- Research Article
- Open Access

# Performance Analysis of SSC Diversity Receiver over Correlated Ricean Fading Channels in the Presence of Cochannel Interference

- Srđan Jovković
^{1}, - Stefan R. Panić
^{2}Email author, - Mihajlo Č. Stefanović
^{2}, - Petar Ć. Spalević
^{3}and - Dragana S. Krstić
^{2}

**2010**:583093

https://doi.org/10.1155/2010/583093

© Srđan Jovković. 2010

**Received:**16 February 2010**Accepted:**19 April 2010**Published:**24 May 2010

## Abstract

In this paper an approach to the performance analysis of a dual-branch switched-and-stay combining (SSC) diversity receiver, operating over interference-limited Ricean correlated fading environment, is presented. Infinite series expressions are obtained for the output signal-to-interference ratio's (SIR) probability density function (PDF) and cumulative distribution function (CDF). Using these new formulae, the outage probability (OP) and the average symbol error probability (ASEP) for modulation schemes such as noncoherent frequency-shift keying (NCFSK) and binary differentially phase-shift keying (BDPSK) are efficiently evaluated. Numerical results, presented into this paper, are graphically presented and analyzed, in order to point out the effects of fading severity and the level of correlation on the system performances.

## Keywords

- Probability Density Function
- Fading Channel
- Outage Probability
- Modulation Scheme
- Cochannel Interference

## 1. Introduction

Space diversity reception, based on using multiple antennas at the reception, is being widely considered as a very efficient technique for mitigating fading and cochannel interference (CCI) effects and improving offered quality of service (QoS) in wireless communication systems. Various techniques for reducing the fading effects and the influence of the cochannel interference (CCI) are used in wireless communication systems [1–3]. Depending on the complexity restriction put on the communication system and the amount of channel state information available at the receiver, several principal types of space diversity techniques can be performed.

However, the least complex space diversity reception technique that can be used in conjunction with coherent, noncoherent, and differentially coherent modulation schemes and has application in many real life communication scenarios is switch-and-stay combining (SSC) technique. 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 signal-to-interference ratio (SIR) drops below a predetermined threshold (SIR-based switched diversity). Then the combiner switches to another branch and stays there regardless of SIR of that branch. This type of diversity can be easily performed, because SIR value is simply measurable in real time, by using specific SIR estimators, in base stations (uplink), mobile stations (downlink) and digital wireless systems.

In communications systems analysis a few statistical models are used to describe fading in wireless environments. The most frequently used distributions are Nakagami-m, Rice, Rayleigh, - , and Weibull. The Rician fading distribution is often used to model propagation paths, consisting of one strong direct line-of-sight (LoS) signal and many randomly reflected and usually weaker signals. Such fading environments are typically encountered in microcellular and mobile satellite radio links. In particular, for mobile satellite communications, the Rician distribution is used to accurately model the mobile satellite channel for single [4], clear-state [5] channel conditions. Then the Rician fading is applicable for modeling the fading channels in frequency domain [6]. Also the Rician K factor characterizes the land mobile satellite channel, during unshadowed periods [7]. The diversity reception over Rician fading channels was previously discussed in [8–11]. The system performances of dual selection combining (SC) over correlated Rician channels are in the presence of CCI analyzed in [11].

There are a number of papers concerning performance analysis of SSC receivers, for example [12–16] Very useful, novel, infinite series expressions are obtained for the output SIR probability density function (PDF) and cumulative distribution function (CDF) of a dual-branch switched-and-stay combining (SSC) diversity receiver, operating over correlated - fading in the presence of cochannel interference (CCI) derived in [12]. This analysis has a high level of generality because - fading distribution model includes as special cases, other important distributions such as Weibull and Nakagami-m (therefore the one-sided Gaussian and Rayleigh are also special cases of it). However the - fading model cannot be reduced only to Ricean fading model, so the analysis from [12] cannot be used for the physical scenario when strong direct (LoS) signal component is present. The performance analysis of the SSC diversity receivers, operating over correlated Ricean fading satellite channels, can be found in [14], but without the consideration of CCI effects. Reference [16] studies the performance of a dual-branch SSC diversity receiver with the switching decision based on SIR, operating over correlated Ricean fading channels in the presence of correlated Nakagami-m distributed CCI. Moreover to the best of the author's knowledge, no analytical study of switch-and-stay combining involving assumed correlated Ricean fading for both desired signal and cochannel interference has been reported in the literature.

In this paper, an approach to the performance analysis of given SSC diversity receiver over correlated Rician fading channels, in the presence of correlated CCI, is presented. In order to study the effectiveness of any modulation scheme and the type of diversity used, it is required to evaluate the system's performance over the channel conditions. Infinite series expressions for PDF and CDF of the output SIR for SSC diversity are derived. Furthermore, important performance measures, such as outage probability (OP) and Average Symbol Error Probability (ASEP) for several modulation schemes such as noncoherent frequency-shift keying (NCFSK) and binary differentially phase-shift keying (BDPSK) are efficiently evaluated and shown graphically for different system parameters in order to point out the effects of fading severity and the level of correlation on the system performances.

## 2. System Model and Received Statistics

It is important to quote that
and
, defined as
and
, denote the average powers of desired and interference signals, respectively.
and
are the modified Bessel function of the first kind of the
th and
th order.
, known as Ricean factor, defines ratio of signal power in dominant component of desired signal over the scattered power while
is, similarly, Ricean factor of the interference signal.
and
are defined as
for
and
for
and similarly
for
and
for
. Finally, with *r* the correlation coefficients are denoted.

## 3. Outage Probability

It can be observed from that figure that OP deteriorates with decrease of the Rice factor
. Also, presented results show branch correlation influence on the OP. Namely, when correlation coefficients *r* increas, OP increases.

## 4. Average Symbol Error Probability

*r*. The comparison of Figures 2 and 3 shows better performance of BDPSK modulation scheme versus NCFSK modulation scheme.

## 5. Conclusion

The system performances of dual SSC system over correlated Rician fading channels in the presence of correlated CCI are analyzed. Crucial statistics metrics for the SSC output SIR are given in the infinite-series form, that is, PDF and CDF. Capitalizing on this, outage probability and average symbol error probability have been obtained and graphically presented, describing their dependence on the correlation coefficient and the fading severity. The main contribution of this paper is analytical study of dual SSC diversity system assuming, for the first time, correlated Rician fading for both desired signal and interference.

## Declarations

## Authors’ Affiliations

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