Generally, wireless systems suffer from Carrier Frequency Offsets (CFO), which results either from the receiver’s oscillator’s impairments or Doppler shifts. The frequency offset between transmitter and receiver local oscillator is a main drawback of OFDM systems. A frequency drift in the receiver’s oscillator would result in a frequency offset in the received signal, this offset consists of two parts: a Fine offset, as a fraction of OFDM subcarrier spacing, and a Coarse offset that is equal to an integer multiple of the subcarrier spacing. Coarse offsets results in two problems; firstly, the modulation symbols are located on the wrong frequency bins, secondly, the pilots used for channel estimation are misplaced leading to a faulty channel estimate and severe signal distortion by the Equalizer. Fine Offsets result in a loss of orthogonality and thus ICI (Inter-Carrier Interference), as the frequency bin of a certain modulation symbol would contain some information about the neighboring symbol bin.

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.