Highly Accurate Closed-Form Approximations to the Sum of α-μVariates and Applications

Sums of fading envelopes occur in several wireless communications applications, such as equal-gain combining, signal detection, outage probability, intersymbol interference, etc. The exact evaluation of the sum statistics is known to be very intricate. One of the purposes of this Letter is to provide highly accurate closed-form approximations to the probability density function and cumulative distribution function of the sum of independent identically distributed (i.i.d.)α-μ(generalized gamma) variates. Based on and as an extension of such an approach, simple precise approximations for the performance metrics of equal-gain combining and maximal-ratio combining receivers operating on i.i.d. /spl alpah/-μ fading channels are proposed. Samples examples are given to illustrate that, for practical purposes, exact and approximate solutions are indistinguishable from each other.     

Transmit antenna selection for decision feedback detection in MIMO fading channels

In this paper, we investigate a transmit antenna selection (TAS) approach for the decision-feedback detector (DFD) over Rayleigh fading channels. In particular, for a multipleinput multiple-output (MIMO) channel with M transmit and N (N ⩾ M) receive antennas, we derive a lower bound on the outage probability for the TAS approach. The selected transmit antennas are those that maximize the post-processing signalto- noise ratio (SNR) at the receiver end. It is shown that the proposed TAS approach achieves a performance close to optimal selection based on exhaustive search, introduced in the literature, but at a lower complexity. Simulation results are presented to validate and demonstrate the performance gain of the proposed TAS approach.     

Performance analysis of dual MRC receiver in correlated hoyt fading channels

Performance of a dual maximal ratio combining receiver has been analyzed in correlated Hoyt fading channels. Analytical expressions for the probability density function of the receiver output signal-to-noise ratio (SNR), average SNR, outage probability and average bit error rate performance for binary, coherent and non-coherent modulations have been presented. Numerical results show that for coherent phase shit-keying and differential phase shift-keying modulations, to achieve an ABER of 10^?7, the required excess SNR is relatively small for correlation coefficient (?) less than 0.5 than it is for ? ≫ 0.5.     

Closed‐Form Expressions for Selection Combining System Statistics over Correlated Generalized‐K Fading Channels in the Presence of Interference

This paper considers the effects of simultaneous correlated multipath fading and shadowing on the performances of a signal‐to‐interference ratio (SIR)‐based dual‐branch selection combining (SC) diversity receiver. This analysis includes the presence of cochannel interference. A generalized fading/shadowing channel model in an interference‐limited correlated fading environment is modeled by generalized‐K distribution. Closed‐form expressions are obtained for probability density function and cumulative distribution function of the SC output SIR, as well as for the outage probability. Based on this, the influence of various fading and shadowing parameter values and the correlation level on the outage probability is examined.     

Feedback gain in multiple antenna systems

Multiple antenna transmission and reception have been shown to significantly increase the achievable data rates of wireless systems. However, most of the existing analysis assumes perfect or no channel information at the receiver and transmitter. The performance gap between these extreme channel assumptions is large and most practical systems lie in between. Therefore, it is important to analyze multiple antenna systems in the presence of partial channel information. We upper bound the outage probability performance of multiple antenna systems with preamble-based channel estimation and quantized feedback. We design causal feedback and power control schemes to minimize this upper bound on outage probability. We consider the following practical issues in our analysis and design: (1) the channel information is imperfect both at the receiver and at the transmitter and (2) part of the total available resources for the system need to be used for estimation and feedback. Our results demonstrate that for block fading channels, sending a periodic preamble and causally receiving channel state information via a feedback channel can lead to substantial gains in the outage performance over any nonfeedback scheme. Most of the gains achieved by perfect feedback can be achieved by very few bits of feedback. Furthermore, it is demonstrated that these outage probability gains can be translated into improvements in frame error rate performance of systems using space-time codes. Thus, implementing a power control, even at the cost of reduced spectral resources for the forward channel is beneficial for block fading channels     

Outage Probability Analysis of Cooperative Diversity Networks Over Weibull and Weibull-Lognormal Channels

This paper presents the analysis of outage probability for a cooperative diversity wireless network using amplify-and-forward relays over independent non-identical distributed Weibull and Weibull-lognormal fading channels for single as well as multiple relays. To reach that end, a closed-from expression for the moment-generating function of the total signal-to-noise-ratio (SNR) at the destination is derived in terms of the tabulated Meijer’s G-function. Since it is hard to determine the exact probability distribution function of the SNR, a tight lower bound approximation is proposed. Simulation results are presented that show that the outage probability lower bound tends to be tight at high SNR values thus verifying the analytical results. The results also show the potential gain of relaying on the outage probability.     

