Thermal Noise Mutual Coupling Effect on the Capacity of MIMO Wireless Systems

In this paper we analyze the impact of mutual cou- pling on MIMO channel capacity, considering its effect on both, signal and thermal noise. We calculate noise correlation matrix in the multi-antenna system with closely spaced antennae by applying the Nyquist's thermal noise theorem. Then, we employ noise correlation matrix in channel capacity formula, that enables the identification of thermal noise correlation contribution on the MIMO channel capacity. In addition, we examine thermal noise correlation due to mutual coupling effect. Our simulation results confirm theoretical analysis that mean and outage MIMO channel capacity is underestimated if noise correlation due to mutual coupling effect is not accounted for. I. INTRODUCTION MULTIPLE-INPUT multiple output (MIMO) wireless sys- tems, characterized by multiple antennas at the transmitter and receiver, have demonstrated the potential for increased capacity by exploiting the spatial properties of the multi- path channel (1). If the channel matrix coefficients are i.i.d (independent identically distributed) complex Gaussian variables, the linear increase in capacity with the number of antenna is possible. The mutual independence of chan- nel coefficients is generally achieved by wide inter-element spacings in multi-element antenna systems. However, it is not practically achievable due to limitation in the physical size of subscriber units. Close antenna spacing results in antenna mutual coupling that affects the communication performance of MIMO wireless systems (2). The general approach in evaluating the impact of antenna mutual coupling on the communication performance of MIMO systems is to examine how mutual coupling affects MIMO sub-channels correlation and MIMO channel capacity. It has been shown that mutual coupling can decrease spatial corre- lation (3). The decrease in spatial correlation is beneficial for the MIMO channel capacity (4). Additional parameters are included into the RF analysis of the mutual coupling effect on MIMO systems in (5), (6) in order to confirm its beneficial characteristics. Although, these prior studies have presented important contributions concerning the effect of array mutual coupling on the communication performance of MIMO systems, they have neglected the mutual coupling effect on thermal noise. The quantitative analysis of the mutual coupling effect on thermal noise is a missing puzzle to complement the analysis of the mutual coupling effect on the communication performance of multi-antenna systems. In this paper, we analyze the thermal noise mutual coupling effect on channel capacity of MIMO systems. 1.We derive the noise correlation matrix which enables the investigation of thermal noise mutual coupling effect on the MIMO channel capacity. We apply the Nyquist's thermal noise theorem (7) to calculate the noise correlation matrix for two- antenna array. Additionally, we calculate noise correlation co- efficients to confirm existence of the thermal noise correlation due to mutual coupling effect for antenna spacing below one wavelength. 2. We develop the MIMO channel capacity formula consid- ering the mutual coupling effect on both, signal and thermal noise. We apply the eigenvalue decomposition to get better insight into the thermal noise mutual coupling effect on MIMO channel capacity. The advantage of eigenvalue decomposition is that it provides information about the signal-to-noise ratio and effectively active number of MIMO sub-channels. 3. Our simulation results show that ergodic and outage channel capacity is underestimated, if mutual coupling effect on thermal noise is not accounted for. The rest of this paper is organized as follows. In Section II, the MIMO system model is given. The mutual coupling effect of signal is discussed in III. Then, the noise correlation matrix is derived IV. The theoretical analysis of the mutual coupling effect on the MIMO channel capacity is presented in V. Simulation results are presented in section VI. Concluding remarks are given in Section VII.