Ranjan K. Mallik

Optimization of cooperative spectrum sensing with energy detection in cognitive radio networks

We consider cooperative spectrum sensing in which multiple cognitive radios collaboratively detect the spectrum holes through energy detection and investigate the optimality of cooperative spectrum sensing with an aim to optimize the detection performance in an efficient and implementable way. We derive the optimal voting rule for any detector applied to cooperative spectrum sensing. We also optimize the detection threshold when energy detection is employed. Finally, we propose a fast spectrum sensing algorithm for a large network which requires fewer than the total number of cognitive radios in cooperative spectrum sensing while satisfying a given error bound.

Analysis of transmit-receive diversity in Rayleigh fading

We analyze the error performance of a wireless communication system employing transmit-receive diversity in Rayleigh fading. By focusing on the complex Gaussian statistics of the independent and identically distributed entries of the channel matrix, we derive a formula for the characteristic function (c.f.) of the maximum output signal-to-noise ratio. We use this c.f. to obtain a closed-form expression of the symbol error probability (SEP) for coherent binary keying. The method is easily extended to obtain the SEP for the coherent reception of M-ary modulation schemes.

Cooperative Spectrum Sensing Optimization in Cognitive Radio Networks

Cognitive radio is being recognized as an intelligent technology due to its ability to rapidly and autonomously adapt operating parameters to changing environments and conditions. In order to reliably and swiftly detect spectrum holes in cognitive radios, spectrum sensing must be used. In this paper, we consider cooperative spectrum sensing in order to optimize the sensing performance. We focus on energy detection for spectrum sensing and find that the optimal fusion rule is the half-voting rule. Next, the optimal detection threshold of energy detection is determined numerically. Finally, we propose a fast spectrum sensing algorithm for a large network which requires fewer than the total number of cognitive radios to perform cooperative spectrum sensing while satisfying a given error bound.

Analysis of hybrid selection/maximal-ratio combining in correlated Nakagami fading

We present an analysis of a hybrid selection/maximal-ratio combining diversity system over an evenly correlated slow frequency-nonselective Nakagami fading channel, where the correlation coefficient between any pair of the diversity branch gain amplitudes is the same, and all average branch signal-to-noise ratios (SNRs) are equal. In this system, the L branches with the largest instantaneous SNR out of N available branches are selected and combined using maximal-ratio combining. From the joint characteristic function (cf) of the instantaneous branch SNRs, we obtain an expression for the cf of the combiner output SNR as a series of elementary cfs. The expression can be conveniently used to obtain the symbol error probability of coherent detection of different M-ary modulation schemes. We illustrate our methodology using M-ary phase-shift keying as an example.

Bounds and approximations for optimum combining of signals in the presence of multiple cochannel interferers and thermal noise

We derive an upper bound and investigate some approximations on the symbol error probability (SEP) for coherent detection of M-ary phase-shift keying, using an array of antennas with optimum combining in wireless systems in the presence of multiple uncorrelated equal-power cochannel interferers and thermal noise in a Rayleigh fading environment. Our results are general and valid for an arbitrary number of antenna elements as well as an arbitrary number of interferers. In particular, the exact SEP is derived for an arbitrary number of antennas and interferers; the computational complexity of the exact solution depends on the minimum number of antennas and interferers. Moreover, closed-form approximations are provided for the cases of dual optimum combining with an arbitrary number of interferers, and of two interferers with an arbitrary number of antenna elements. We show that our bounds and approximations are close to Monte Carlo simulation results for all cases considered in this paper.

Performance of dual-diversity predetection EGC in correlated Rayleigh fading with unequal branch SNRs

The bit error probability (BEP) for coherent detection of binary signals with dual-diversity predetection equal gain combining is derived using the Beaulieu (1991) series. In particular, we consider a correlated Rayleigh fading channel with unequal branch signal-to-noise ratios. The BEP expression is in terms of the power correlation coefficient of the branches, is easy to compute, and depicts clearly the effect of correlated fading on the error performance.

Performance analysis of space-time coding with imperfect channel estimation

We analyze the error performance of a space-time coding system using N transmit and M receive antennas with imperfect channel estimation in flat Rayleigh fading. A least-squares estimate of the channel matrix is obtained by using a sequence of pilot code vectors. The estimate is found to be perturbed by an M/spl times/N perturbation matrix with zero-mean circular Gaussian entries. Using the characteristic function of the decision variable, we derive a closed-form expression for the pairwise error probability (PEP). From the same expression, the PEP in case of perfect channel estimation is also obtained. Numerical results show the degradation in performance due to imperfect channel estimation that can be compensated by increasing the number of receive antennas.

Secure Transmission With Antenna Selection in MIMO Nakagami-m Fading Channels

This paper considers transmit antenna selection (TAS) and receive generalized selection combining (GSC) for secure communication in the multiple-input-multiple-output wiretap channel, where confidential messages transmitted from an NA-antenna transmitter to an NB-antenna legitimate receiver are overheard by an NE-antenna eavesdropper. We assume that the main channel and the eavesdroppers channel undergo Nakagami-m fading with fading parameters mB and mE, respectively. In order to assess the secrecy performance, we present a new unifying framework for the average secrecy rate and the secrecy outage probability. We first derive expressions for the probability density function and the cumulative distribution function of the signal-to-noise ratio with TAS/GSC, from which we derive exact expressions for the average secrecy rate and the secrecy outage probability. We then derive compact expressions for the asymptotic average secrecy rate and the asymptotic secrecy outage probability for two distinct scenarios: 1) the legitimate receiver is located close to the transmitter, and 2) the legitimate receiver and the eavesdropper are located close to the transmitter. For these scenarios, we present new closed-form expressions for several key performance indicators: 1) the capacity slope and the power offset of the asymptotic average secrecy rate, and 2) the secrecy diversity order and the secrecy array gain of the asymptotic secrecy outage probability. For the first scenario, we confirm that the capacity slope is one and the secrecy diversity order is mBNBNA. For the second scenario, we confirm that the capacity slope and the secrecy diversity order collapse to zero.

Minimum selection GSC in independent Rayleigh fading

We analyze the error performance of minimum selection generalized selection combining (MS-GSC), in which the minimum number of diversity branches are selected such that their combined signal-to-noise ratio (SNR) is above a given threshold. A flat Rayleigh fading channel with independent and distinctly distributed branch SNR is considered. By transforming the ordered instantaneous branch SNR to their differences, we derive the distribution of the number of selected branches in closed-form. We then modify the derivation of this distribution to get the characteristic function (c.f.) of the combiner output SNR. This c.f. is used to obtain the symbol error probability for different coherent digital modulation schemes.

The inverse of a tridiagonal matrix

In this paper, explicit formulae for the elements of the inverse of a general tridiagonal matrix are presented by first extending results on the explicit solution of a second-order linear homogeneous difference equation with variable coefficients to the nonhomogeneous case, and then applying these extended results to a boundary value problem. A formula for the characteristic polynomial is obtained in the process. We also establish a connection between the matrix inverse and orthogonal polynomials. In addition, the case of a cyclic tridiagonal system is discussed.