Bandwidth efficient block codes for Rayleigh fading channels

It is shown that the effective code length (ECL) of a short ECL block modulation code (BCM) is the dominant factor in its performance over a Rayleigh fading channel. To demonstrate this, three new BCM codes are presented as examples. Their performances are evaluated and compared on both Gaussian and fading channels.<>     

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     

Concatenated coding performance for FSK modulation ontime-correlated Rician fading channels

We present an analytical method for evaluating the performance of noninterleaved concatenated codes over channels modeled as a nonfrequency selective correlated Rician fading channel with a known power spectral density. The main idea is to model the communication system from the modulator input to the demodulator output as a finite state channel (FSC) model, and apply powerful enumeration techniques to such a discrete channel in order to gain useful information on the system performance. The concatenated scheme makes use of two codes; Reed-Solomon codes are employed for the outer code, and binary block codes are used as the inner code. Next, the method is extended to study the effect on the performance when an interleaving with finite depth is incorporated into the communication system. A comparison between symbol and bit interleaving is made. Finally, we study the potential gain produced when channel information is passed on to the outer decoder in the form of an erasure symbol. In all cases, analytical expressions for the probability of the number of error symbols produced by the FSC model were obtained in terms of a coefficient in a formal power series. This is an interesting alternative approach with respect to computer simulations     

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     

Diagonal block space-time code design for diversity and coding advantage over flat fading channels

The potential promised by multiple transmit antennas has raised considerable interest in space-time coding for wireless communications. In this paper, we propose a systematic approach for designing space-time trellis codes over flat fading channels with full antenna diversity and good coding advantage. It is suitable for an arbitrary number of transmit antennas with arbitrary signal constellations. The key to this approach is to separate the traditional space-time trellis code design into two parts. It first encodes the information symbols using a one-dimensional (M,1) nonbinary block code, with M being the number of transmit antennas, and then transmits the coded symbols diagonally across the space-time grid. We show that regardless of channel time-selectivity, this new class of space-time codes always achieves a transmit diversity of order M with a minimum number of trellis states and a coding advantage equal to the minimum product distance of the employed block code. Traditional delay diversity codes can be viewed as a special case of this coding scheme in which the repetition block code is employed. To maximize the coding advantage, we introduce an optimal construction of the nonbinary block code for a given modulation scheme. In particular, an efficient suboptimal solution for multilevel phase-shift-keying (PSK) modulation is proposed. Some code examples with 2-6 bits/s/Hz and two to six transmit antennas are provided, and they demonstrate excellent performance via computer simulations. Although it is proposed for flat fading channels, this coding scheme can be easily extended to frequency-selective fading channels.     

Rateless coding over fading channels

We propose a framework for communication over fading channels utilizing rateless codes. An implementation using fountain codes is simulated, demonstrating that such a scheme has advantages in efficiency, reliability and robustness over conventional fixed-rate codes, particularly when channel state information is not available at the transmitter.     

On performance analysis for signaling on correlated fading channels

A general approach is presented for analyzing the performance of digital signaling with multichannel reception on correlated fading channels. The approach is based on: (i) exploiting the complex Gaussian model for the joint distribution of the fading on the multiple channels; and (ii) applying recent results on the unified performance analysis of digital signaling on fading channels using alternative representations of the Q(·) and related functions. Numerical results that illustrate the effect of correlation on the diversity gain from multichannel reception are also presented     

A universal lattice code decoder for fading channels

We present a maximum-likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver. The decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point. By judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment     

Bandwidth efficient parallel concatenated coding schemes

The authors propose a solution to the parallel concatenation of trellis codes with multilevel amplitude/phase modulations and a suitable iterative decoding structure. Examples are given for throughputs 2bit/s/Hz with 8PSK and 16QAM signal constellations. For parallel concatenated trellis codes in the examples, rate 2/3 and 4/5, 16-state binary convolutional codes with Gray code mapping are used. The performances of these codes are within 1 dB of the Shannon limit at a bit error probability of 10^-6 for a given throughput. This outperforms all codes reported in the past for the same throughput     

Space-time-Doppler block coding for correlated time-selective fading channels

Coping with time-selective fading channels is challenging but also rewarding, especially with multiantenna systems, where joint space-Doppler diversity and coding gains can be collected to enhance performance of wireless mobile links. These gains have not been quantified, and space-time coded systems maximizing joint space-Doppler benefits have not been designed. Based on a parsimonious basis expansion model for the underlying time-selective (and possibly correlated) channels, we quantify these gains in closed form. Furthermore, we develop space-time-Doppler coded systems that guarantee the maximum possible space-Doppler diversity, along with the largest coding gains within all linearly coded systems. Our three novel designs exploit knowledge of the maximum Doppler spread, and each offers a uniquely desirable tradeoff, including high spectral efficiency, low decoding complexity, and high performance. Our analytical results are confirmed by simulations and reveal the relative of merits of our three designs in comparison with an existing approach.     

