Sensitivity of Multi Carrier 2 Dimensional Spreading Systems to Carrier Phase Noise

Phase noise is a topic of theoretical and practical interest in electronic circuits. Although progress has been made in the characterization of its description, there is still considerable gaps in its effect especially on the multi carrier spreading systems. In this paper, we investigate the impact of a local oscillator phase noise on the multi carrier 2 dimensional spreading systems known as OFDM-CDMA. The contribution of this paper is twofold. First, we use some properties of random matrix and free probability theory to give a simplified expression of the signal to interference and noise ratio SINR obtained after equalization and despreading. The latter is independent of the actual value of the spreading codes of different users and depends principally on the complex amplitudes of the estimated channel coefficients. Second, we use this expression to derive new weighting functions which are very interesting for the RF engineers when they design the frequency synthesizer. Simulation results are provided to discuss and validate our model