Amir Nasri

Adaptive L_p—Norm Spectrum Sensing for Cognitive Radio Networks

In cognitive radio (CR) systems, reliable spectrum sensing techniques are required in order to avoid interference to the primary users of the spectrum. Whereas most of the existing literature on spectrum sensing considers impairment by additive white Gaussian noise (AWGN) only, in practice, CRs also have to cope with various types of non-Gaussian noise such as man-made impulsive noise, co-channel interference, and ultra-wideband interference. In this paper, we propose an adaptive Lp-norm detector which does not require any a priori knowledge about the primary user signal and performs well for a wide range of circularly symmetric non-Gaussian noises with finite moments. We analyze the probabilities of false alarm and missed detection of the proposed detector in Rayleigh fading in the low signal-to-noise ratio regime and investigate its asymptotic performance if the number of samples available for spectrum sensing is large. Furthermore, we consider the deflection coefficient for optimization of the Lp-norm parameters and discuss its connection to the probabilities of false alarm and missed detection. Based on the deflection coefficient an adaptive algorithm for online optimization of the Lp-norm parameters is developed. Analytical and simulation results show that the proposed Lp-norm detector yields significant performance gains compared to conventional energy detection in non-Gaussian noise and approaches the performance of the locally optimal detector which requires knowledge of the noise distribution.

Performance and Optimization of Amplify-and-Forward Cooperative Diversity Systems in Generic Noise and Interference

Cooperative diversity systems have received significant attention recently as a distributed means of exploiting the inherent spatial diversity of wireless networks. In this paper, we consider a cooperative diversity system consisting of a source, a destination, and multiple single-hop amplify-and-forward relays, and provide a mathematical framework for the asymptotic analysis of this system in generic noise and interference for high signal-to-noise ratios. Assuming independent Rayleigh fading for all links in the network and orthogonal relay-destination channels, we obtain simple and elegant closed-form expressions for the asymptotic symbol and bit error rates valid for arbitrary linear modulation formats, arbitrary numbers of relays, and arbitrary types of noise and interference with finite moments including co-channel interference, ultra-wideband interference, impulsive ε-mixture noise, generalized Gaussian noise, and Gaussian noise. Furthermore, we exploit the derived analytical error rate expressions to develop power allocation, relay selection, and relay placement schemes that are asymptotically optimal in environments with generic noise and interference. In general, the power allocation problem results in a geometric program which can be solved efficiently numerically. For the special case of only one relay, we provide a closed-form result for the optimal power allocation. Simulation results confirm our analysis and illustrate that, in non-Gaussian noise, the proposed power allocation, relay selection, and relay placement schemes lead to large performance gains compared to their conventional counterparts optimized for Gaussian noise.

Performance of BICM-SC and BICM-OFDM systems with diversity reception in non-gaussian noise and interference

In this paper, we present a general mathematical framework for performance analysis of single-carrier (SC) and orthogonal frequency division multiplexing (OFDM) systems employing popular bit-interleaved coded modulation (BICM) and multiple receive antennas. The proposed analysis is applicable to BICM systems impaired by general types of fading (including Rayleigh, Ricean, Nakagami-m, Nakagami-q, and Weibull fading) and general types of noise and interference with finite moments such as additive white Gaussian noise (AWGN), additive correlated Gaussian noise, Gaussian mixture noise, co-channel interference, narrowband interference, and ultra-wideband interference. We present an approximate upper bound for the bit error rate (BER) and an accurate closed-form approximation for the asymptotic BER at high signal-to-noise ratios for Viterbi decoding with the standard Euclidean distance branch metric. For the standard rate-1/2 convolutional code the proposed approximate upper bound and the asymptotic approximation become tight at BERs of 10-6 and 10-12, respectively. However, if the code is punctured to higher rates (e.g. 2/3 or 3/4), the asymptotic approximation also becomes tight at a BER of 10-6. Exploiting the asymptotic BER approximation we show that the diversity gain of BICM systems only depends on the free distance of the code, the type of fading, and the number of receive antennas but not on the type of noise. In contrast their coding gain strongly depends on the noise moments. Our asymptotic analysis shows that as long as the standard Euclidean distance branch metric is used for Viterbi decoding, BICM systems optimized for AWGN are also optimum for any other type of noise and interference with finite moments.

