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ABSTRACT: A comprehensive performance analysis of the energy detector over fading channels with single antenna reception or with antenna diversity reception is developed. For the no-diversity case and for the maximal ratio combining (MRC) diversity case, with either Nakagami-m or Rician fading, expressions for the probability of detection are derived by using the moment generating function (MGF) method and probability density function (PDF) method. The former, which avoids some difficulties of the latter, uses a contour integral representation of the Marcum-Q function. For the equal gain combining (EGC) diversity case, with Nakagami-m fading, expressions for the probability of detection are derived for the cases L =2,3,4 and L >; 4, where L is the number of diversity branches. For the selection combining (SC) diversity, with Nakagami-m fading, expressions for the probability of detection are derived for the cases L =2 and L >; 2. A discussion on the comparison between MGF and PDF methods is presented. We also derive several series truncation error bounds that allow series termination with a finite number of terms for a given figure of accuracy. These results help quantify and understand the achievable improvement in the energy detector's performance with diversity reception. Numerical and simulation results are also provided.
IEEE Transactions on Communications 10/2011; · 1.68 Impact Factor
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ABSTRACT: Several time-division multiple-access (TDMA) cooperative wireless relay protocols and their performances have recently been developed by Nabar, Bolcskei, and Kneubuhler. Their work, however, is limited to an upper bound-based performance analysis for Rayleigh fading. We thus provide an exact analysis of two of their protocols in single-relay and multiple-relay networks over independent identically distributed (i.i.d.) Nakagami- m fading channels. Our analysis is focused on an Alamouti-coded system with two-stage protocols, fixed-gain amplify-and-forward (AF) relays, and maximal ratio combiner (MRC) reception. The performance metrics are the capacity, the diversity order, and the symbol error rate (SER). The closed-form moment-generating function (MGF) of the total end-to-end signal-to-noise ratio (SNR) is derived. The MGF is then used to derive the diversity order and the SER of M -ary phase-shift keying ( M -PSK) and M -ary quadrature amplitude modulation ( M -QAM). It is found that the end-to-end SNR for relaying with orthogonal channels is higher than that of nonorthogonal relay channels. The diversity order of a multiple-relay network ( n relays) in a Nakagami- m environment is shown to be ( n + 1) m . The closed-form SER expressions for relay-destination links with high SNRs and static relay-destination links are derived. Numerical and simulation results are provided to verify the analysis.
IEEE Transactions on Vehicular Technology 02/2010; · 1.92 Impact Factor
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ABSTRACT: Detection of an unknown deterministic signal by using an energy detector is of promising for cognitive radio networks. In this paper, a new approach is proposed to analyze the performance of the energy detector. It is based on the contour integral representation of the Marcum-Q function and the use of the moment generating function (MGF) of the signal-to-noise ratio (SNR). A new decision variable is constructed for the case of maximal ratio combining (MRC) reception. With its help and the MGF based approach, the performance of the MRC energy detector over i.i.d. Rician fading channels is analyzed. This case is intractable with the conventional probability density function (PDF) based approach. Further the detection probability of MRC combined energy detector over Nakagami-m fading branches is derived. The simulation results are presented to support the developed MGF based method, decision variable formulation and derivations. The detector performance is evaluated over different fading and diversity parameters with the help of numerical and simulation examples.
Communications Workshops, 2009. ICC Workshops 2009. IEEE International Conference on; 07/2009
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ABSTRACT: Blind sensing for identifying unused frequency bands is of particular interest in cognitive radio and ultra wide-band applications. Energy detection is one such method proposed to identify the presence of an unknown band-limited deterministic signal. In this paper, by using an alternative series representation of the Marcum-Q function, the exact average detection probability over the Nakagami-m fading channel is derived. Moreover, we formulate the decision variable of a selection diversity combined energy detector and derive the exact average detection and false alarm probabilities.
