Pilot-symbol-assisted LDPC coded BICM over correlated Rayleigh fading channels

Pilot-symbol-assisted low-density parity-check (LDPC)-coded bit-interleaved coded modulation (BICM) is analyzed using the density evolution (DE) and the extrinsic information-transfer (EXIT) chart for correlated Rayleigh fading channels. The key parameter (the power correlation coefficient) is identified, and the threshold degradation is quantified. The optimal tradeoff of energy allocation between pilots and coded symbols is found to be sensitive to the normalized Doppler spread of the channel, the interpolation filter, the modulation scheme, and the pilot selection. In addition, a simple upper bound on the performance of any receiver that performs joint iterative decoding and channel estimation is derived. Extension to irregular code design is also discussed.     

Threshold of LDPC-coded BICM for Rayleigh fading

We analyze the threshold and convergence of LDPC coded bit interleaved coded modulation over Rayleigh fading channels. We compute the system threshold using the discretized density evolution and the extrinsic information transfer (EXIT) chart, and verify its effectiveness by simulation. Simulated detector output pdf is used to compute the variable node EXIT curve. It is shown that the convergence SNR observed from the transfer curves matches the density evolution threshold perfectly, and the EXIT chart actually provides a more computational efficient approach to estimate the threshold. An irregular code design example using the EXIT chart is given.     

Large-SNR error probability analysis of BICM with uniform interleaving in fading channels

This paper studies the average error probability of bit-interleaved coded modulation with uniform interleaving in fully-interleaved fading channels. At large signal-to-noise ratio, the dominant pairwise error events are mapped into symbols with Hamming weight larger than one, causing a flattening of the error probability. Closed-form expressions for the error probability with general modulations are provided. For interleavers of practical length, the flattening is noticeable only at very low values of the error probability.     

Distribution of burst error lengths in Rayleigh fading radio channels

A method for measuring burst errors which occur in v.h.f. or u.h.f. digital land mobile radio channels is described. Then it is noted that the cumulative distribution of burst error lengths in a Rayleigh fading channel is approximately governed by the log-normal distribution.     

Diversity transform for fading channels

This paper investigates a transform that provides diversity to words of symbols transmitted over fading channels. This diversity transform (DRT) does not alter the distance between the input words nor the bandwidth or the information rate. The transform is based on an orthonormal transform and thus increases the channel alphabet. A considerable diversity gain is achieved over Rayleigh fading channel with perfect channel state information (CSI) and interleaving. The transform performances are evaluated both analytically and by simulation, and optimal transforms are determined for specific channels. Finally, a simple nonoptimal decoding scheme is developed, which provides a powerful and practical technique to transfer information over fading channels with or without coding     

Signaling constellations for fading channels

The performance of various coherent 8-ary and 16-ary modulations in additive white Gaussian noise (AWGN) and slowly fading channels are analyzed. New expressions for the exact symbol error rates (SER) in fading with diversity combining are derived for any two-dimensional signaling format having polygonal decision boundaries. Maximal ratio combining, equal gain combining, and selection combining are considered. The SER formulas obtained make it possible for the first time to optimize parameters of various constellations precisely and to determine,which constellation has the lowest probability of error. For example, a star constellation such as that specified in the CCITT V.29 standard can be improved by adjusting the amplitude ratios of the points in the constellation to save about 0.63 dB power in AWGN without sacrificing the phase error tolerance, while maintaining the same error rate. The sensitivity of each constellation to phase error is presented and comparisons are made. Six 8-ary signal sets and 11 16-ary signal sets are examined using the new symbol error probability formulas to determine best signal sets for fading channels     

Adaptive coded modulation for fading channels

We apply coset codes to adaptive modulation in fading channels. Adaptive modulation is a powerful technique to improve the energy efficiency and increase the data rate over a fading channel. Coset codes are a natural choice to use with adaptive modulation since the channel coding and modulation designs are separable. Therefore, trellis and lattice codes designed for additive white Gaussian noise (AWGN) channels can be superimposed on adaptive modulation for fading channels, with the same approximate coding gains. We first describe the methodology for combining coset codes with a general class of adaptive modulation techniques. We then apply this methodology to a spectrally efficient adaptive M-ary quadrature amplitude modulation (MQAM) to obtain trellis-coded adaptive MQAM. We present analytical and simulation results for this design which show an effective coding gain of 3 dB relative to uncoded adaptive MQAM for a simple four-state trellis code, and an effective 3.6-dB coding gain for an eight-state trellis code. More complex trellis codes are shown to achieve higher gains. We also compare the performance of trellis-coded adaptive MQAM to that of coded modulation with built-in time diversity and fixed-rate modulation. The adaptive method exhibits a power savings of up to 20 dB     

