We consider fractional uplink power control in a cellular system. Interference caused to neighbouring cells is analysed in a single-slope path loss model. Closed form approximations of the average interference, the average inverse interference, and the achievable rate are derived. There exists infinitely many combinations of FPC parameters in a cell, giving rise to the same interference level at neighbouring cells. Hence, power control can be implemented individually for each cell to achieve a cell-specific quality of service.

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.

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.

This paper investigates the finite signal-to-noise ratio (SNR) diversity-multiplexing trade-off (DMT) of point-to-point wireless channels assisted by multiple relays. Results are derived for both amplify-and-forward (AF) and decode-and-forward (DF) relaying protocols. For the AF protocol, we derive accurate approximations for the system outage probability when the relays are clustered between the source and destination. For the case where all the relays are clustered near the destination, an exact closed-form expression for the system outage probability is obtained. For the DF protocol, under general multiple relaying configurations, we derive an exact closed-form expression for the system outage probability. The outage results for AF and DF are used subsequently to yield expressions for the finite-SNR DMT. We also extract the conventional asymptotic DMTs as special cases of the finite-SNR results, and demonstrate that the asymptotic DMTs can significantly overestimate the level of diversity that is achievable for practical error rates and SNRs.

This paper considers the analytical performance of primary users (PUs) subject to interference due to secondary users (SU) in an underlay cognitive radio system over Rayleigh fading. In particular, we focus on a more general spatial configuration where the interfered PU, not only located at the center of the cell, is having a protective region which is free of SUs and the SUs are distributed over a finite area in contrast to the commonly used infinite area assumption. We first characterize the statistical properties of the aggregate interference at the PU due to SUs, by deriving new exact closed form expressions for the moment generating function, cumulants, first, second and third moments and first order expansions of the cumulative distribution functions corresponding to propagation scenarios with path loss factors, two and four. We then investigate the PU performance by presenting new analytical expressions for the outage probability, amount of fading as well as the diversity order and coding gain. Our results indicate that the PU can achieve the full diversity gain given a non-zero protective region around the PU.

This paper investigates the following general problem relating to ordered random processes: givennindependent but not necessarily identical random processes, how frequently, on average, does any given process become one of thepth (p=1,2,...,n-1) largest processes? This is a fundamental problem arising in the design and analysis of contemporary multidimensional wireless communication systems (e.g., multiantenna, multiuser) employing opportunistic selection. We formulate this problem as one involving the level crossing rate (LCR) of a carefully defined ordered random process across the zero threshold, which we solve by developing a new mathematical framework based on the theory of permanents. For the case where the processes correspond to time-varying Rayleigh fading channels, we present exact closed-form formulas for the LCR, simplified tight upper bounds, as well as asymptotic results fornandpapproaching infinity but with fixed ratio. These results reveal interesting fundamental limits for the LCR, and are shown to given meaningful insight even for small values ofnandp. We further use our mathematical framework to characterize the required per-branch and overall switching rate of a generalized selection combining diversity receiver, allowing for different average powers for each branch. With the aid of majorization theory, we demonstrate that the overall switching rate is maximized when the power delay profile is uniform.

This paper derives analytical expressions for the eigenvalues of so-called gamma-Wishart random matrices, which arise in the context of multiple-input multiple-output (MIMO) transmission over land-mobile-satellite (LMS) communication channels. Such matrices are representative of complex noncentral Wishart matrices, but with randomly varying noncentrality parameter following a distribution closely related to the matrix-variate gamma. For these matrices, we derive exact closed form expressions for the distribution functions of the extreme eigenvalues (i.e., the maximum and minimum). These results are remarkably simple, and are useful for the performance analysis of MIMO transmission techniques over LMS channels.

Given n independent but not necessarily identical random processes, this paper investigates the general problem of determining how frequently, on average, any given process becomes at least the p-th (p = 1, 2, . . . , n - 1) largest among all processes. This problem requires determining the level crossing rate (LCR) of a carefully defined ordered process, which we solve by developing a general mathematical framework based on the theory of permanents. Our results are very general and may be applicable for a wide range of engineering applications which involve ordered random processes. To demonstrate the applicability to wireless communications, we present closed-form formulas for the LCR for the case where the processes correspond to time-varying Rayleigh fading channels, and use these to characterize the required switching rate for a particular branch of a generalized selection combining diversity receiver.

Interference management is a major issue in underlay cognitive radio networks. In this paper, we focus on characterizing the statistics of the aggregate interference experienced by a primary user and evaluate its performance through important metrics such as outage probability, bit error rate and amount of fading. In previous works, the infinite interferers area assumption prevailed since it mainly simplifies the analysis. In contrast, we investigate the more realistic finite area, and further consider various practical spatial configurations. Two of the possible applications the proposed finite reconfigurable model can advocate are the IEEE 802.22 (WRAN) digital TV scenario and the aggregate interference considering different path loss exponents. We first derive the exact moment generating function (MGF) of the interference, then quantify the mean, the variance, and the skewness. Subsequently, the primary system performances are evaluated leading to novel expressions based on the interference MGF.

This paper investigates orthogonal space-time block coded transmission for a multiple-input multiple-output (MIMO) channel with non-coherent amplify-and-forward relaying in a situation where the source-relay and relay-destination channels undergo Rayleigh and Rician fading respectively. Fading coefficients of the Rician channel are independent but not necessarily identically distributed. We derive exact expressions for the moment generating function, first and second moments of the instantaneous signal-to-noise ratio at the destination to statistically characterize the system behavior. We then analyze the system performance by deriving new analytical expressions for the bit error rate and amount of fading. These performance metrics reveal that strong line of sight components between relay-destination link always limit the performance promised by MIMO scattering environment when both nodes have multiple antennas.