Lp-Norm Spectrum Sensing for Cognitive Radio Networks Impaired by Non-Gaussian Noise

In cognitive radio (CR) systems reliable spectrum sensing techniques are required in order to avoid interference to the primary users of the spectrum. Whereas most of the existing literature on spectrum sensing considers impairment by additive white Gaussian noise (AWGN) only, in practice, CRs also have to cope with various types of non-Gaussian noise such as man-made impulsive noise, co-channel interference, and ultra-wideband interference. In this paper, we propose robust Lp-norm detectors which do not require any a priori knowledge about the primary user signal and perform well for a wide range of non-Gaussian noises. Furthermore, we analyze the probabilities of false alarm and missed detection of the proposed detectors in the low signal-to-noise ratio regime. For optimization of Lp-norm detection we propose a direct approach based on minimization of the probability of false alarm for a given probability of missed detection and a simpler approach based on maximization of the deflection coefficient of the detector. Analytical and simulation results show that the proposed Lp-norm detectors achieve significant performance gains over conventional energy detection in non-Gaussian noise.

Unified asymptotic analysis of linearly modulated signals in fading, non-Gaussian noise, and interference

In this paper, we present a unified asymptotic symbol error rate (SER) analysis of linearly modulated signals impaired by fading and (possibly) non-Gaussian noise, which in our definition also includes interference. The derived asymptotic closed-form results are valid for a large class of fading and noise processes. Our analysis also encompasses diversity reception with equal gain and selection combining and is extended to binary orthogonal modulation. We show that for high signal-to-noise ratios (SNRs) the SER of linearly modulated signals depends on the Mellin transform of the probability density function (pdf) of the noise. Since the Mellin transform can be readily obtained for all commonly encountered noise pdfs, the provided SER expressions are easy and fast to evaluate. Furthermore, we show that the diversity gain only depends on the fading statistic and the number of diversity branches, whereas the combining gain depends on the modulation format, the type of fading, the number of diversity branches, and the type of noise. An exception are systems with a diversity gain of one, since their combining gain and asymptotic SER are independent of the type of noise. However, in general, in a log-log scale for high SNR the SER curves for different types of noise are parallel but not identical and their relative shift depends on the Mellin transforms of the noise pdfs.

Adaptive L p -norm diversity combining in non-gaussian noise and interference

In this paper, we introduce an adaptive Lp-norm metric for robust coherent, differential, and noncoherent diversity combining in non-Gaussian noise and interference. We consider the general case where all diversity branches may use different combining weights and different Lp-norms. We derive a general closed-form expression for the asymptotic bit error rate (BER) for Lp-norm combining in independent non-identically distributed Ricean fading and non-Gaussian noise and interference with finite moments. The asymptotic BER expression reveals that the diversity gain of Lp-norm combining is independent of the type of noise and the metric parameters. In contrast, the combining gain depends on both the type of noise and the metric parameters. Thus, the asymptotic BER can be minimized by optimizing the Lp-norm metric parameters for the underlying type of noise. For this purpose finite difference stochastic approximation (FDSA) and localized random search (LRS) algorithms are developed. Both adaptive algorithms do not require any a priori knowledge about the underlying noise and are able to track changes in the noise statistics. Simulation results confirm the validity of the derived asymptotic BER expressions, the effectiveness of the proposed adaptive algorithms, and the excellent performance of the proposed adaptive Lp-norm metric compared to other popular metrics.

Analysis of Narrowband Communication Systems Impaired by MB-OFDM UWB Interference

In this paper, we investigate the effect of multi-band orthogonal frequency division multiplexing (MB-OFDM) ultra-wideband (UWB) interference on narrowband (NB) receivers. For this purpose, we first derive the exact moment generating function of MB-OFDM UWB interference. Based on this result, we develop analytical expressions for the amplitude probability distribution (APD) and the bit error rate (BER) of a binary phase-shift keying NB receiver. These expressions can be efficiently numerically evaluated and the presented analysis is general enough to encompass non-fading and various fading NB channels. We show that for NB signals with, respectively, much smaller and much larger bandwidths than the MB-OFDM sub-carrier spacing a Gaussian approximation (GA) and an impulsive GA (IGA) of the MB-OFDM UWB interference lead to accurate performance predictions. However, for most NB channel models and signal bandwidths the exact BER analysis has to be used to obtain meaningful results. An exception is the Rayleigh fading NB channel where both GA and IGA yield tight approximations of the exact BER regardless of the NB signal bandwidth.