Tracking loop for fading dispersive channels

An optimum closed-loop symbol synchronizer operating over fading dispersive channels is developed. It is shown that the optimum tracking synchronizer is a multiplier that forms the product of the received signal and a filtered version of it, the filter impulse response is the first derivative with respect to time (or frequency) of the autocorrelation function of the signal part of the received waveform. It is proved that for small misalignment the control signal vector is an incrementally linear function of the error vector. For a Gaussian-shaped scattering function, a simple closed-loop structure is obtained and expressions for tracking error statistics are derived. The dependency of such statistics on the signal-to-noise ratio and on the spread of the channel is investigated     

Modulation diversity for frequency-selective fading channels

In this article, modulation diversity (MD) for frequency-selective fading channels is proposed. The achievable performance with MD is analyzed and a simple design criterion for MD codes for Rayleigh-fading channels is deduced from an upper bound on the pairwise error probability (PEP) for single-symbol transmission. This design rule is similar to the well-known design rule for MD codes for flat fading and does not depend on the power-delay profile of the fading channel. Several examples for MD codes with prescribed properties are given and compared. Besides the computationally costly optimum receiver, efficient low-complexity linear equalization (LE) and decision-feedback equalization (DFE) schemes for MD codes are also introduced. Simulations for the widely accepted COST fading models show that performance gains of several decibels can be achieved by MD combined with LE or DFE at bit-error rates (BERs) of practical interest. In addition, MD also enables the suppression of cochannel interference.     

Linear predictive receivers for fading channels

The authors discuss maximum likelihood sequence detection (MLSD) based on prediction techniques for linearly modulated digital signals transmitted over fading channels. Efficient implementations of the sequence detector are investigated and a general formulation for computing the prediction coefficients is derived. Furthermore, the equivalence of different existing prediction-based receivers is shown     

On coding for block fading channels

This work considers the achievable performance for coded systems adapted to a multipath block-fading channel model. This is a particularly useful model for analyzing mobile-radio systems which employ techniques such as slow frequency-hopping under stringent time-delay or bandwidth constraints for slowly time-varying channels. In such systems, coded information is transmitted over a small number of fading channels in order to achieve diversity. Bounds on the achievable performance due to coding are derived using information-theoretic techniques. It is shown that high diversity can be achieved using relatively simple codes as long as very high spectral efficiency is not required. Examples of simple block codes and carefully chosen trellis codes are given which yield, in some cases, performances approaching the information-theoretic bounds     

Variable-rate variable-power MQAM for fading channels

We propose a variable-rate and variable-power MQAM modulation scheme for high-speed data transmission over fading channels. We first review results for the Shannon capacity of fading channels with channel side information, where capacity is achieved using adaptive transmission techniques. We then derive the spectral efficiency of our proposed modulation. We show that there is a constant power gap between the spectral efficiency of our proposed technique and the channel capacity, and this gap is a simple function of the required bit-error rate (BER). In addition, using just five or six different signal constellations, we achieve within 1-2 dB of the maximum efficiency using unrestricted constellation sets. We compute the rate at which the transmitter needs to update its power and rate as a function of the channel Doppler frequency for these constellation sets. We also obtain the exact efficiency loss for smaller constellation sets, which may be required if the transmitter adaptation rate is constrained by hardware limitations. Our modulation scheme exhibits a 5-10-dB power gain relative to variable-power fixed-rate transmission, and up to 20 dB of gain relative to nonadaptive transmission. We also determine the effect of channel estimation error and delay on the BER performance of our adaptive scheme. We conclude with a discussion of coding techniques and the relationship between our proposed modulation and Shannon capacity     

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.     

Bandwidth scaling for fading multipath channels

We show that very large bandwidths on fading multipath channels cannot be effectively utilized by spread-spectrum systems that (in a particular sense) spread the available power uniformly over both time and frequency. The approach is to express the input process as an expansion in an orthonormal set of functions each localized in time and frequency. The fourth moment of each coefficient in this expansion is then uniformly constrained. We show that such a constraint forces the mutual information to 0 inversely with increasing bandwidth. Simply constraining the second moment of these coefficients does not achieve this effect. The results suggest strongly that conventional direct-sequence code-division multiple-access (CDMA) systems do not scale well to extremely large bandwidths. To illustrate how the interplay between channel estimation and symbol detection affects capacity, we present results for a specific channel and CDMA signaling scheme     