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.

We analyze the optimality of beamforming in multiple-input single-output relay channels without a direct link between the source and the destination. Assuming that the source has access to the channel correlation information, and that the relay operates in amplify and forward mode with a long term power constraint, we first show that the optimal transmission strategy is to transmit along the eigen-vectors of the transmit correlation matrix. The optimality of beamforming is then studied via the power allocation problem at the source. In particular, we derive a necessary and sufficient condition under which beamforming achieves the capacity. Our results demonstrate that the finite relay gain decreases the range at which beamforming is optimal.

This paper considers orthogonal space-time block coded transmission for a multiple-input multiple-output channel (MIMO) with non-coherent amplify-and-forward (AF) relaying in Rayleigh fading. We first characterize the statistical properties of the instantaneous signal-to-noise ratio (SNR) at the destination, by deriving new exact closed form expressions for the moment generating function, cumulants, and first and second moments. These results show a reciprocity relationship between the number of antennas at the relay and destination. The probability density function and cumulative distribution function of the SNR are also derived for certain system configurations, and for various asymptotic regimes. We then investigate the system performance by presenting new analytical expressions for the symbol error rate, outage probability, amount of fading, as well as the diversity order and array gain. Our results indicate that the proposed scheme can achieve the maximum diversity order of the non-coherent AF MIMO relay channel.

This paper considers orthogonal space-time block coded (OSTBC) transmission for non-regenerative multiple- input multiple-output dual-hop channels. We focus on scenarios where the relay does not have access to instantaneous channel state information, and as such operates according to a noncoherent amplify-and-forward protocol based on a long-term power constraint. We investigate the performance of the proposed OSTBC approach by employing tools from finite-dimensional random matrix theory. In particular, we derive exact closed-form expressions for the moment generating function, high order cumulants, and first and second moments of the signal-to-noise ratio at the destination. Based on these results, we also derive analytical expressions for the symbol error rate with M-ary phase-shift keying, and the amount of fading.

In this paper, we derive exact closed form bit error rate (BER) or symbol error rate (SER) expressions for orthogonal frequency division multiplexing (OFDM) systems with carrier frequency offset (CFO). We consider the performance of an OFDM system subject to CFO error in additive white Gaussian noise (AWGN), frequency flat and frequency selective Rayleigh fading channels. The BER/ SER performances of BPSK and QPSK modulation schemes are analyzed for AWGN and frequency-flat Rayleigh fading channels while BPSK is considered for frequency-selective Rayleigh fading channels. 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.

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.

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.

We derive the exact cumulative distribution function (c.d.f.) of the minimum eigenvalue of a correlated complex non-central Wishart matrix. This result is in the form of a simple infinite series with fast convergence, and applies for the important case where the non-centrality matrix has rank one. Simplified asymptotic expressions for the c.d.f. are given for large matrix dimensions, as well as first-order expansions around the origin. The eigenvalue distributions in this paper have various important applications to multiple-input multiple-output (MIMO) communication systems, as well other scientific areas such as econometrics and multivariate statistics.

This paper derives the joint density of the diagonal elements of a 3 times 3 complex non-central Wishart matrix. This distribution arises in a number of applications including synthetic aperture radar, extra-solar planet detection, and multi-antenna wireless communications. The density expression is in the form of an infinite series representation which converges rapidly and is easy to compute.

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.

In this paper, we derive new infinite series representations for the quadrivariate Nakagami-m distribution and cumulative distribution functions (cdf). we make use of the Miller's approach and the Dougall's identity to derive the joint density function. The classical joint density function of exponentially correlated Nakagami-m variables can be identified as a special case of our joint density function. Our results are based on the most general arbitrary correlation matrix possible. Moreover, the trivariate density function and cdf for an arbitrary correlation matrix is also derived from our main result. Bounds on the error resulting from truncation of the infinite series are also presented. Finally, numerical results are presented to verify the accuracy of our formulation.

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.

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.

In this paper, we investigate the classical problem of finding the probability density function of the sum of Nakagami-m random variables. An exact infinite series formula is derived for the sum of three identically and independently distributed (i.i.d.) Nakagami-m random variables and subsquently it is extended to the sum of four and in general M number of random variables. A detailed discussion on the cumulative density function (cdf) of the sum of three Nakagami-m variables is also given. The newly derived probability density functions are used to analyze the performance of dual and triple predetection equal gain combining (EGC) receiver over Nakagami-m fading environment. Selected numerical plots are provided to compare the results with the approximate results available in the literature and to illustrate the validity of the results.

Exact expression for the joint density of the trivariate Rician variables is not available in the open literature. In this paper, we derive new infinite series representations for the joint probability density function (pdf) and the joint cumulative distribution function (cdf) of three correlated Rician random variables. The cdf and chf of bivariate Rician density are also derived as special cases of the trivariate case. The most celebrated Millers approach is used here in deriving the trivariate Rician distribution . Bounds on the error resulting from truncating the infinite series are also presented.

We investigate the pairwise error probability (PEP) bounds for space-time trellis codes (STTC) in Nakagami-m fading channels with the arbitrary fading severity parameter, m. We derive an analytical expression for PEP upper bound in the case of two transmit antennas in terms of the higher transcendental functions, such as the Appell hypergeometric function or the Lauricella function, over uncorrelated and correlated Nakagami-m fading channels. Furthermore, we show that the probability bound for the general multiple transmit antenna scenario can also be expressed as an integral involving nested summations.