Complex-field coding for OFDM over fading wireless channels

Orthogonal frequency-division multiplexing (OFDM) converts a time-dispersive channel into parallel subchannels, and thus facilitates equalization and (de)coding. But when the channel has s close to or on the fast Fourier transform (FFT) grid, uncoded OFDM faces serious symbol recovery problems. As an alternative to various error-control coding techniques that have been proposed to ameliorate the problem, we perform complex-field coding (CFC) before the symbols are multiplexed. We quantify the maximum achievable diversity order for independent and identically distributed (i.i.d.) or correlated Rayleigh-fading channels, and also provide design rules for achieving the maximum diversity order. The maximum coding gain is given, and the encoder enabling the maximum coding gain is also found. Simulated performance comparisons of CFC-OFDM with existing block and convolutionally coded OFDM alternatives favor CFC-OFDM for the code rates used in a HiperLAN2 experiment.     

Variable-rate coding for slowly fading Gaussian multiple-access channels

We consider a nonergodic multiple-access Gaussian block-fading channel where a fixed number of independent and identically distributed (i.i.d.) fading coefficients affect each codeword. Variable-rate coding with input power constraint enforced on a per-codeword basis is examined. A centralized power and rate allocation policy is determined as a function of the previous and present fading coefficients. The power control policy that optimizes the expected rates is obtained through dynamic programming and the average capacity region and the average capacity region per unit energy are characterized. Moreover, we study the slope of spectral efficiency curve versus E/sub b//N/sub 0/ (dB), and we quantify the penalty incurred by time-division multiple access (TDMA) over superposition coding in the low-power regime.     

Diversity analysis of space-time coding in cascaded Rayleigh fading channels

Cascaded Rayleigh distribution is used to model multipath fading in mobile-to-mobile communication scenarios and provides a better fit to experimental data in such scenarios compared to the conventional Rayleigh channel model. In this letter, we derive an exact expression for the pairwise error probability (PEP) of space-time trellis codes over the cascaded Rayleigh fading channel, which is in the form of a simple single finite-range integral. Through the derived PEP expression, we present the maximum diversity order achievable over such channels and demonstrate the performance degradation in comparison to conventional Rayleigh channels. Monte-Carlo simulations are further demonstrated to confirm the analytical results.     

Bandwidth efficient QPSK in cochannel interference and fading

The performances of QPSK in the presence of cochannel interference in both nonfading and fading environments are analyzed. Three approaches for representing the cochannel interference are investigated. These are a precise error probability method, a sum of sinusoids (sinusoidal) model, and a Gaussian interference model. In addition to determining precise results for the performance of QPSK in cochannel interference, we examine the validity of these two interference models in both additive white Gaussian noise (AWGN) environments and in different flat fading environments; Rayleigh, Ricean, and Nakagami. Nyquist pulse shaping is considered and the effects of cross channel ISI produced by the cochannel interference are accounted for in the precise interference model. Also accounted for are the random symbol and carrier timing offsets of the interfering signals. Two performance criteria are considered. These are the average bit error rate and the interference penalty. The latter is defined as the increase in signal-to-noise power ratio (SNR) required by a system with cochannel interference in order to maintain the same BER as a system without interference. Attention is given, in particular, to the outdoor microcellular fading environment. In this environment, the fading experienced by the interfering signals may be represented by a Rayleigh-fading model while the fading experienced by the desired signal may be represented by a Ricean or a Nakagami-fading model     

General random coding bounds: AWGN channels to MIMO fading channels

Random coding bounds are obtained for multiple-input multiple-output (MIMO) fading channels. To derive the result in a compact and easy-to-evaluate form, a series of combinatorial codeword enumeration problems are solved for input-constrained MIMO fading channels. The bounds obtained in this paper are shown useful as performance prediction measures for MIMO systems which employ turbo-like block codes as the outer code to derive the space-time inner code. The error exponents for MIMO channels are also derived from the bounds, and then compared with the classical Gallager error exponents as well as the channel capacities. The random coding bounds associated with the maximum likelihood receiver exhibit good match with the extensive system simulation results obtained with a turbo-iterative receiver.     

