Modulation Diversity in Fading Channels with a 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 the receiver. With an unquantized receiver, coding based on algebraic rotations is known to achieve maximum modulation coding diversity. On the other hand, with a quantized receiver, algebraic rotations may not guarantee gains in 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 channel training/estimation technique to estimate the channel. We show that our coding/training/estimation scheme and minimum distance decoding achieves an error probability performance similar to that achieved with perfect channel knowledge.

Error exponent analysis of energy-based bayesian spectrum sensing under fading channels

This paper analyzes the error exponents in Bayesian decentralized spectrum sensing, i.e., the detection of occupancy of the primary spectrum by a cognitive radio, with probability of error as the performance metric. At the individual sensors, the error exponents of a Central Limit Theorem (CLT) based detection scheme are analyzed. At the fusion center, a K-out-of-N rule is employed to arrive at the overall decision. It is shown that, in the presence of fading, for a fixed number of sensors, the error exponents with respect to the number of observations at both the individual sensors as well as at the fusion center are zero. This motivates the development of the error exponent with a certain probability as a novel metric that can be used to compare different detection schemes in the presence of fading. The metric is useful, for example, in answering the question of whether to sense for a pilot tone in a narrow band (and suffer Rayleigh fading) or to sense the entire wide-band signal (and suffer log-normal shadowing), in terms of the error exponent performance. The error exponents with a certain probability at both the individual sensors and at the fusion center are derived, with both Rayleigh as well as log-normal shadow fading. Numerical results are used to illustrate and provide a visual feel for the theoretical expressions obtained.

Adaptive constellation rotation scheme for two-user fading MAC with quantized fade state feedback

With no Channel State Information (CSI) at the users, transmission over the two-user Gaussian Multiple Access Channel with fading and finite constellation at the input, will have high error rates due to multiple access interference (MAI). However, perfect CSI at the users is an unrealistic assumption in the wireless scenario, as it would involve extremely large feedback overheads. In this paper we propose a scheme which removes the adverse effect of MAI using only quantized knowledge of fade state at the transmitters such that the associated overhead is nominal. One of the users rotates its constellation relative to the other without varying the transmit power to adapt to the existing channel conditions, in order to meet certain predetermined minimum Euclidean distance requirement in the equivalent constellation at the destination. The optimal rotation scheme is described for the case when both the users use symmetric M-PSK constellations at the input, where M = 2(gimel), gimel being a positive integer. The strategy is illustrated by considering the example where both the users use QPSK signal sets at the input. The case when the users use PSK constellations of different sizes is also considered. It is shown that the proposed scheme has considerable better error performance compared to the conventional non-adaptive scheme, at the cost of a feedback overhead of just log log(2) (M-2/8 - M/4 + 2)] + 1 bits, for the M-PSK case.

Trellis coded modulation scheme for the fading relay channel

A decode and forward protocol based Trellis Coded Modulation (TCM) scheme for the half-duplex relay channel, in a Rayleigh fading environment, is presented. The proposed scheme can achieve any spectral efficiency greater than or equal to one bit per channel use (bpcu). A near-ML decoder for the suggested TCM scheme is proposed. It is shown that the high Signal to Noise Ratio (SNR) performance of this near-ML decoder approaches the performance of the optimal ML decoder. Based on the derived Pair-wise Error Probability (PEP) bounds, design criteria to maximize the diversity and coding gains are obtained. Simulation results show a large gain in SNR for the proposed TCM scheme over uncoded communication as well as the direct transmission without the relay.

An adaptive modulation scheme for two-user fading MAC with quantized fade state feedback

For transmission over the two-user Gaussian Multiple Access Channel with fading and finite constellation at the inputs, we propose a scheme which uses only quantized knowledge of fade state at users with the feedback overhead being nominal. One of the users rotates its constellation without varying the transmit power to adapt to the existing channel conditions, in order to meet certain pre-determined minimum Euclidean distance requirement in the equivalent constellation at the destination. The optimal modulation scheme has been described for the case when both the users use symmetric M-PSK constellations at the input, where M = 2λ, λ being a positive integer. The strategy has been illustrated by considering examples where both the users use QPSK signal set at the input. It is shown that the proposed scheme has considerable better error performance compared to the conventional non-adaptive scheme, at the cost of a feedback overhead of just [log2 (M2/8 - M/4 + 2)] + 1 bits, for the M-PSK case.

Achievable secrecy sum-rate in a fading MAC-WT with power control and without CSI of eavesdropper

We consider a two user fading Multiple Access Channel with a wire-tapper (MAC-WT) where the transmitter has the channel state information (CSI) to the intended receiver but not to the eavesdropper (eve). We provide an achievable secrecy sum-rate with optimal power control. We next provide a secrecy sum-rate with optimal power control and cooperative jamming (CJ). We then study an achievable secrecy sum rate by employing an ON/OFF power control scheme which is more easily computable. We also employ CJ over this power control scheme. Results show that CJ boosts the secrecy sum-rate significantly even if we do not know the CSI of the eve's channel. At high SNR, the secrecy sum-rate (with CJ) without CSI of the eve exceeds the secrecy sum-rate (without CJ) with full CSI of the eve.

