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In this paper, the transmission of orthogonal space–time block codes (OSTBCs) in amplify-and-forward (AF) multiple-input–multiple-output (MIMO) relay networks, with imperfect channel state information (CSI), is considered. Individual channel estimation and time-efficient cascaded (for estimating the product of channel matrices) channel estimation protocols are used for estimating the channel matrices required for decoding of OSTBC data at the destination. We derive tight approximations for the moment-generating function (m.g.f.) of the received signal-to-noise ratio at the destination node with imperfect CSI, by ignoring higher order noise terms, in Rayleigh fading. Using the derived m.g.f. expression, we obtain the analytical symbol error rate (SER) of the AF MIMO relay system for general OSTBCs with $M$-ary phase-shift keying constellation. The diversity order of the MIMO OSTBC relay system is also derived for some special cases by using the SER expression. [ABSTRACT FROM PUBLISHER]

We propose cognitive spectrum sharing with generalized selection combining (GSC) at the secondary user (SU) in the presence of multiple primary transceivers with outdated channel information. Our main motivation is to determine the impact of GSC and outdated channel information on the outage probability of cognitive spectrum sharing subject to two practical power constraints: 1) maximum transmit power at the SU transmitter and 2) peak interference temperature at the primary user (PU) receiver. We derive new closed-form expressions for the exact and asymptotic outage probability in Rayleigh fading. Our expressions provide concise representations of the diversity order and the array gain. We confirm that the diversity order of GSC is entirely dependent on the secondary network and is equal to the available number of receiver antennas at the SU. This result is consistent with those of maximal-ratio combining (MRC) and selection combining (SC) in cognitive spectrum sharing. More importantly, our results show that the outage probability decreases with the increasing correlation coefficient of the outdated channel. [ABSTRACT FROM PUBLISHER]

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.

In this letter, we propose a beamforming and combining scheme for a two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network. An approximate expression for the symbol error rate of the scheme in Rayleigh fading for M-ary phase-shift keying is obtained based on the moment generating function of the instantaneous received signal-to-noise ratio. The diversity order is also analytically derived. It is shown by simulations that the proposed scheme outperforms existing schemes for beamforming and combining in two-way AF MIMO relay systems. We also discuss beamforming and combining in a two-way AF MIMO relay system with estimated channel gains. [ABSTRACT FROM PUBLISHER]

It also reports simulation-based comparison study with other optimization algorithms such as particle swarm optimization, differential evolution, and whale optimization algorithm. The experiment results of the algorithm in the form of precision are compared with conventional algorithms to draw conclusions about the efficacy of the proposed algorithm. In the paper titled "Analysis of Amplitude Scintillation and Positioning Error of IRNSS/GPS/SBAS Receiver for Heavy Rainy Days", the authors examine the characteristics of amplitude scintillation on an IRNSS/SBAS/GPS receiver with all seven satellites of the Indian Regional Navigation Satellite System (IRNSS) at the low-altitude station IITRAM, Ahmedabad, on days with heavy rain. In the paper "Model Order Reduction Based Power System Stabilizer Design Using Improved Whale Optimization Algorithm", the authors present an optimization technique I viz i . improved whale optimization for designing a power system stabilizer using model-order reduction for a modified single machine infinite bus system. [Extracted from the article]

Cooperative diversity through decode-and-forward (DF) relaying is an effective method for improving the performance of mobile wireless systems. We consider here the performance of a cooperative diversity system in which the relay employs the DF protocol to transmit data from a source to a destination using binary phase-shift keying (BPSK). A flat Rayleigh fading environment with statistically independent links is assumed. The optimum receiver for this system is presented, and from the decision rule, the end-to-end symbol error probability (SEP) is derived. Numerical results on the SEP are obtained and compared with those for a suboptimum receiver, which does not need the channel state information of the source-to-relay link. [ABSTRACT FROM PUBLISHER]

We consider a space-time coded system in a correlated Rayleigh flat fading environment with imperfect channel estimation. Two receiver structures are considered: a suboptimum receiver and the optimum maximum likelihood receiver. The system performance of both receivers is analyzed in terms of the pairwise error probability. [ABSTRACT FROM AUTHOR]

The average of the product of two Gaussian Q-functions having arguments as different scaled versions of the same Nakagami distributed fading gain magnitude is derived in closed-form. Both the cases when (1) the fading parameter is an integer, and (2) the fading parameter is an odd multiple of one-half, are considered. The results are applied to evaluating in closed-form (a) the symbol error probability (SEP) of rectangular quadrature amplitude modulation with maximal-ratio combining in independent Nakagami fading, and (b) the outage probability of a two-user synchronous code-division multiple-access system having signal-to-noise ratio (SNR) imbalance among users in Nakagami fading. It is found in application (a) that with increase in the degree of fading, the robustness to decision distance imbalance between in-phase and quadrature signals increases. In addition, there exists an optimum decision distance ratio at which the SEP has a minimum. In application (b), we find that the outage probability increases sharply with SNR imbalance factor at low SNR imbalance and tends to reach saturation as the imbalance increases. [ABSTRACT FROM AUTHOR]

