Generalized Selection Combining Research Articles

Adaptive generalised selection-combining receiver over time-varying mobile communication channel

An adaptive generalised selection-combining (GSC) receiver is proposed for time-varying frequency selective fading channel. The receiver adaptively selects and combines a subset of diversity branches out of the available branches and discards the others. This is performed by comparing the maximum likelihood (ML) metric of each diversity branch with a threshold. The branches that are lower than the threshold are selected and combined using maximal ratio combiner. The proposed adaptive GSC receiver dynamically adjusts the threshold value according to the time variations of the channel. Equalisation and data detection are performed after combining using ML sequence estimation implemented by Viterbi algorithm. The minimum survivor technique is employed to reduce the complexity of the receiver. An upper bound for the probability of error of the proposed receiver is derived. The performance of the proposed adaptive GSC receiver is compared with the performance of different threshold GSC receivers.

Joint Statistics of Partial Sums of Ordered Exponential Variates and Performance of GSC RAKE Receivers over Rayleigh Fading Channel

Spread spectrum receivers with generalized selection combining (GSC) RAKE reception were proposed and have been studied as alternatives to the classical two fundamental schemes: maximal ratio combining and selection combining because the number of diversity paths increases with the transmission bandwidth. Previous work on performance analyses of GSC RAKE receivers based on the signal to noise ratio focused on the development of methodologies to derive exact closed-form expressions for various performance measures. However, some open problems related to the performance evaluation of GSC RAKE receivers still remain to be solved such as the exact performance analysis of the capture probability and an exact assessment of the impact of self-interference on GSC RAKE receivers. The major difficulty in these problems is to derive some joint statistics of ordered exponential variates. With this motivation in mind, we capitalize in this paper on some new order statistics results to derive exact closed-form expressions for the capture probability and outage probability of GSC RAKE receivers subject to self-interference over independent and identically distributed Rayleigh fading channels, and compare it to that of partial RAKE receivers.

Performance of Adaptive MS-GSC in the Presence of Cochannel Interference

Minimum-selection generalized selection combining (MS-GSC) has been proposed as a power-saving variant of conventional generalized selection combining (GSC). Existing performance results of this scheme are limited to interference-free environments under multipath fading. This paper addresses the scenario when the received desired signal on each diversity branch is corrupted by multiple interfering signals and background noise, wherein desired and undesired signals undergo mutually independent Rayleigh fading. In the absence of perfect tracking of the instantaneous interference power on diversity branches, the adaptation thresholds that are set on the combined signal-to-noise ratio (SNR) to enhance either the spectral efficiency or power efficiency in noise-limited environments may not guarantee the target performance. This paper aims to study the effect of cochannel interference on the performance of bandwidth- and power-efficient SNR-based MS-GSC. Through the analysis, new analytical results for some important performance measures of adaptive MS-GSC schemes are presented. Numerical comparisons to clarify the impact of cochannel interference on the achieved performance of the adaptation schemes under consideration are provided.

Generalised selection combining diversity performance of multi-element antenna systems via a stochastic electromagnetic-circuit methodology

A stochastic electromagnetic-circuit methodology for evaluating the generalised selection combining (GSC) diversity performance of coupled and arbitrarily terminated multi-element antenna (MEA) systems when operating in Rayleigh fading environments is proposed. The methodology is based on the effective length matrix, which connects the incident electric fields to the received voltage and current vectors, and on the newly introduced stochastic generation of realistic propagation environments by means of the angular power density functions and the cross polarisation power ratio of the incoming plane waves. The generated statistical ensemble of voltage and current vectors is then used to determine the receive GSC diversity performance metrics, that is mean effective gain (MEG), envelope correlation coefficient (ρe) and effective diversity gain (EDG). Two compact MEA configurations comprising two and four printed inverted F antennas (IFA) operating in a uniform propagation scenario at the 5.2 GHz band are investigated under various GSC schemes, which include the selection (SC) and the maximal ratio (MRC) as special cases. The simulated values of MEG, ρe and EDG under the MRC scheme are in excellent agreement to those obtained from well-established closed-form methodologies.