Simple and accurate methods for outage analysis in cellular mobileradio systems-a unified approach

Two unified expressions for computing the refined outage criterion (which considers the receiver noise) in cellular mobile radio systems are derived using the Laplace and Fourier inversion formulas. Since these expressions do not impose any restrictions on the signal statistics while being easy to program, they provide a powerful tool for outage analysis over generalized fading channels. We also assess compatibility and applicability of previously published approaches that treat noise as cochannel interference (noise-limited model) or consider a minimum detectable receiver signal threshold and receiver noise. The outage probability in an interference-limited case can be evaluated directly by setting the minimum power threshold to zero. The analysis of correlated interferers is presented. Results are also developed for a random number of interferers. Several new closed-form expressions for the outage probability are also derived. Some previous studies have suggested approximating Rician desired signal statistics by a Nakagami-m (1960) model (with positive integer fading severity index) to circumvent the difficulty in evaluating the outage in Rician fading. The suitability of this approximation is examined by comparing the outage performance under these two fading conditions. Surprisingly, some basic results for Nakagami-m channel have been overlooked, which has led to misleadingly optimistic results with the Nakagami-m approximation model. However, similar approximation for the interferer signals is valid     

Outage Performance of Cognitive AF Relay Networks with Imperfect CSI Based on Geometrical Analysis

This paper studies the outage performance of a cognitive Amplify-and-forward (AF) relay network subject to Rayleigh fading.Under the condition of imperfect Channel state information (CSI) estimations of the links from the secondary system to the Primary user (PU),the closed-form upper and lower bounds of the outage probability are derived through a geometrical analysis method.An asymptotic analysis of the outage probability is also derived in the high Signal-to-noise ratio (SNR) regime to gain additional insights on the system.The simulation results corroborate our theoretical analysis,and the effectiveness of the geometrical analysis method is verified with the conventional approach as a benchmark.The asymptotic results are very tight with the analytical lower bound in the high SNR regime.It also can be observed from the simulation results that the impact of the number of relays as well as the imperfect CSI on the outage probability and the diversity order.     

Power and rate control with outage constraints in CDMA wireless networks

A radio power control strategy to achieve maximum throughput for the up-link of CDMA wireless systems with variable spreading factor is investigated. The system model includes slow and fast fading, rake receiver, and multi-access interference caused by users with heterogeneous data sources. The quality of the communication is expressed in terms of outage probability, while the throughput is defined as the sum of the users' transmit rates. The outage probability is accounted for by resorting to a lognormal approximation. A mixed integer-real optimization problem P1, where the objective function is the throughput under outage probability constraints, is investigated. Problem P1 is solved in two steps: firstly, we propose a modified problem P2 to provide feasible solutions, and then the optimal solution is obtained with an efficient branch-and-bound search. Numerical results are presented and discussed to assess the validity of our approach.     

Outage probability of SC receiver over exponentially correlated K fading channels

A mathematical expression for the outage probability of a selection combining diversity receiver with an arbitrary number of input branches is presented for exponentially correlated K fading channels. Numerical and simulation results are plotted and the effect of correlation, number of diversity branches and fading parameter on the outage performance of the receiver is studied. Results suggest that a correlation coefficient less than 0.5 may be used in practice.     

Capacity of MIMO Rician channels

This paper presents exact results on the capacity of multiple-input-multiple-output (MIMO) Rician channels when perfect channel state information (CSI) is assumed at the receiver but the transmitter has neither instantaneous nor statistical CSI. It first derives the exact expression for the average mutual information (MI) rate of MIMO Rician fading channels when the fading coefficients are independent but not necessarily identically distributed. The results for the independent and identically distributed (i.i.d.) MIMO Rician and Rayleigh fading channels are also obtained as special cases. These results are derived using a different approach than the one used by Telatar for the i.i.d. Rayleigh case. The complementary cumulative distribution function (CCDF) of the MI is also obtained using a Gaussian approximation. The CDF of MI can serve as an upper bound to the outage probability of nonergodic MIMO Rician channels. Numerical results confirm that for a fixed channel gain, a strong tine-of-sight component decreases the channel capacity due to the lack of scattering.     

How fading affects CDMA: an asymptotic analysis with linearreceivers

Using asymptotic analysis, we study the effect of frequency-flat fading on code division multiple access (CDMA) systems with linear receivers and random spreading sequences. Specifically, we let the number of users grow without bound, while the ratio of number of users to spreading sequence length is kept fixed to a value α. We treat separately the cases of slow fading (nonergodic channel) and of fast fading (ergodic channel). For the former channel, we derive the outage probability, while for the latter we compute the channel capacity. In both cases, multiple classes of users with different qualities of service are dealt with. As α→∞, the system throughput tends to the same limit of 1.44 bit/symbol as for the nonfading channel with both single-user matched filter (SUMF) and linear minimum mean-square-error (MMSE) receivers. The outage probability exhibits a floor for all α with the SUMF receivers, while with MMSE receiver the floor is present only for α>1. We also address the tradeoffs involved in the allocation of available bandwidth between spreading and coding     

Asymptotic SEP for M-PSK Signals overα-μFading Channels

The α-μfading is a general physical model recently rewritten from the Stacy (or generalized gamma) distribution, encompassing a variety of fading environments such as Rayleigh, Nakagami-m, and Weibull fading. We characterize the asymptotic average symbol error probability (SEP) at a high signalto- noise ratio (SNR)?specifically, the high-SNR slope and power gain?in terms of two physical fading parametersαandμ. We further extend the asymptotic SEP analysis to a multiple-input multiple-output diversity system employing orthogonal space? time block codes inα-μfading channels.     

