink beamforming for wideband CDMA over Rayleigh-fading channels

A new approach to adaptive downlink beamforming to combat fast Rayleigh fading is presented. In this approach, the antennas at the base transceiver station form transmit beam patterns according to the prediction of downlink channels. The channel prediction is a linear prediction based on the autoregressive model, which is downsampled to extend the memory span given fixed model order. For a wideband code-division multiple-access downlink, pre-RAKE transmission is employed to achieve the multipath diversity gain. In particular, we combine pseudoinverse directions of arrival beamforming with pre-RAKE transmission to alleviate self-interference. The beamforming weights are adjusted within a downlink frame to compensate the predicted fading. We give measures of the prediction and beamforming performance and evaluate the impact of prediction errors on the downlink. Ray tracing simulations in a three-dimensional urban physical model show that the predictive downlink beamforming outperforms the conventional beamforming over Rayleigh-fading channels.     

The capacity of discrete-time memoryless Rayleigh-fading channels

We consider transmission over a discrete-time Rayleigh fading channel, in which successive symbols face independent fading, and where neither the transmitter nor the receiver has channel state information. Subject to an average power constraint, we study the capacity-achieving distribution of this channel and prove it to be discrete with a finite number of mass points, one of them located at the origin. We numerically compute the capacity and the corresponding optimal distribution as a function of the signal-to-noise ratio (SNR). The behavior of the channel at low SNR is studied and finally a comparison is drawn with the ideal additive white Gaussian noise channel     

Optimal power allocation for relayed transmissions over Rayleigh-fading channels

Relayed transmission is a way to attain broader coverage by splitting the communication link from the source to the destination into several shorter links/hops. One of the main advantages of this communication technique is that it distributes the use of power throughout the hops. This implies longer battery life and lower interference introduced to the rest of the network. In this context, this paper investigates the optimal allocation of power over these links/hops for a given power budget. All hops are assumed to be subject to independent Rayleigh fading. Outage probability which is the probability that the link quality from source to destination falls below a certain threshold is used as the optimization criterion. Numerical results show that optimizing the allocation of power enhances the system performance, especially if the links are highly unbalanced in terms of their average fading power or if the number of hops is large. Interestingly, they also show that nonregenerative systems with optimum power allocation can outperform regenerative systems with no power optimization.     

The asymptotic capacity of multiple-antenna Rayleigh-fading channels

We consider the asymptotic behavior of the capacity of multiple-antenna Rayleigh-fading channels in the limit as the transmit and receive arrays become large. We show that the capacity converges in distribution to a Gaussian random variable, and give closed-form formulas for its mean and variance. These results enable us to derive the first asymptotic formula for outage rates, as well as a sharper estimate of the error in previously reported asymptotic formulas for ergodic capacity. Although these formulas are asymptotic, we show by simulation that they are often quite accurate, even for relatively small arrays.     

A robust PN code tracking algorithm for frequency selective Rayleigh-fading channels

In this letter, we propose a new tracking scheme that is robust against multipath fading for pseudonoise (PN) code tracking in direct-sequence-spread spectrum systems. The proposed scheme employs an adaptive filter whose taps are adapted using a block least-mean square algorithm and it results in minimizing the effect of multipath interference on the tracking performance. We show that the mean-squared tracking error performance of the proposed scheme is not affected by the presence of closely spaced paths (e.g., one to three chips), unlike that of conventional delay locked loops. We also show that the tap-weight distribution of the filter provides accurate estimates of the multipath delays. For example, at E/sub b//N/sub 0/=5 dB, 98% of the time the path estimates lie within one sample (1/5 of a chip) from the actual delays. Furthermore, simulation results suggest that multipath delays over a wide range of terminal speeds can be tracked successfully. The proposed scheme is well suited for wideband code-division multiple-access systems where a large number of closely-spaced multipath components need to be tracked and used in RAKE combining.     

Error probability minimizing pilots for OFDM with M-PSK modulation over Rayleigh-fading channels

Orthogonal frequency division multiplexing (OFDM) with pilot symbol assisted channel estimation is a promising technique for high rate transmissions over wireless frequency-selective fading channels. In this paper, we analyze the symbol error rate (SER) performance of OFDM with M-ary phase-shift keying (M-PSK) modulation over Rayleigh-fading channels, in the presence of channel estimation errors. Both least-squares error (LSE) and minimum mean-square error (MMSE) channel estimators are considered. For prescribed power, our analysis not only yields exact SER formulas, but also quantifies the performance loss due to channel estimation errors. We also optimize the number of pilot symbols, the placement of pilot symbols, and the power allocation between pilot and information symbols, to minimize this loss, and thereby minimize SER. Simulations corroborate our SER performance analysis, and numerical results are presented to illustrate our optimal claims.     