Error analysis of generalized selection combining over relay channel

Cooperative communication is a recently popular concept which allows single-antenna devices to benefit from spatial diversity. The performance analysis of cooperative communication using generalized selection combining (GSC) over independent not necessarily identically distributed Nakagami- m fading channels is presented and compared with that of the conventional maximal ratio combining (MRC) and selection combining (SC) schemes. With the aid of Padé approximants theory, new closed-form expression is derived for the moment-generating function (MGF) of the GSC output signal-to-noise ratio (SNR). MGF is an important tool for researching the system performance. In this paper, the average bit-error probability is accurately approximated using the well-known MGF approach. Numerical results show that the proposed mathematical analysis is accurate and that for the more severe fading cases, the GSC receivers are closer to the optimum MRC receivers.

BER Analysis of Multi-Hop Decode-and-Forward Relaying with Generalized Selection Combining

Generalized selection combining (GSC) was recently proposed as a low-complexity diversity combining technique for diversity-rich environments. This letter proposes a multi-hop Decode-and-Forward Relaying (MDFR) scheme in conjunction with GSC and describes its performance in terms of average bit error probability. We have shown that the proposed protocol offers a remarkable diversity advantage over direct transmission as well as the conventional decode-and-forward relaying (CDFR) scheme. Simulation results are also given to verify the analytical results.

Average SNR of maximum ratio transmission with selection combining

Two kinds of selection combining schemes including generalized selection combining (GSC) and generalized order selection combining (GOSC) are investigated. In the GSC scheme, L strongest diversity branches from a total of R diversity branches are selected and coherently combined by maximal ratio combining. GOSC means that the Lth strongest diversity branch from R diversity branches is selected for reception. Closed-form expressions for the average signal-to-noise ratios of maximum ratio transmission with GSC and GOSC are derived in Rayleigh fading channels.

Performance Evaluation of Generalized Selection Combiners Over Slow Fading with Estimation Errors

In this paper we derive closed-form expressions for the single-user adaptive capacity of generalized selection combining (GSC) system, taking into account the effect of imperfect channel estimation at the receiver. The channel considered is a slowly varying spatially independent flat Rayleigh fading channel. The complex channel estimate and the actual channel are modelled as jointly Gaussian random variables with a correlation that depends on the estimation quality. Three adaptive transmission schemes are analyzed: (1) optimal power and rate adaptation; and (2) constant power with optimal rate adaptation, and (3) channel inversion with fixed rate. In addition to deriving an exact expression for the capacity of the aforementioned adaptive schemes, we analyze the impact of channel estimation error on the capacity statistics and the symbol error rate for GSC systems. The capacity statistics derived in this paper are the moment generating function, complementary cumulative distribution function and probability density function for arbitrary number of receive antennas. Moreover, exact closed-form expressions for M-PAM/PSK/QAM employing GSC are derived. As expected, the channel estimation error has a significant impact on the system performance.

Performance of Cellular Mobile Systems Employing SNR-Based GSC in the Presence of Rayleigh and Nakagami-$q$ Cochannel Interferers

This paper studies the performance of cellular mobile systems employing a signal-to-noise ratio (SNR)-based generalized selection combining (GSC) algorithm in the presence of background white noise and multiple cochannel interfering signals. Closed-form expressions are derived for the received signal-to-interference-plus-noise ratio (SINR) distribution and outage probability, considering the case when the interfering signals experience mixed Rayleigh and Nakagami-q fading conditions, and the desired signal replicas are attenuated by flat Rayleigh fading. These expressions are obtained via the new representation of the total interference-to-noise ratio (INR) distribution for the mixed mode of fading experienced by different interferers. The derived expressions for the aforementioned statistical measures are valid for an arbitrary number of interferers and system diversity order and can be employed to investigate the impact of various system and fading parameters on the performance measures. Several case studies can be deduced from the results presented in this paper, including interference-limited systems, wherein the impact of white noise can be neglected.

