K. D. Prathapasinghe Dharmawansa

Linear estimation of correlated data in wireless sensor networks with optimum power allocation and analog modulation

In this paper, we study the energy-efficient distributed estimation problem for a wireless sensor network where a physical phenomena that produces correlated data is sensed by a set of spatially distributed sensor nodes and the resulting noisy observations are transmitted to a fusion center via noise- corrupted channels. We assume a Gaussian network model where (i) the data samples being sensed at different sensors have a correlated Gaussian distribution and the correlation matrix is known at the fusion center, (ii) the links between the local sensors and the fusion center are subject to fading and additive white Gaussian noise (AWGN), and the fading gains are known at the fusion center, and (iii) the central node uses the squared error distortion metric. We consider two different distortion criteria: (i) individual distortion constraints at each node, and (ii) average mean square error distortion constraint across the network. We determine the achievable power-distortion regions under each distortion constraint. Taking the delay constraint into account, we investigate the performance of an uncoded transmission strategy where the noisy observations are only scaled and transmitted to the fusion center. At the fusion center, two different estimators are considered: (i) the best linear unbiased estimator (BLUE) that does not require knowledge of the correlation matrix, and (ii) the minimum mean- square error (MMSE) estimator that exploits the correlations. For each estimation method, we determine the optimal power allocation that results in a minimum total transmission power while satisfying some distortion level for the estimate (under both distortion criteria). The numerical comparisons between the two schemes indicate that the MMSE estimator requires less power to attain the same distortion provided by the BLUE and this performance gap becomes more dramatic as correlations between the observations increase. Furthermore, comparisons between power-distortion region achieved by the theoretically optimum system and that achieved by the uncoded system indicate that the performance gap between the two systems becomes small for low levels of correlation between the sensor observations. If observations at all sensor nodes are uncorrelated, the uncoded system with MMSE estimator attains the theoretically optimum system performance.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.

An exact error probability analysis of OFDM systems with frequency offset

In this paper, we derive exact closed form bit error rate (BER) or symbol error rate (SER) expressions for OFDM systems with carrier frequency offset (CFO). We consider the performance of an OFDM system subject to CFO error in frequency flat Rayleigh fading channel with BPSK and QPSK modulation schemes. Our results can easily be reduced to the respective analytical error rate expressions for the OFDM systems without CFO error. Furthermore, the simulation results are provided to verify the accuracy of the new error rate expressions

Envelope and phase distribution of two correlated gaussian variables

Probability density functions (pdfs) 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 pdfs 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.

Multiple Primary User Spectrum Sensing in the Low SNR Regime

We consider multi-antenna cooperative spectrum sensing in cognitive radio networks, when there are multiple primary users and/or multipath channels. A noise-uncertainty-free detector that is optimal in the low signal to noise ratio regime is analyzed. We derive the moments of the test statistics involved, which lead to simple and accurate analytical formulae for the key performance metrics. The approximative false alarm and detection probabilities as well as receiver operating characteristic are given in closed form. From the considered simulation settings, performance gain over several known detection algorithms is observed in scenarios with relatively low signal to noise ratio.

On the exact distribution of the scaled largest eigenvalue

In this paper we study the distribution of the scaled largest eigenvalue of complex Wishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have been derived for the probability density function and the cumulative distribution function. The derived results involve only finite sums of polynomials. These results are obtained by taking advantage of properties of the Mellin transform for products of independent random variables.

Ergodic Capacity and Beamforming Optimality for Multi-Antenna Relaying with Statistical CSI

We investigate the capacity and beamforming optimality of multi-antenna relaying systems, given access to statistical channel information at the relay and source. Multi-antenna relay configurations are considered, for which the source as well as either the relay or destination have multiple antennas, and the relay operates with amplify-and-forward. We first compute the optimal transmission strategies at both the source and relay, and derive necessary and sufficient conditions for which beamforming achieves capacity. To gain more insight, we then employ tools from stochastic majorization theory to characterize the impact of the destination correlation and the relay gain on the capacity and beamforming optimality range. These results demonstrate some intriguing behavior, which arises due to the joint interplay between the transmit power, relay gain, and level of correlation at the destination. It is shown, among other things, that for certain transmit powers and relay gains, the beamforming optimality region becomes independent of the destination correlation. By relaxing the beamforming optimality condition, we also derive a simple explicit upper bound which gives further insights into the joint effect of the SNR and the transmit correlation on the beamforming optimality range.

Extreme eigenvalue distributions of some complex correlated non-central Wishart and gamma-Wishart random matrices

Let

New series representation for the trivariate non-central chi-squared distribution

\mathbf{W}

Finite-SNR Diversity-Multiplexing Trade-Off of Dual Hop Multiple-Relay Channels

be a correlated complex non-central Wishart matrix defined through

Diagonal distribution of a complex non-central Wishart matrix: A new trivariate non-central chi-squared density

\mathbf{W}=\mathbf{X}^H\mathbf{X}