The multivariate α-μ distribution

An infinite series formulation for the multivariate α-μ joint probability density function with arbitrary correlation matrix and non-identically distributed variates is derived. The expression is exact and general and includes all of the results previously published in the literature concerning the distributions comprised by the α-μ distribution. The general expression is then particularized to an indeed very simple, approximate closed-form solution. In addition, a multivariate joint cumulative distribution function is obtained, again in simple, closed-form manner. As an application example, the exact and approximate performances of the selection combining scheme given in terms of the outage probability is shown. Approximate and exact results are very close to each other for small as well as medium values of correlation.     

Performance analysis of SSC diversity receiver over correlated Ricean fading channels in presence of co-channel interference

A novel infinite-series-based approach for the performance analysis of a dual-branch switched-and-stay combining (SSC) diversity receiver operating over Ricean correlated fading channels in the presence of correlated Nakagami-m distributed co-channel interference (CCI) is presented. The performance analysis is based on outage probability (P_out) and average bit error probability (ABEP) criteria.     

Energy‐efficient outage‐constrained power allocation based on statistical channel knowledge for dual‐hop cognitive relay networks

This paper investigates the power allocation problem in decode‐and‐forward cognitive dual‐hop systems over Rayleigh fading channels. In order to optimize the performance of the secondary network in terms of power consumption, an outage‐constrained power allocation scheme is proposed. The secondary nodes adjust their transmit power subject to an average interference constraint at the primary receiver and an outage probability constraint for the secondary receivers while having only statistical channel knowledge with respect to the primary nodes. We compare this approach with a power allocation scheme based on instantaneous channel state information under a peak interference constraint. Analytical and numerical results show that the proposed approach, without requiring the constant interchange of channel state information, can achieve a similar performance in terms of outage probability as that of power allocation based on instantaneous channel knowledge. Moreover, the transmit power allocated by the proposed approach is considerably smaller than the power allocated by the method based on instantaneous channel knowledge in more than 50% of the time. Copyright © 2015 John Wiley & Sons, Ltd.     

Selection diversity for wireless communications in Nakagami-fadingwith arbitrary parameters

By means of analytical and numerical methods, the probability of error and the outage probability of a selection diversity RAKE receiver system employing direct sequence/code division multiple access (DS/CDMA) is derived. A noise-limited propagation environment is modeled as a Nakagami (1960)-fading channel with arbitrary fading parameters and unequal mean power at the receiver. New analytical expressions are derived for the average probability of error and outage probability. Binary detection schemes are considered including binary phase-shift keying (PSK) and frequency-shift keying (FSK). Both coherent and noncoherent detection is considered as well as identical and arbitrary fading. It is shown that the effect of arbitrary fading on system performance is significant and may not be ignored     

On the outage probability of large scale decode-and-forward relay wireless networks

This paper considers a wireless network consisting of large number of clusters, wherein each cluster represents a decode-and-forward (DF) relay network. Two main scenarios according to the distances among the nodes in the network are investigated. In the case of deterministic distances, the outage probability is obtained in a closed-form expression. Whereas for the case when these distances are independent random variables, the framework of Stochastic Geometry (SG) is exploited for deriving the closed-form of the outage probability in case of Rayleigh fading channel. Furthermore, a lower and upper bound for the outage probability in case of general fading channel have been also provided. Numerical simulations are carried out to validate the derived analytical expressions, and to illustrate how the obtained results can be utilized in interference management of such networks.     

Outage probability of multiple-input single-output (MISO) systems with delayed feedback

We investigate the effect of feedback delay on the outage probability of multiple-input single-output (MISO) fading channels. Channel state information at the transmitter (CSIT) is a delayed version of the channel state information available at the receiver (CSIR). We consider two cases of CSIR: (a) perfect CSIR and (b) CSI estimated at the receiver using training symbols. With perfect CSIR, under a short-term power constraint, we determine: (a) the outage probability for beamforming with imperfect CSIT (BF-IC) analytically, and (b) the optimal spatial power allocation (OSPA) scheme that minimizes outage numerically. Results show that, for delayed CSIT, BF-IC is close to optimal for low SNR and uniform spatial power allocation (USPA) is close to optimal at high SNR. Similarly, under a longterm power constraint, we show that BF-IC is better for low SNR and USPA is better at high SNR. With imperfect CSIR, we obtain an upper bound on the outage probability with USPA and BF-IC. Results show that the loss in performance due to imperfection in CSIR is not significant, if the training power is chosen appropriately.     

Performance of M-MRC receivers over TWDP fading channels

An expression of characteristic function of signal-to-noise ratio (SNR) for two waves with diffused power (TWDP) fading channel is derived. Using this expression, the expression for the probability density function (PDF) of the output SNR of maximal ratio combining (MRC) receiver is obtained. Expressions for the performance matrix of MRC receiver over TWDP fading channels are also deduced. PDF based approach is followed to derive expressions of outage probability and average symbol error rate for coherent and non-coherent m-ary modulation schemes. Effects of the number of branches M and the fading parameters K and Δ on the system performance are studied. The results obtained are verified by Monte Carlo simulation.