A sequential soft-decision decoder for Reed-Solomon codes appliedto encoded PSK in Rayleigh-fading channels

A soft-decision stack algorithm with a variable-bias-term branch metric and accurate channel state information estimate is applied to a Reed-Solomon-encoded phase-shift keying (PSK) system in the presence of memoryless Rayleigh fading. To compensate for the variable decoding delay inherent in sequential decoding algorithms, a time-out mechanism is used by the inner decoder: if a time-out occurs before complete decoding of a given block, the decoder declares an erasure. An erasures-and-errors correction decoding algorithm is implemented at the outer decoder to recover any incorrect or incompletely decoded inner code words. Simulation results show that significant improvement over uncoded modulation can be achieved with this approach with moderate cost in decoding complexity     

Improved approximate maximum-likelihood receiver for differential space-time block codes over Rayleigh-fading channels

In this paper, an approximate maximum-likelihood (ML) receiver for differential space-time block codes is investigated. The receiver is derived from the ML criterion and is shown to mitigate error floor occurring in a conventional differential receiver very well. Because the receiver employs knowledges of signal-to-noise ratio (SNR) and fading rate, we study mismatched cases when these parameters are not accurate. It is shown that the receiver is more sensitive to the mismatched parameters when the fading rate is high. Then, a union bound on the bit error probability is derived. The bounds show good agreement with the simulation results at high fading rate and at high SNR. Finally, a modified receiver, denoted as multistage receiver, is proposed to compensate the so-called intrablock interference caused by the time-varying characteristic of the channel within a transmission block. The multistage receiver offers further reduction of error floor of about half order of magnitude as compared with an approximate ML receiver.     

Performance of Alamouti transmit diversity over time-varying Rayleigh-fading channels

We analyze the impact of a time-varying Rayleigh-fading channel on the performance of an Alamouti transmit-diversity scheme. We propose several optimal and suboptimal detection strategies for mitigating the effects of a time-varying channel, and derive expressions for their bit-error probability as a function of the channel correlation coefficient /spl rho/. We find that the maximum-likelihood detector that optimally compensates for the time-varying channel is very tolerant to time-varying fading, attaining full diversity order even for the extreme case of /spl rho/=0. In contrast, although lower in complexity, the suboptimal schemes suffer a diversity penalty and are thus suitable only for slowly fading channels.     

On the capacity of spatially correlated MIMO Rayleigh-fading channels

In this paper, we investigate the capacity distribution of spatially correlated, multiple-input-multiple-output (MIMO) channels. In particular, we derive a concise closed-form expression for the characteristic function (c.f.) of MIMO system capacity with arbitrary correlation among the transmitting antennas or among the receiving antennas in frequency-flat Rayleigh-fading environments. Using the exact expression of the c.f., the probability density function (pdf) and the cumulative distribution function (CDF) can be easily obtained, thus enabling the exact evaluation of the outage and mean capacity of spatially correlated MIMO channels. Our results are valid for scenarios with the number of transmitting antennas greater than or equal to that of receiving antennas with arbitrary correlation among them. Moreover, the results are valid for an arbitrary number of transmitting and receiving antennas in uncorrelated MIMO channels. It is shown that the capacity loss is negligible even with a correlation coefficient between two adjacent antennas as large as 0.5 for exponential correlation model. Finally, we derive an exact expression for the mean value of the capacity for arbitrary correlation matrices.     

Capacity maximizing MMSE-optimal pilots for wireless OFDM over frequency-selective block Rayleigh-fading channels

The location, number, and power of pilot symbols embedded in multicarrier block transmissions over rapidly fading channels, are important design parameters affecting not only channel estimation performance, but also channel capacity. Considering orthogonal frequency-division multiplexing (OFDM) systems with decoupled information-bearing symbols from pilot symbols transmitted over wireless frequency-selective Rayleigh-fading channels, we show that equispaced and equipowered pilot symbols are optimal in terms of minimizing the mean-square channel estimation error. We also design the number of pilots, and the power distributed between information bearing and pilot symbols, using as criterion a lower bound on the average capacity. Numerical results corroborate our theoretical findings.     

Optimum multiuser noncoherent DPSK detection in generalized diversity Rayleigh-fading channels

The jointly optimum multiuser noncoherent detector for differential phase-shift keying (DPSK) modulation over the generalized diversity Rayleigh-fading (GDRF) channel is derived and analyzed. The GDRF channel includes time/frequency/receiver antenna diversity and allows fading correlations between the various diversity branches of each user. Noncoherent detection here refers to the case where the receiver has neither knowledge of the instantaneous phases nor of the envelopes of the users' channels. Upper and lower bounds on the bit-error probability of the optimum detector are derived for a given user. For fast fading, when the fading coefficients vary from one symbol interval to the next (but are still essentially constant over one symbol interval), the detector asymptotically (for high signal-to-noise ratios (SNRs)) reaches an error floor, which is bounded from below and above for different fast fading scenarios. For slow fading, when the channel is constant for at least two consecutive symbol intervals, the upper bound is shown to converge asymptotically to the lower bound. Thus, the asymptotic efficiency of optimum multiuser DPSK detection can be determined and is found to be positive. In contrast to coherent detection, however, it is smaller than unity in general. Since the asymptotic efficiency is independent of the interfering users' signal strengths, the optimum detector is near-far resistant. While optimum multiuser detection is exponentially complex in the number of users, its performance provides the benchmark for suboptimal detectors. In particular, it is seen that the previously suggested post-decorrelative detectors can be far from satisfactory.