Relay Subset Selection and Fair Power Allocation for Best and Partial Relay Selection in Generic Noise and Interference

Best relay selection (BRS) has received considerable attention in the literature as it makes efficient use of the system resources and achieves full diversity. Partial relay selection (PRS) is an alternative to BRS and performs relay selection based on local channel state information (CSI) only at the expense of a loss in diversity. Although, in practice, relays may be deployed in unfavorable environments exposing them to non-Gaussian impairments, existing analyses and design guidelines for BRS and PRS are limited to additive white Gaussian noise channels. In this paper, we analyze the error rate of BRS and PRS in the asymptotic regime of high signal-to-noise ratio (SNR) for amplify-and-forward (AF) relays and impairment by generic noise and interference. The derived analytical results are valid for Gaussian and non-Gaussian noises with finite moments, independent and non-identically distributed Rayleigh fading, and arbitrary linear modulation schemes. In order to reduce the signaling overhead required for CSI acquisition, we propose a relay subset selection scheme for BRS and PRS. Furthermore, to guarantee fairness in energy resource usage across the relays, we introduce a fair and flexible power allocation scheme with energy consumption constraints which does not affect the achievable diversity gain. The proposed relay subset selection and power allocation schemes only require knowledge of the average CSI of the links and certain moments of the noises impairing the relays and the destination.

Asymptotic BEP and SEP of quadratic diversity combining receivers in correlated ricean fading, non-gaussian noise, and interference

In this paper, we study the asymptotic behavior of the bit-error probability (BEP) and the symbol-error probability (SEP) of quadratic diversity combining schemes such as coherent maximum-ratio combining (MRC), differential equal-gain combining (EGC), and noncoherent combining (NC) in correlated Ricean fading and non-Gaussian noise, which in our definition also includes interference. We provide simple and easy-to-evaluate asymptotic BEP and SEP expressions which show that at high signal-to-noise ratios (SNRs) the performance of the considered combining schemes depends on certain moments of the noise and interference impairing the transmission. We derive general rules for calculation of these moments and we provide closed-form expressions for the moments of several practically important types of noise such as spatially dependent and spatially independent Gaussian mixture noise, correlated synchronous and asynchronous co-channel interference, and correlated Gaussian interference. From our asymptotic results we conclude that (a) the asymptotic performance loss of binary frequency-shift keying (BFSK) with NC compared to binary phase-shift keying (BPSK) with MRC is always 6 dB independent of the type of noise and the number of diversity branches, (b) the asymptotic performance loss of differential EGC compared to MRC is always 3 dB for additive white Gaussian noise but depends on the number of diversity branches and may be larger or smaller than 3 dB for other types of noise, and (c) not only fading correlation but also noise correlation negatively affects the performance of quadratic diversity combiners.

Error Rate Performance of Network-Coded Cooperative Diversity Systems

In this paper, we study network-coded cooperative diversity (NCCD) systems comprising multiple sources, one relay, and one destination. The relay detects the packets received from all sources and performs Galois field network coding. We propose a simple cooperative maximum-ratio combining scheme for the destination which is shown to achieve the maximum diversity gain of the system. Furthermore, we provide a mathematical framework for the asymptotic analysis of NCCD systems with M-ary modulation for high signal-to-noise ratios. Based on this framework, we derive simple and elegant closed- form expressions for the asymptotic symbol and bit error rates which provide significant insight into the impact of various system and channel parameters on performance and can be exploited for performance optimization. Simulation results confirm the accuracy of the presented analysis and show that large performance gains are possible by optimizing the power allocation in NCCD systems based on the developed analytical results.