Electrical and Computer Engineering, 2009. CCECE '09. Canadian Conference on; 06/2009
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ABSTRACT: Probability density functions (pdf's) are derived for the phase and amplitude (envelope) of the complex gain X +jY (j = radic-1), where X and Y are two correlated non zero-mean Gaussian random variables. The pdf of the amplitude is derived as an infinite series, but reduces to a closed-form expression when the means are zero. The classical Rayleigh and Rician pdf's turn out to be special cases of the derived pdf. This pdf is used to analyze the error performance of non-coherent binary frequency shift keying (BFSK) with in-phase/quadrature(I/Q) imbalance over an additive white Gaussian noise (AWGN) channel. The resulting bit error rate (BER) expression is derived as an infinite series. The analytical expressions are validated by simulation, and the I/Q imbalance related performance degradation is quantified. Convergence of the PDF series and the BER series is established.
IEEE Transactions on Communications 05/2009; · 1.68 Impact Factor
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ABSTRACT: This paper derives a new infinite series representation for the trivariate non-central chi-squared distribution when the underlying correlated Gaussian variables have a tridiagonal form of an inverse covariance matrix. The joint probability density function is derived using Miller's approach and Dougall's identity. Moreover, the trivariate cumulative distribution function (cdf) and characteristic function (chf) are also derived. Finally, the bivariate non-central chi-squared distribution and some known forms are shown to be special cases of the more general distribution. However, the derivation of non-central chi-squared distribution for an arbitrary covariance matrix seems intractable via Miller's approach. Two applications of the newly derived results are provided for performance analysis of multiple input multiple output (MIMO) systems with transmit antenna selection over a correlated Rician fading environment. Some numerical results are also presented to verify the accuracy of the analytical expressions.
IEEE Transactions on Communications 04/2009; · 1.68 Impact Factor
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ABSTRACT: An exact expression for the joint density of three correlated Rician variables is not available in the open literature. In this letter, we derive new infinite series representations for the trivariate Rician probability density function (pdf) and the joint cumulative distribution function (cdf). Our results are limited to the case where the inverse covariance matrix is tridiagonal. This case seems the most general one that is tractable with Miller¿s approach and cannot be extended to more than three Rician variables. The outage probability of triple branch selective combining (SC) receiver over correlated Rician channels is presented as an application of the density function.
IEEE Transactions on Communications 01/2009; · 1.68 Impact Factor
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ABSTRACT: In this paper, using Miller's approach and Dougall's identity, we derive new infinite series representations for the quadrivariate Nakagami-m joint density function, cumulative distribution function (cdf) and characteristic functions (chf). The classical joint density function of exponentially correlated Nakagami-m variables can be identified as a special case of the joint density function obtained here. Our results are based on the most general arbitrary correlation matrix possible. Moreover, the trivariate density function, cdf and chf for an arbitrary correlation matrix are also derived from our main result. Bounds on the series truncation error are also presented. Finally, we develop several representative applications: the outage probability of triple branch selection combining (SC), the moments of the equal gain combining (EGC) output signal to noise ratio (SNR) and the moment generation function of the generalized SC(2,3) output SNR in an arbitrarily correlated Nakagami-m environment. Simulation results are also presented to verify the accuracy of our theoretical results.
IEEE Transactions on Wireless Communications 01/2008; · 2.59 Impact Factor
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ABSTRACT: In this paper, we derive a new infinite series representation for the trivariate non-central chi-squared distribution when the underlying correlated Gaussian variables have tridiagonal form of inverse covariance matrix. We make use of the Miller's approach and the Dougall's identity to derive the joint density function. Moreover, the trivariate cumulative distribution function (cdf) and characteristic function (chf) are also derived. Finally, bivariate noncentral chi-squared distribution and some known forms are shown to be special cases of the more general distribution. However, non-central chi-squared distribution for an arbitrary covariance matrix seems intractable with the Miller's approach.
Vehicular Technology Conference, 2007. VTC2007-Spring. IEEE 65th; 05/2007
