 Research Article
 Open Access
SSC Diversity Receiver over Correlated Fading Channels in the Presence of Cochannel Interference
 Petar Ć. Spalević^{1},
 Stefan R. Panić^{2}Email author,
 Ćemal B. Dolićanin^{3},
 Mihajlo Č. Stefanović^{2} and
 Aleksandar V. Mosić^{2}
https://doi.org/10.1155/2010/142392
© Petar Ć. Spalević et al. 2010
 Received: 16 August 2009
 Accepted: 31 January 2010
 Published: 9 March 2010
Abstract
This paper studies the performances of a dualbranch switchedandstay combining (SSC) diversity receiver, operating over correlated fading in the presence of cochannel interference (CCI). Very useful, novel, infinite series expressions are obtained for the output signal to interference ratio's (SIR's) probability density function (PDF) and cumulative distribution function (CDF). The performance analysis is based on an outage probability (OP) and an average bit error probability (ASEP) criteria. ASEP is efficiently evaluated for modulation schemes such as noncoherent frequencyshift keying (NCFSK) and binary differentially phaseshift keying (BDPSK). The effects of various parameters, such as input SIR unbalance, the level of correlation between received desired signals and interferences, nonlinearity of the environment, and fading severity on systems performances are graphically presented and analyzed.
Keywords
 Fading Channel
 Probability Distribution Function
 Outage Probability
 Modulation Scheme
 Symbol Error Probability
1. Introduction
Various techniques for reducing the fading effects and the influence of the cochannel interference (CCI) are used in wireless communication systems [1]. The two main goals of the diversity techniques are upgrading the transmission reliability without increasing transmission power and bandwidth and increasing the channel capacity. Space diversity is an efficient method for amelioration of system's quality of service (QoS) when multiple receiver antennas are used. There are several principal types of combining techniques and division, that can be generally performed depending on the complexity restriction put on the communication system and the amount of channel state information available at the receiver.
However, switch and stay combining (SSC) is the least complex and can be used in conjunction with coherent, noncoherent, and differentially coherent modulation schemes. In general, with SSC diversity considered in this paper, the receiver selects a particular branch until its signaltonoise ratio (SNR) drops below a predetermined threshold. When this happens, the combiner switches to another branch and stays there regardless of whether the SNR of that branch is above or below the predetermined threshold [1–3]. In fading environments as in cellular systems, where the level of CCI is sufficiently high as compared to the thermal noise, SSC selects a particular branch until its signaltointerference ratio (SIR) drops below a predetermined threshold (SIRbased switched diversity). Then the combiner switches to another branch and stays there regardless of SIR of that branch. This type of diversity, in which switching is based on the SIR value, can be measured in real time both in base stations (uplink) and in mobile stations (downlink) using specific SIR estimators.
The multipath fading in wireless communications is modelled by several distributions including Weibull, Nakagamim Hoyt, Rayleigh, and Rice. By considering two important phenomena inherent to radio propagation, namely, nonlinearity and clustering, the  fading model was proposed and discussed in [4–7]. The model provides a very good fit to measured data over a wide range of fading conditions. The  distribution is written in terms of physicallybased fading parameters, namely, and . Roughly speaking, is related to the nonlinearity of the environment, whereas is associated with the number of multipath clusters. The diversity reception over  fading channels was previously discussed in [8–11].
There is a number of papers concerning performance analysis of SSC receivers, for example, [12–15]. The performance analysis of SSC diversity receivers, operating over correlated Ricean fading satellite channels, can be found in [13], where the performance is evaluated based on a bunch of novel analytical formulae for the outage probability (OP), average symbol error probability (ASEP), channel capacity (CC), the amount of fading (AoF), and the average output SNR obtained in infinite series form. The similar performance analysis of the switched diversity receivers operating over correlated Weibull fading channels in terms of OP, ASEP, moments, and moment generating function (MGF) can be found in [14]. Reference [15] studies the performance of a dualbranch SSC diversity receiver with the switching decision based on SIR, operating over correlated Ricean fading channels in the presence of correlated Nakagamim distributed CCI. Moreover to the best of author's knowledge, no analytical study of switch and stay combining involving assumed correlated  fading for both desired signal and cochannel interference has been reported in the literature.
In this paper, desired signal and CCI are considered to be affected by  fading distribution, which is adequate for multipath waves, propagating in a nonhomogenous environment. An approach to the performance analyses of given SSC diversity receiver is presented. Effectiveness of any modulation scheme and the type of diversity used is studied thought evaluating the system's performance over the channel conditions. Infinite series expressions for probability distribution function (PDF) and cumulative distribution function (CDF) of the output SIR for SSC diversity are derived. Furthermore, infinite series expression for important performance measure, such as OP, is obtained. An OP is shown graphically for different system parameters. Using infinite series formulae, ASEP is efficiently evaluated for several modulation schemes such as noncoherent frequencyshift keying (NCFSK) and binary differentially phaseshift keying (BDPSK). This analysis has a high level of generality because  fading distribution model includes as special cases other important distributions such as Weibull and Nakagamim (therefore the onesided Gaussian and Rayleigh are also special cases of it).
2. System Model and Received Statistics
Independent fading assumes antenna elements in diversity systems to be placed sufficiently apart, which is not general case in practice due to insufficient spacing between antennas. When diversity system is applied on small terminals with multiple antennas, correlation arises between branches. Now, due to insufficient antennae spacing, desired signal envelopes and experience correlative  fading, with joint distribution [5]:
Similarly, due to insufficient antennae spacing, envelopes of interference and are correlated with joint  distribution [5]:
It is important to quote that and denote the desired and interfering signal power correlation coefficients defined as , and , respectively. For the desired signal with correlated envelopes and the arbitrary power parameters , connected with the nonlinearity of the environment, , explained in [5], denote the root mean values of desired signal. Similarly denote the root mean values of interferer signal. Parameters and are associated with the number of multipath clusters through which desired and interference signals propagate, and they are defined in the terms of normalized variances as in [5, 11]. and are, respectively, the covariance and variance operators, and stands for Gamma function [16]. defines generalized Laguerre polynomial with the property of [17]
Let and represent the instantaneous SIR on the diversity branches, respectively [18]. The joint PDF of and and can be expressed by [18, 19]
Substituting (1), (2), and (3) in (4), we get
where with
where denotes , denotes denotes , with denoting the Pochhammer symbol [16]. Derivation of this expression is presented in the appendix. Let represent the instantaneous SIR at the SSC output, and the predetermined switching threshold for the both input branches. Following [20], the PDF of SIR is given by
where , according to [20], can be expressed as . Moreover, can be expressed as infinite series
with , being the Gaussian hypergeometric function [16], and
In the same manner, the can be expressed as
Similarly, the CDF of the SSC output SIR, that is, the is given by [11, 20]
By substituting (5) in and (10) in and can be expressed as the following infinite series, respectively,
with
Terms need to be summed in (12) to achieve accuracy at the 7th significant digit.
, , , , τ  =  =  


