An Analytic Approach for Calculating Frame Erasue Rate in Cellular GSM Networks

The Quality of Service (QoS) of a GSM system is quantified in terms of Bit Error Rate (BER) and Frame Erasure Rate (FER) observed by the user. The problem of obtaining analytical expressions for BER and FER in a fading channel with multiple cochannel interferers (CCI) is an extremely complex mathematical problem. The reason for this complexity is that the involvement of several GSM physical layer modules is required to obtain an expression for the probability of bit error. Besides, one needs to obtain the statistical properties of faded cochannel interferers in order to obtain the raw BER of GMSK modulation. Thus, error rate metrics are usually obtained by simulating the GSM physical layer rather than treating the problem analytically. A reliable interface between system and link level models can be obtained by evaluating the BER and FER in terms of the Signal-to-Interference Ratio (SIR) analytically, instead of the pre-defined statistical mapping data usually used in literature. In this work, bounds on the uplink BER and FER are obtained for the GSM physical layer assuming a CCI limited system where both the desired and interference signals are subjected to Rayleigh fading. The analysis considers GMSK modulation, convolutional coding and Frequency Hopping.