Carrier Frequency Offset in VSF-OFCDM Systems with Subcarrier Grouping: Analysis, Estimation and Correction

We investigate the effect of carrier frequency offset (CFO) on the performance of downlink variable spreading factor (VSF) orthogonal frequency and code division multiple access (OFCDM) systems when subcarrier grouping is used. An analytic expression of the signal to interference and noise ratio (SINR) is derived for the VSF-OFCDM with CFO for the case of maximal ratio combining (MRC) and equal gain combining (EGC) receivers. Numerical results show that, when the total spreading factor is fixed, a system with higher frequency domain spreading factor is more sensitive to CFO than that with lower frequency domain spreading factor. Also, for high Eb/No, EGC has better bit error rate performance than MRC due to the greater interference amplification present in MRC which compounds the effect of the loss of orthogonality. Due to the adverse impact of the CFO on VSF-OFCDM systems, we propose a correction scheme based on the maximum likelihood principle. We then use a gradient algorithm to estimate and minimize the effect of CFO in a tracking mode. Our results show that the BER performance in the low SINR environment can be improved significantly with few number of iterations for different spreading factors.