 5  5 

 5  7 

 5  9 

 6  9 

 6  9 

 8  9 

 9  9 

 9  10 

 10  11 
3. Outage Probability
4. Average Symbol Error Probability
The ASEP ( ) can be evaluated by averaging the conditional symbol error probability for a given SIR, that is, , over the PDF of , that is, [8]:
where depends on applied modulation scheme. For BDPSK and NCFSK modulation schemes the conditional symbol error probability for a given SIR threshold can be expressed by , where for BDPSK and for NCFSK [14]. Hence, substituting (7) into (17) gives the following ASEP expression for the considered dualbranch SSC receiver:
5. Conclusion
In this paper, the system performances of a dualbranch SSC diversity receiver over correlated  channels are analyzed based on SIR. Fading between the diversity branches and between interferers is correlated and  distributed. The complete statistics for the SSC output SIR is given in the infinite series expressions form, that is, PDF, CDF, and OP. Using these new formulae, ASEP was efficiently evaluated for some modulation schemes such as DPSK and NCFSK. The main contribution of this analysis for dualbranch signal combiner is that it has been done for a general case of  (Generalized Gamma) distribution, which includes as special cases important other distributions such as Weibull and Nakagamim (therefore, the OneSided Gaussian and Rayleigh are also special cases of it), so our analysis has a high level of generality.
Declarations
Authors’ Affiliations
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