We consider an antipodal signaling system using wavelet modulation (WM) with scale diversity over a frequency-selective fading channel. The channel introduces a random gain for each scale. These scale gains are estimated by sending a block of pilot symbols before the data. Coherent demodulation is carried out along with maximal-ratio combining using the estimated scale gains. From the characteristic function of the resulting decision variable, we analyze the bit error performance. For the case of large signal-to-noise ratio (SNR), we obtain a closed-form expression for the bit error probability (BEP). It is seen that BEP decreases with increase in the number of pilot symbols. We also find a significant improvement in BEP with increase in the number of scales for a fixed pilot length. It is also found that, when compared with frequency diversity, WM can perform better over a certain range of SNR, with the range decreasing with increase in the number of scales. [ABSTRACT FROM AUTHOR]

We consider a space-time block coded system having L time slots and using decision feedback channel estimation with a finite window size. The channel matrix estimate is updated every L time slots by: 1) a least-squares (LS) estimate and 2) a minimum mean-square error (MMSE) estimate. Using a Markov model of the decision process, we analyze the decoding error probability (DEP) of this scheme in Rayleigh fading. The transition probability matrix is obtained by simulation of the decision process for a system using the Alamouti code. From this matrix, the DEP can be computed for any time shift. We find from computations that the DEP increases with increase in the time shift but tends to saturate with time to a steady-state value. It is also observed that both the state and the transition probabilities tend to saturate with the increase in average signal-to-noise ratio per diversity branch. [ABSTRACT FROM AUTHOR]

In this letter, we analyze the performance of the minimum mean-square error (MMSE) detector for a code-division multiple-access system employing binary phase-shift keying. The performance is measured in terms of the probability distribution and the average number of correctly decoded users. We consider the case of equipower users having equicorrelated signature waveforms. The distribution of the number of correctly decoded users is expressed as an integral over sum of products of Gaussian Q-functions. From it, a closed-form expression for the average number of correctly decoded users is derived. [ABSTRACT FROM AUTHOR]

In a communication system using receive diversity and linear combining in the presence of cochannel interference (CCI), optimum combining (OC) is known to give the best error performance since it maximizes the instantaneous signal-to-interference-plus-noise ratio of the combiner output, and consequently, in the presence of Gaussian interference plus noise, it minimizes the error rate. However, this is based on the assumption that a perfect estimate of the channel is available. Channel estimation methods in reality use some overhead. When the channel is time-invariant, the estimation error decreases with increase in the amount of overhead, like the number of pilot symbols. With the growing need for high data rate applications, the amount of overhead that can be allocated for the estimation of the channel needs to be reduced, and the channel estimation error cannot be ignored. In this situation, replacing the channel by its imperfect estimate in the OC weight vector no longer results in an optimum scheme. We have to find an optimum scheme based on the channel estimation method and the detection criterion, which results in what we call optimized diversity combining (ODC). Here we focus on ODC resulting from a pilot symbol based maximum likelihood (ML) channel estimation method applied to a correlated flat Rayleigh fading channel in the presence of CCI and additive noise. The channel is randomly time-invariant during the reception of pilot and data symbols. The decision rule, which is optimum in the ML sense, is derived using concepts of Gaussian and Wishart statistics. Numerical results show that ODC can perform significantly better than OC with imperfect channnel estimates by appropriate choice of system parameters. [ABSTRACT FROM AUTHOR]

Consider a wireless communication system in flat fading with N transmit and M receive antennas using space-time block coding, where N ⊗ 1 code vectors are transmitted over L symbol intervals, resulting in an N ⊗ L code matrix. A least-squares estimate (LSE) as well as a minimum mean-square estimate (MMSE) of the M ⊗ N channel matrix is obtained from a sequence of pilot code vectors. For the case of linear square (i.e., with N = L) orthogonal codes over constant envelope constellations, we obtain an expression for the exact decoding error probability (DEP) for coherent maximum-likelihood decoding. We also find the coding gain for high average signal-to-noise ratio (SNR) per diversity branch in the case of Rayleigh fading. A comparison between both channel-estimation techniques is done in terms of the average pilot-power-to-signal-power ratio (APPSPR). It is found that MMSE requires lower pilot power than LSE for the same DEP and the same average SNR per diversity branch. In addition, the error performance with LSE approaches that with MMSE, with an increase of average SNR per branch or an increase of APPSPR. [ABSTRACT FROM AUTHOR]