Adaptive importance sampling for fading channels

The authors present an adaptive importance sampling (AIS) technique for estimating the bit error rate of a communications system over a correlated Rayleigh channel. The technique reduces the computer simulation time significantly and simplifies the procedure of choosing an optimally-based density function of the channel fading process     

Universal decoding for frequency-selective fading channels

We address the problem of universal decoding in unknown frequency-selective fading channels, using an orthogonal frequency-division multiplexing (OFDM) signaling scheme. A block-fading model is adopted, where the bands' fading coefficients are unknown yet assumed constant throughout the block. Given a codebook, we seek a decoder independent of the channel parameters whose worst case performance relative to a maximum-likelihood (ML) decoder that knows the channel is optimal. Specifically, the decoder is selected from a family of quadratic decoders, and the optimal decoder is referred to as a quadratic minimax (QMM) decoder for that family. As the QMM decoder is generally difficult to find, a suboptimal QMM decoder is derived instead. Despite its suboptimality, the proposed decoder is shown to outperform the generalized likelihood ratio test (GLRT), which is commonly used when the channel is unknown, while maintaining a comparable complexity. The QMM decoder is also derived for the practical case where the fading coefficients are not entirely independent but rather satisfy some general constraints. Simulations verify the superiority of the proposed QMM decoder over the GLRT and over the practically used training sequence approach.     

Feedback-rate control in fading channels

A feedback-rate control scheme recently proposed by Cavers for the incoherent detection of binary signals transmitted over a slowly fading Rayleigh channels is shown to be optimum for coherent systems.     

Deconstructing multiantenna fading channels

Accurate and tractable channel modeling is critical to realizing the full potential of antenna arrays in wireless communications. Current approaches represent two extremes: idealized statistical models representing a rich scattering environment and parameterized physical models that describe realistic scattering environments via the angles and gains associated with different propagation paths. However, simple rules that capture the effects of scattering characteristics on channel capacity and diversity are difficult to infer from existing models. We propose an intermediate virtual channel representation that captures the essence of physical modeling and provides a simple geometric interpretation of the scattering environment. The virtual representation corresponds to a fixed coordinate transformation via spatial basis functions defined by fixed virtual angles. We show that in an uncorrelated scattering environment, the elements of the channel matrix form a segment of a stationary process and that the virtual channel coefficients are approximately uncorrelated samples of the underlying spectral representation. For any scattering environment, the virtual channel matrix clearly reveals the two key factors affecting capacity: the number of parallel channels and the level of diversity. The concepts of spatial zooming and aliasing are introduced to provide a transparent interpretation of the effect of antenna spacing on channel statistics and capacity. Numerical results are presented to illustrate various aspects of the virtual framework.     

LMMSE detection for DS-CDMA systems in fading channels

The linear minimum mean-squared-error (LMMSE) criterion can be used to obtain near-far resistant receivers in direct-sequence code-division multiple-access systems. The standard version of the LMMSE receiver (postcombining LMMSE) minimizes the mean-squared error between the filter output and the true transmitted data sequence. Since the detector depends on the channel coefficients of all users, it cannot be implemented adaptively in fading channels due to severe tracking problems. A modified criterion for deriving LMMSE receivers (precombining LMMSE) in fading channels is presented. The precombining LMMSE receiver is independent of the users' complex channel coefficients, and it effectively converts the time-varying Rayleigh fading channel to an equivalent fixed additive white Gaussian noise channel from the point of view of updating the detector. The performance of the LMMSE receivers in fading channels is studied via computer simulations and numerical analysis. The results show that the postcombining LMMSE receiver has potentially larger capacity, but it cannot be used in fast fading channels. The precombining LMMSE receiver has slightly worse capacity than the postcombining LMMSE receiver, but remarkably larger capacity than the conventional RAKE receiver at the signal-to-noise ratios of practical interest     

A new class of iterative equalizers for space-time BICM over MIMO block fading multipath AWGN channel

This paper addresses the issue of advanced equalization methods for space-time communications over multiple-input multiple-output block fading channel with intersymbol interference. Instead of resorting to conventional multiuser detection techniques (based on the straightforward analogy between antennas and users), we adopt a different point of view, and separate time equalization from space equalization, thus introducing a higher degree of freedom in the overall space-time equalizer design. Time-domain equalization relies on minimum mean-square error criterion and operates on multidimensional modulation symbols, whose individual components can be detected in accordance with another criterion. In particular, when the optimum maximum a posteriori criterion is chosen, substantial performance gains over conventional space-time turbo equalization have been observed for different transmission scenarios, at the price of an increased, albeit manageable, computational complexity.