A trivariate nakagami-m distribution with arbitrary covariance matrix and applications to generalized-selection diversity receivers

This paper deals with a trivariate Nakagami-m distribution derived from the diagonal elements of a Wishart matrix. For this distribution, infinite series representations for its probability density and cumulative distribution functions are derived having an arbitrary covariance matrix and integer-order fading parameters. Moreover, upper bounds on the error resulting from truncating the infinite series are obtained. Based on the derived formulas, the performance of triple-branch generalized selection combining (GSC) receivers is analyzed. For this type of receivers, the outage and the average bit error probability for a variety of modulation schemes are analytically obtained. The performance of GSC receivers is compared to that of conventional selection and maximal-ratio diversity schemes. In order to check the accuracy and convergence of the derived formulas, various performance evaluation results are presented and compared to equivalent simulation ones.

Generalized receiver selection combining schemes for alamouti MIMO systems with MPSK

Analytical results for the symbol error rate (SER) of M-ary phase shift keying (MPSK) in a slow, flat Rayleigh fading channel for a multiple-input multiple-output (MIMO) system using an Alamouti transmission scheme and generalized selection combining (GSC) scheme are given. Two new receiver selection schemes, generalized space-time sum-of-squares (GSTSoS) selection diversity and generalized space-time sum-of-magnitudes (GSTSoM) selection diversity are proposed. The first provides the same performance as conventional GSC, and the second provides slightly poorer performance, but neither requires channel state information and both have much simpler implementations. The SER of MPSK in Rayleigh fading using these two selection schemes is studied and compared to that of conventional GSC. The effects of channel estimation errors on each selection scheme are examined.

Finger management schemes for RAKE receivers with a minimum call drop criterion

We propose and analyze in this letter new finger management techniques which are applicable for RAKE receivers operating in the soft handover region. These schemes employ "distributed" types of generalized selection combining (GSC) and minimum selection GSC schemes in order to minimize the impact of sudden connection loss of one of the active base stations. By accurately quantifying the average error rate, we show through numerical examples that our newly proposed distributed schemes offer a clear advantage in comparison with their conventional counterparts.

Impact of Nonidentical Branches on the Switching Rate of Generalized Selection Combining in Rayleigh Fading Channels

In this paper, we extend the switching rate analysis of M out of N generalized selection combining (GSC) in an earlier paper of Cavers and Ho to the case of nonidentical branches. Despite the fact that nonidentical branches introduce a correlation between the difference of the Mth and the M + 1th strongest signals u(t) and its derivative u acute(t), we were able to derive an analytical expression for the switching rate of the GSC receiver under this condition (independence between u(t) and u acute(t) is crucial in obtaining the simple results in Cavers and Ho). Our numerical results agree with the intuition that having nonidentical branches reduces the switching rate. The more dissimilar the branches are, the larger the reduction. While this lowering of the switching rate allows the GSC receiver more time to dwell on the selected signals, hence producing more accurate channel estimates for coherent combining, the bit-error rate of GSC, unfortunately, is higher when the branches are not identical.

Symbol Error Rate Expression for Decode-and-Forward Relaying Using Generalized Selection Combining over Rayleigh Fading Channels

Cooperative transmission is an efficient approach to improve the performance of wireless communications over fading channels without the need for physical co-located antenna arrays. In this paper, we propose a novel cooperative protocol with selective decode-and-forward relays and generalized selection combining (GSC) technique at destination. The advantage of this scheme is that it not only allows us to optimize the structure of destination but also to fully exploit the diversity offered by the channels with an appropriate number of chosen strongest paths. For an arbitrary number of relays, an exact and closed-form expression of the Symbol Error Rate (SER) is derived for M-ary PSK in independent but not identically distributed Rayleigh fading channels. Various simulations are performed and their results exactly match the results of analyses.

