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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 are still considerable gaps in its effects especially on multi-carrier spreading systems. In this paper, we investigate the impact of a local oscillator phase noise on the multi-carrier 2 dimensional (2D) spreading systems based on a combination of orthogonal frequency division multiplexing (OFDM) and code division multiple access (CDMA) and known as OFDM-CDMA. The contribution of this paper is multifold. First, we use some properties of random matrix and free probability theory to give a simplified expression of signal to interference and noise ratio (SINR) obtained after equalization and despreading. This expression is independent of the actual value of the spreading codes and depends mainly on the complex amplitudes of estimated channel coefficients. Secondly, we use this expression to derive new weighting functions which are very interesting for the radio frequency (RF) engineers when they design the frequency synthesizer. Therefore, based on these asymptotic results, we adapt a new method to predict the bit error rate (BER) at the output of the channel decoder by using an effective SINR value. We show by simulations the validity of our models and that at a given BER, the required signal to noise ratio (SNR) may easily increase due to the carrier phase noise.

On the system level prediction of joint time frequency spreading systems with carrier phase noise