Near-Optimal Detection Thresholds for Bayesian Spectrum Sensing Under Fading

This paper considers the problem of energy-based, Bayesian spectrum sensing in cognitive radios under various fading environments. Under the well-known central limit theorem based model for energy detection, we derive analytically tractable expressions for near-optimal detection thresholds that minimize the probability of error under lognormal, Nakagami-m, and Weibull fading. For the Suzuki fading case, a generalized gamma approximation is provided, which saves on the computation of an integral. In each case, the accuracy of the theoretical expressions as compared to the optimal thresholds are illustrated through simulations.

Error exponent analysis of energy-based Bayesian decentralized spectrum sensing under fading

This paper considers decentralized spectrum sensing, i.e., detection of occupancy of the primary users' spectrum by a set of Cognitive Radio (CR) nodes, under a Bayesian set-up. The nodes use energy detection to make their individual decisions, which are combined at a Fusion Center (FC) using the K-out-of-N fusion rule. The channel from the primary transmitter to the CR nodes is assumed to undergo fading, while that from the nodes to the FC is assumed to be error-free. In this scenario, a novel concept termed as the Error Exponent with a Confidence Level (EECL) is introduced to evaluate and compare the performance of different detection schemes. Expressions for the EECL under general fading conditions are derived. As a special case, it is shown that the conventional error exponent both at individual sensors, and at the FC is zero. Further, closed-form lower bounds on the EECL are derived under Rayleigh fading and lognormal shadowing. As an example application, it answers the question of whether to use pilot-signal based narrowband sensing, where the signal undergoes Rayleigh fading, or to sense over the entire bandwidth of a wideband signal, where the signal undergoes lognormal shadowing. Theoretical results are validated using Monte Carlo simulations. (C) 2015 Elsevier B.V. All rights reserved.

Nearest neighbour decoding and pilot-aided channel estimation in stationary Gaussian flat-fading channels

We study the information rates of non-coherent, stationary, Gaussian, multiple-input multiple-output (MIMO) flat-fading channels that are achievable with nearest neighbour decoding and pilot-aided channel estimation. In particular, we analyse the behaviour of these achievable rates in the limit as the signal-to-noise ratio (SNR) tends to infinity. We demonstrate that nearest neighbour decoding and pilot-aided channel estimation achieves the capacity pre-logwhich is defined as the limiting ratio of the capacity to the logarithm of SNR as the SNR tends to infinityof non-coherent multiple-input single-output (MISO) flat-fading channels, and it achieves the best so far known lower bound on the capacity pre-log of non-coherent MIMO flat-fading channels. © 2011 IEEE.

Gaussian fading is the worst fading

The capacity of peak-power limited, single-antenna, noncoherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary and ergodic fading processes of a given spectral distribution function and whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log. The assumption that the law of the fading process has no mass point at zero is essential in the sense that there exist stationary and ergodic fading processes whose law has a mass point at zero and that give rise to a smaller pre-log than the Gaussian process of equal spectral distribution function. An extension of these results to multiple-input single-output (MISO) fading channels with memory is also presented. © 2006 IEEE.

Gaussian fading is the worst fading

The capacity of peak-power limited, single-antenna, non-coherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary & ergodic fading processes of a given spectral distribution function whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log. © 2006 IEEE.

Nearest neighbour decoding with pilot-assisted channel estimation for fading multiple-access channels

This paper studies a noncoherent multiple-input multiple-output (MIMO) fading multiple-access channel (MAC). The rate region that is achievable with nearest neighbour decoding and pilot-assisted channel estimation is analysed and the corresponding pre-log region, defined as the limiting ratio of the rate region to the logarithm of the signal-to-noise ratio (SNR) as the SNR tends to infinity, is determined. © 2011 IEEE.

On bandlimited fading channels at high SNR

This paper provides an overview of results on the capacity of noncoherent, multiple-input multiple-output (MIMO) flat-fading channels with a bandlimited power spectral density. The focus is on results that concern the capacity at high signal-to-noise ratio (SNR). In particular, the capacity pre-log, defined as the limiting ratio of the capacity to the logarithm of the SNR as the SNR tends to infinity, is studied. It is observed that the capacity pre-log is a function of the number of antennas as well as of the bandwidth of the fading channel's power spectral density. It is further observed that the capacity pre-log can be achieved with a simple communication system where the data detection and the channel estimation are performed separately. © 2011 ACM.

GMI and mismatched-CSI outage exponents in MIMO block-fading channels

We study transmission over multiple-antenna blockfading channels with imperfect channel state information at both the transmitter and receiver. Specifically, we investigate achievable rates based on the generalized mutual information. We then analyze the corresponding outage probability in the high signal-to-noise ratio regime. © 2013 IEEE.