Adaptive rake combining in the soft handover region

We propose and analyze new finger assignment schemes which are applicable for RAKE reception in the soft handover region. These schemes rely on variants of the conventional generalized selection combining (GSC) and the minimum selection GSC schemes in order to choose an acceptable base station and its corresponding paths. Relying on some recently derived results on order statistics, we investigate the average error rate performance as well as the average number of estimated and combined paths of the proposed schemes over independent and identically distributed Rayleigh fading channels. The mathematical formalism is illustrated with few selected numerical results that show the tradeoff between performance and processing power consumption.

Performance of generalized selection combining receivers in K fading channels

In this letter, we present a moment generating function (MGF) based performance analysis of generalized selection combining (GSC) receivers operating over independent and identically distributed (i.i.d.) K fading channels. Analytical expressions for the marginal MGF of the signal-to-noise ratio of a single diversity branch for integer plus one-half values of the fading parameter are obtained and used to efficiently evaluate the average error probability of GSC receivers.

Performance of Coded Systems with Generalized Selection Diversity in Nakagami Fading

We investigate the performance of coded diversity systems employing generalized selection combining (GSC) over Nakagami fading channels. In particular, we derive a numerical evaluation method for the cutoff rate of the GSC systems. In addition, we derive a new union bound on the bit-error probability based on the code's transfer function. The proposed bound is general to any coding scheme with a known weight distribution such as convolutional and trellis codes. Results show that the new bound is tight to simulation results for wide ranges of diversity order, Nakagami fading parameter, and signal-to-noise ratio (SNR).

Finger assignment schemes for RAKE receivers with multiple-way soft handover

We propose and analyze new finger assignment techniques that are applicable for RAKE receivers in the soft handover (SHO) region. Specifically, extending the results for the case of two-base station (BS), we consider the multi-BS situation, attack the statistics of several correlated generalized selection combining (GSC) stages, and provide closed-form expressions for the statistics of the output signal-to-noise ratio (SNR). By investigating the tradeoff among the error performance, the average number of required path estimations/comparisons, and the SHO overhead, we show through numerical examples that the new schemes offer commensurate performance in comparison with more complicated GSC-based diversity systems while requiring a smaller estimation load and SHO overhead.

Soft handover overhead reduction by RAKE reception with finger reassignment

We propose and analyze in this paper a new finger assignment technique that is applicable for RAKE receivers when they operate in the soft handover (SHO) region. This scheme employs a new version of generalized selection combining (GSC). More specifically, in the SHO region, the receiver uses by default only the strongest paths from the serving base station (BS) and only when the combined signal-to-noise ratio (SNR) falls below a certain pre-determined threshold, the receiver uses more resolvable paths from the target BS to improve the performance. Hence, relying on some recent results on order statistics we attack the statistics of two correlated GSC stages and provide the approximate but accurate closed-form expressions for the statistics of the output SNR. By investigating the tradeoff among the error performance, the path estimation load, and the SHO overhead, we show through numerical examples that the new scheme offers commensurate performance in comparison with more complicated GSC-based diversity systems while requiring a smaller estimation load and SHO overhead.

Tradeoff Analysis of Performance and Complexity on GSECps Diversity Combining Scheme

Generalized switch and examine combining (GSEC) was recently proposed as a low-complexity diversity combining scheme for diversity-rich environment. In this paper, we present and analyze a modified version of GSEC scheme, termed as GSEC with post-examine selection (GSECps). The GSECps scheme operates in the same way as GSEC when channel conditions are favorable and becomes equivalent to the generalized selection combining (GSC) scheme otherwise. We show, through a thorough and accurate tradeoff analysis of performance versus complexity, that GSECps can deliver a better performance-complexity tradeoff than both GSEC and GSC schemes.