Modulation Diversity in Fading Channels with Quantized Receiver

In this paper, we address the design of codes which achieve modulation diversity in block fading single-input single-output (SISO) channels with signal quantization at receiver and low-complexity decoding. With an unquantized receiver, coding based on algebraic rotations is known to achieve modulation coding diversity. On the other hand, with a quantized receiver, algebraic rotations may not guarantee diversity. Through analysis, we propose specific rotations which result in the codewords having equidistant component-wise projections. We show that the proposed coding scheme achieves maximum modulation diversity with a low-complexity minimum distance decoder and perfect channel knowledge. Relaxing the perfect channel knowledge assumption we propose a novel training/estimation and receiver control technique to estimate the channel. We show that our coding/training/estimation scheme and minimum distance decoding achieve an error probability performance similar to that achieved with perfect channel knowledge

Algebraic number theory and code design for Rayleigh fading channels

Algebraic number theory is having an increasing impact in code design for many different coding applications, such as single antenna fading channels and more recently, MIMO systems. Extended work has been done on single antenna fading channels, and algebraic lattice codes have been proven to be an effective tool. The general framework has been settled in the last ten years and many explicit code constructions based on algebraic number theory are now available. The aim of this work is to provide both an overview on algebraic lattice code designs for Rayleigh fading channels, as well as a tutorial introduction to algebraic number theory. The basic facts of this mathematical field will be illustrated by many examples and by the use of a computer algebra freeware in order to make it more accessible to a large audience

Symbol Error Rates of Maximum-Likelihood Detector: Convex/Concave Behavior and Applications

Convexity/concavity properties of symbol error rates (SER) of the maximum likelihood detector operating in the AWGN channel (non-fading and fading) are studied. Generic conditions are identified under which the SER is a convex/concave function of the SNR. Universal bounds for the SER 1st and 2nd derivatives are obtained, which hold for arbitrary constellations and are tight for some of them. Applications of the results are discussed, which include optimum power allocation in spatial multiplexing systems, optimum power/time sharing to decrease or increase (jamming problem) error rate, and implication for fading channels.Comment: To appear in 2007 IEEE International Symposium on Information Theory (ISIT 2007), Nice, June 200

Full-Rate, Full-Diversity Adaptive Space Time Block Coding for Transmission over Rayleigh Fading Channels

A full-rate, full-diversity Adaptive Space Time Block Coding (ASTBC) scheme based on Singular Value Decomposition (SVD) is proposed for transmission over Rayleigh fading channels. The ASTBC-SVD scheme advocated is capable of providing both full-rate and full-diversity for any number of transmit antennas, Nt, provided that the number of receive antennas, Nr, equals to Nt. Furthermore, the ASTBC-SVD scheme may achieve an additional coding gain due to its higher product distance with the aid of the block code employed. In conjunction with SVD, the “water-filling” approach can be employed for adaptively distributing the transmitted power to the various antennas transmit according to the channel conditions, in order to further enhance the attainable performance. Since a codeword constituted by Nt symbols is transmitted in a single time slot by mapping the Nt symbols to the Nt transmit antennas in the spatial domain, the attainable performance of the ASTBC-SVD scheme does not degrade, when the channel impulse response values vary from one time slot to the next. Hence, the proposed ASTBC-SVD scheme is attractive in the context of both uncorrelated and correlated Rayleigh fading channels. The performance of the proposed scheme was evaluated, when communicating over uncorrelated Rayleigh fading channels. Explicitly, an Eb/N0 gain of 2.5 dB was achieved by the proposed ASTBC-SVD scheme against Alamouti’s scheme [1], when employing Nt = Nr = 2 in conjunction with 8PSK

Analytical Matched Filter Bound for M-QAM Hierarchical Constellations with Diversity Reception in Multipath Rayleigh Fading Channels