A new analysis of direct-sequence pseudonoise code acquisition onRayleigh fading channels

Accurate performance evaluation of direct-sequence pseudonoise code acquisition on Rayleigh fading channels is investigated. For fading channels the homogeneous Markov chain model, used to characterize the acquisition process over additive white Gaussian noise channels, is no longer valid due to the correlations between cell detections incurred by fading. Hence, the traditional direct and flow-graph approaches for performance evaluation of the code acquisition are not applicable to fading channels. In this paper, a new analysis is proposed for accurate evaluation of the acquisition performance on Rayleigh fading channels. The analysis is quite general and can include various search strategies, types of correlators, and test methods with different performance measures: probability mass function and/or moments of acquisition time. Analytical and simulation results show that the new method predicts the acquisition performance very accurately     

Spectral efficient protocols for half-duplex fading relay channels

We study two-hop communication protocols where one or several relay terminals assist in the communication between two or more terminals. All terminals operate in half-duplex mode, hence the transmission of one information symbol from the source terminal to the destination terminal occupies two channel uses. This leads to a loss in spectral efficiency due to the pre-log factor one-half in corresponding capacity expressions. We propose two new half-duplex relaying protocols that avoid the pre-log factor one-half. Firstly, we consider a relaying protocol where a bidirectional connection between two terminals is established via one amplify-and-forward (AF) or decode-and-forward (DF) relay (two-way relaying). We also extend this protocol to a multi-user scenario, where multiple terminals communicate with multiple partner terminals via several orthogonalize-and-forward (OF) relay terminals, i.e., the relays orthogonalize the different two-way transmissions by a distributed zero-forcing algorithm. Secondly, we propose a relaying protocol where two relays, either AF or DF, alternately forward messages from a source terminal to a destination terminal (two-path relaying). It is shown that both protocols recover a significant portion of the half-duplex loss     

Reed-Solomon error control coding for Rayleigh fading channels withfeedback

The use of nonbinary block error control codes over Rayleigh fading channels with feedback is examined. It is assumed that the fading is slow with respect to the rate of symbol transmission. Expressions are derived for the probabilities of channel symbol error and erasure, which are in turn used to develop expressions for code symbol error and erasure. Two erasure generation mechanisms are considered, one based on the existence of channel amplitude side information, the other not. This analytical framework is used to evaluate the performance of the Reed-Solomon/hybrid-ARQ protocol (RS/HARQ) over fading channels with feedback. The RS/HARQ system uses erasure decoding in a hybrid-ARQ protocol to provide excellent reliability performance at the expense of a reduction in throughput. The RS/HARQ protocol allows for the variation of the erasure threshold and the effective diameter of the decoding operation     

Concatenated coding with inner trellis codes for fading channels

It is known that concatenated coding can significantly enhance the performance of digital communication systems operating over fading channels when compared to uncoded or single-coded systems. The price to be paid for such an improvement, however, is a substantial increase in the required bandwidth. In this paper, we consider the use of a concatenation scheme in which the inner code is a trellis-coded modulation (TCM) system. The analysis is carried out for two different outer codes: a binary Golay code and a non-binary Reed-Solomon code. Results obtained for the Rayleigh and Rician fading channels through analytical bounds indicate that the use of this system does provide a significant reduction in the bit error probability, a fact that is also verified through computer simulation. Unlike a traditional concatenated system, the proposed method achieves the coding gain while maintaining acceptable bandwidth efficiency.     

Multifrequency trellis coding with low delay for fading channels

An L-frequency trellis coding scheme designed for fading channels that provides diversity up to order L is described. L-frequency coding is advantageous over channel coding schemes that achieve implicit time-diversity through trellis coding in conjunction with time-interleaving because it requires negligible end-to-end delay. The authors derive an upper-bound for the probability of symbol error of the L-frequency code. Based on this upper-bound, they then deduce the design criteria for optimum L-frequency codes. A numerical approximation to this upper-bound and the design of a two-state and two four-state, two-frequency codes are presented. Through simulations, it was found that relative to the traditional dual frequency diversity approach, the two-state and four-state codes achieve 3- and 4-dB coding gains, respectively. This energy efficiency gain can be translated into a spectral efficiency gain. A brief discussion on the difference in code design techniques for the Gaussian channel and the fading channel is also presented