Error Performance Analysis for Equal Gain Combining with Gaussian Noise and Co-channel Interference in Nakagami-m Fading Channel

The performance analysis of noncoherent M-ary Frequency Shift Keying (NMFSK) in noise and co-channel interference limited environment in mobile communication system is considered. The closed form expression for Symbol Error Probability (SEP) is derived employing equal gain combining for Nakagami fading channel. The effect of Symbol Interference Ratio (SIR) on SEP in presence of signal to noise ratio (SNR) is studied. The analysis is restricted to the case of equal interferer powers. Introduction The performance of mobile radio system is affected by noise, multipath fading and the co-channel interface [1]. Several techniques like diversity scheme, additive arrays, equalization etc. can be utilized to combat the effect of miultipath fading and to reduce the co-channel interference. In general space diversity is useful in mitigating the fading effect and Co-Channel Interference (CCI) by weighting and combining the received signals from all antenna branches [2]. There are three combining techniques namely, Maximum Ratio Combiner (MRC), Selective Combining (SC) and Equal Gain Combiner (EGC) for space diversity [3]. In MRC technique two receivers are employed for two branch diversity and the receiver circuit is very complicated .At the same time, although h in EGC there is only one dB degradation as compared to MRC but the circuit is relatively simple. The outage probability of cellular system for EGC with CCI in Nakagami fading channel was studied by Abu-Dayya and Beauliu [4] with equal interferer powers. The same study was performed by author [5] using mean signal using mean signal power to mean interferer powers. EGC with co-channel interference for Rayleigh fading channel was studied by 322 Shailendra Jain and M. Tiwari Soug et. al. [6] for both equal and unequal power distributor, Chayan and Aalo [7] and Winter [8] have discussed the effect of CCI with MRC and OS combing technique. The detection of Binary Phase Shift Keying (BPSK) in the presence of interference and noise has been presented by various authors [9-12]. In this paper, we have derived the closed form expression using characteristics function for probability of error for noncoherent M-ary Frequency Shift Keying (NMFSK) with Post Detection EGC for correlated Nakagami fading channel in presence of noise and interference. Here, we have presented the effect of Signal to Noise Ratio (SNR) and Signal to Interference Ratio (SIR) both on the probability of error. The organization of paper is as follows. Section IInd contains the correlated Nakagami fading model and their characteristics function. Symbol Error Probability (SEP) expression have been derived in section III. Numerical results have been presented in section IV. Section V, contains the concluding remarks of paper. System Model Let us assume S(t) be a complex base band information bearing signal with average energy 2Es. The received signal at kth diversity branch is given as ( ) ( ) ( ) ( ) ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ × ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + + = ∑ = t c f j e t n t S C t s C t N i k i ik sk k π γ 2 1 Re (1) Where k= 1, 2, .......L; s T t ≤ ≤ 0 i=1, 2,.........N; Ts is symbol interval Si(t) is the ith complex interfering signal. L is the number of channels. N is the number of interfering signals. Csk is the kth channel vector of desired signal and it is defined as Csk = sk j e sk φ α − (2) Where sk α is the random magnitude of fade Ci,k is the kth channel vector of ith interfering signal and it is expressed as ik ik e C ik φ α − = (3) Where ik α is the amplitude and ik φ is the phase of interfering user channel We assume Ci and Cs are mutually independent. nk(t) represents the AWGN which is complex valued with zero mean and N0 variance. All the {nk(t)} are assumed to be independent. They are also independent of channel gain vectors. We assume αsk’s and αik’s are correlated variables. Nakagami probability density for fading amplitudes of desired and interfering signal can be written as Error Performance Analysis for Equal Gain Combining 323 ( ) ( ) ⎟⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎝ ⎛ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ Ω Γ = Ω − − sk r sk m sk m sk m e r m m r f sk sk sk sk 2 1 2 2 α (4) and ( ) ( ) ⎟⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎝ ⎛ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ Ω Γ = Ω − − ik r ik m ik m ik m ik e r m m r f ik ik ik 2 1 2 2 α (5) Where msk and mik are fading parameters defined as ( ) [ ] 2 2 2 sk sk sk sk E m Ω − Ω = α (6) ( ) [ ] 2 2 2 ik ik ik ik E m Ω − Ω = α (7) Variances [ ] 2 sk sk Eα = Ω And [ ] 2 ik sk Eα = Ω So, instantaneous Signal to Interference Pulse Noise Ratio (SINR) defined as ∑ = + = N