In this paper, we derive matched filter bound (MFB) expressions for the performance of hierarchical quadrature amplitude modulations (M-HQAM) over time-discrete multipath Rayleigh fading environments with diversity. The expressions are valid for multipath environments where different paths and antennas can be correlated. Since hierarchical constellations are usually employed to achieve unequal bit error protection, the MFB expressions are given in terms of the individual bit error rate (BER) for the different bit streams. Although typically the MFB is obtained assuming slow time varying channels, fast varying channels are also considered in this paper

Design and Performance Analysis of Non-Coherent Detection Systems with Massive Receiver Arrays

Harvesting the gain of a large number of antennas in a mmWave band has mainly been relying on the costly operation of channel state information (CSI) acquisition and cumbersome phase shifters. Recent works have started to investigate the possibility to use receivers based on energy detection (ED), where a single data stream is decoded based on the channel and noise energy. The asymptotic features of the massive receiver array lead to a system where the impact of the noise becomes predictable due to a noise hardening effect. This in effect extends the communication range compared to the receiver with a small number of antennas, as the latter is limited by the unpredictability of the additive noise. When the channel has a large number of spatial degrees of freedom, the system becomes robust to imperfect channel knowledge due to channel hardening. We propose two detection methods based on the instantaneous and average channel energy, respectively. Meanwhile, we design the detection thresholds based on the asymptotic properties of the received energy. Differently from existing works, we analyze the scaling law behavior of the symbol-error-rate (SER). When the instantaneous channel energy is known, the performance of ED approaches that of the coherent detection in high SNR scenarios. When the receiver relies on the average channel energy, our performance analysis is based on the exact SER, rather than an approximation. It is shown that the logarithm of SER decreases linearly as a function of the number of antennas. Additionally, a saturation appears at high SNR for PAM constellations of order larger than two, due to the uncertainty on the channel energy. Simulation results show that ED, with a much lower complexity, achieves promising performance both in Rayleigh fading channels and in sparse channels

Error Rates of the Maximum-Likelihood Detector for Arbitrary Constellations: Convex/Concave Behavior and Applications

Motivated by a recent surge of interest in convex optimization techniques, convexity/concavity properties of error rates of the maximum likelihood detector operating in the AWGN channel are studied and extended to frequency-flat slow-fading channels. Generic conditions are identified under which the symbol error rate (SER) is convex/concave for arbitrary multi-dimensional constellations. In particular, the SER is convex in SNR for any one- and two-dimensional constellation, and also in higher dimensions at high SNR. Pairwise error probability and bit error rate are shown to be convex at high SNR, for arbitrary constellations and bit mapping. Universal bounds for the SER 1st and 2nd derivatives are obtained, which hold for arbitrary constellations and are tight for some of them. Applications of the results are discussed, which include optimum power allocation in spatial multiplexing systems, optimum power/time sharing to decrease or increase (jamming problem) error rate, an implication for fading channels ("fading is never good in low dimensions") and optimization of a unitary-precoded OFDM system. For example, the error rate bounds of a unitary-precoded OFDM system with QPSK modulation, which reveal the best and worst precoding, are extended to arbitrary constellations, which may also include coding. The reported results also apply to the interference channel under Gaussian approximation, to the bit error rate when it can be expressed or approximated as a non-negative linear combination of individual symbol error rates, and to coded systems.Comment: accepted by IEEE IT Transaction

Capacity of Underspread Noncoherent WSSUS Fading Channels under Peak Signal Constraints

We characterize the capacity of the general class of noncoherent underspread wide-sense stationary uncorrelated scattering (WSSUS) time-frequency-selective Rayleigh fading channels, under peak constraints in time and frequency and in time only. Capacity upper and lower bounds are found which are explicit in the channel's scattering function and allow to identify the capacity-maximizing bandwidth for a given scattering function and a given peak-to-average power ratio.Comment: To be presented at IEEE Int. Symp. Inf. Theory 2007, Nice, Franc