Statistic Characteristics of M-ary Fsk Signal in the Presence of Gaussian Noise, Impulse Noise and Variable Signal Amplitude

In this paper we consider a system for coherent demodulation of M-ary FSK signals in the presence of Gaussian noise, impulse noise and variable signal amplitude. These annoyances can seriously degrade the performance of communication systems [1]-[3]. In the paper [4], the performance evaluation of several types of FSK and CPFSK receivers was investigated in detail using the modified moment’s method. Also, the error probability of the cross-correlator receiver for binary digital frequency modulation detection is studied using theoretical analysis and computer simulations [5]. In [6], average bit-error probability performance for optimum diversity combining of noncoherent FSK over Rayleigh channels is determined. Performance analysis of wide-band M-ary FSK systems in Rayleigh fading channels is given in [7]. The influence of impulsive noise in noncoherent M-ary digital systems is observed in the paper [8]. In order to view an influence of the Gaussian noise, impulse noise and variable signal amplitude on the performances of an M-ary FSK system, we derived the probability density function of an M-ary FSK receiver output signal, the joint probability density function of output signal and its derivative, and the joint probability density function of output signal at two time instants. The bit error probability, the signal error probability and an outage probability can be determined by the probability density function of an output signal. Also, the moment generating function, the cumulative distribution of output signals and the moment and variance of output signals can be derived by probability density function of output signals. An average level crossing rate and an average fade derivation of an output signal process can be calculated by the joint probability density of the output signals and its derivative. An expression for calculation autocorrelation function can be derived by a joint probability density function of the output signals at two time instants. By using Winner-Hinchine theorem, the spectral power density function of an output M-ary FSK signal can be obtain. Based on this, the results obtained in this paper have a great significance. This paper is organized as follows: the first section is the introduction. In the second section the model of the M-ary FSK system is defined. The expressions for the probability density function of the output signal and the joint probability density function of the output signal and its derivative at one time instant are obtained in the third section. In the next, fourth section, the characteristics of the signal on the output of an M-ary FSK receiver at two time instants is given. The fifth section presents the numerical results in the case M=2. The last section is the conclusion.