We present closed-form lower bounds for the performance of multihop transmissions with nonregenerative relays over not necessarily identically distributed Nakagami-m fading channels. The end-to-end signal-to-noise ratio is formulated and upper bounded by using an inequality between harmonic and geometric means of positive random variables (RVs). Novel closed-form expressions are derived for the moment generating function, the probability density function, and the cumulative distribution function of the product of rational powers of statistically independent Gamma RVs. These statistical results are then applied to studying the outage probability and the average bit-error probability for phase-and frequency-modulated signaling. Numerical examples compare analytical and simulation results, verifying the tightness of the proposed bounds. [ABSTRACT FROM AUTHOR]

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 SNRs is considered. By transforming the ordered instantaneous branch SNRS 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 (cf.) of the combiner output SNR. This cf. is used to obtain the symbol error probability for different coherent digital modulation schemes. [ABSTRACT FROM AUTHOR]

We analyze the error performance of an improved hybrid selection/maximal-ratio combining (H-S/MRC) technique called minimum selection H-S/MRC in flat Rayleigh fading for coherent digital modulation schemes. Here the minimum number of diversity branches are selected such that their combined signal-to-noise ratio is above a given threshold. We derive a closed-form expression for the distribution of the number of selected branches. This distribution is used to obtain the symbol error probability. [ABSTRACT FROM AUTHOR]

The pseudo-Wishart distribution arises when a Hermitian matrix generated from a complex Gaussian ensemble is not full-rank. It plays an important role in the analysis of communication systems using diversity in Rayleigh fading. However, it has not been extensively studied like the Wishart distribution. Here, we derive some key aspects of the complex pseudo-Wishart distribution. Pseudo-Wishart and Wishart distributions are treated as special forms of a Wishart-type distribution of a random Hermitian matrix generated from independent zero-mean complex Gaussian vectors with arbitrary covariance matrices. Using a linear algebraic technique, we derive an expression for the probability density function (pdf) of a complex pseudo-Wishart distributed matrix, both for the independent and identically distributed (i.i.d.) and non-i.i.d. Gaussian ensembles. We then analyze the pseudo-Wishart distribution of a rank-one Hermitian matrix. The distribution of eigenvalues of Wishart and pseudo-Wishart matrices is next considered. For a matrix generated from an i.i.d. Gaussian ensemble, we obtain an expression for the characteristic function (cf) of eigenvalues in terms of a sum of determinants. We present applications of these results to the analysis of multiple-input multiple-output (MIMO) systems. The purpose of this work is to make researchers aware of the pseudo-Wishart distribution and its implication in the case of MIMO systems in Rayleigh fading, where the transmitted signals are independent but the received signals are correlated. The results obtained provide a powerful analytical tool for the study of MIMO systems with correlated received signals, like systems using diversity and optimum combining, space-time systems, and multiple-antenna systems. [ABSTRACT FROM AUTHOR]

Consider a Rake receiver for coherent binary antipodal signaling with: 1) a delayed received signal configuration; 2) weight estimation by matched filtering using the reference signal along with the decisions of the previous M symbol intervals; and 3) predetection maximal ratio combining (MRC). The weight estimation errors here are not independent of the additive noise, and do not fit into the Ganssian weighting error model for MRC. Here we analyze the error performance of the receiver by obtaining the conditional symbol error probability, conditioned on past decisions, from the characteristic function of the decision variable, and getting the unconditional error probability (UEP) for a block of M consecutive symbols using a Markov model of the decision process. The channel is Rayleigh fading with independent and identically distributed branch gains. Results show that the error performance of the Gaussian distributed weighting error model is a bound for that of multiple symbol weight estimation by matched filtering, and the steady state UEP decreases with increase of M, but the amount of decrease reduces as M increases. [ABSTRACT FROM AUTHOR]

Presents the expressions for multivariate Rayleigh and exponential probability density functions (pdfs) generated from correlated Gaussian random variables. Presentation of a general integral form of the pdfs; Derivation of a general expression for the multivariate exponential characteristic function in terms of determinants; Use of the series and determinant expressions for the exponential cfs.

We derive an upper bound and investigate some approximatious 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. [ABSTRACT FROM AUTHOR]

Presents a study which derived the bit error probability for coherent detection of binary signals with dual-diversity predetection equal gain combining using the Beauliue series. Analysis of predetection equal gain combining with dual diversity in Rayleigh fading; Expression for the bit error probability; Mechanism of the equal gain combining.