This paper describes investigations into the antenna mutual coupling (MC) effect on channel estimation and capacity of a multiple-input multiple-output (MIMO) wireless communication system. The presented investigations close the gap existing in the previous works which assessed the effect of mutual coupling on MIMO capacity under the assumption of availability of perfect channel state information (CSI) at the receiver. The new approach assumes that the perfect CSI is not available due to channel estimation errors. The investigations are carried out for different spacing between array antenna elements producing a varying effect of mutual coupling on the channel estimation and the resulting MIMO channel capacity.

It has been shown in recent works that a wireless communication system can achieve an increased capacity by using multiple element antennas at transmitter and receiver by applying a suitable signal processing scheme [

In order to realize the advantages of MIMO, two conditions have to be satisfied. One requires the presence of a rich scattering environment, and the other one entails accurate channel state information (CSI) to be available at the receiver [

It is known that the finite antenna spacing in array antennas introduces spatial correlation. This finite spacing is also responsible for mutual coupling which adversely affects signal transmission and reception due to the resulting antenna impedance mismatch. The mutual coupling effect is especially pronounced in tightly spaced arrays. Because of a considerable demand for compact size mobile station (MS) terminals, the effect of mutual coupling cannot be neglected and thus has to be taken into account while assessing the MIMO link performance. The problem of mutual coupling in MIMO systems for the case of peer-to-peer communication has been addressed via simulations and measurements in [

Obtaining an accurate CSI can be accomplished using suitable channel estimation methods. The methods based on the use of training sequences, known as the training-based channel estimation methods, are the most popular. In [

In this paper, the overall effect of antenna mutual coupling on performance of an MIMO wireless system is investigated. The channel capacity that provides the overall measure of MIMO system performance is determined assuming an imperfect CSI is available at the receiver. A closed-form mathematical expression for the MIMO channel capacity that includes channel estimation errors is derived. The effects of mutual coupling on channel estimation and resulting capacity are investigated via computer simulations using a suitable MIMO channel model.

The rest of the paper is organized as follows. Section

Generally, a wireless communication channel is described by the relationship between the input signal

Similarly, the entropy of

The upper bond mutual information of MIMO can be written as,

If power is equally allocated to each subchannel, which is easy to realize in practice, then (

For training based channel estimation methods, the relationship between the received signal and the training sequence is assumed as given by:

The goal is to estimate the complex channel matrix

Using the LS method, the estimated channel matrix can be written in the form [

The SLS method further reduces the estimation error that is obtained in the LS method. The improvement is given by the scaling factor

In practical cases,

Combining the above with (

An uncorrelated Rayleigh channel is ideal. In practical cases, an MIMO channel is usually correlated due to the propagation environment. Consequently, the estimation error matrix is correlated rather than i.i.d. In this case, the variances of elements in the error matrix are not equal to each other and the error correlation matrix is not diagonal. Therefore, (

In the undertaken investigations, the Kronecker channel model [

Here, it is assumed that the transmitting and receiving sides of MIMO system are equipped with vertically polarized wire dipole antennas. The scattering environment is represented by circles of uniformly distributed scattering objects surrounding the transmitting and receiving nodes. In this case, the spatial correlation matrix elements can be obtained using the Clark’s model as given by,

The required correlation matrices

The mutual coupling in an array of collinear side-by-side wire dipoles can be modeled using the theory described in [

Figure

A 4

Capacity versus transmitter antenna spacing

Capacity versus receiver antenna spacing

Figure

MSE of training-based channel estimation for a 4

MMSE MSE versus transmitter antenna spacing

SLS MSE versus receiver antenna spacing

This time, computer simulations for MIMO channel capacity include both mutual coupling effects as well as channel estimation errors. MMSE method is assumed to be used to estimate the channel matrix (CSI). Again, both the transmitter and receiver are assumed to be equipped with 4-element uniform array antennas. The antenna elements are assumed to be wire dipoles having length of 0.5

Figure

(a) Channel capacity considering MMSE estimation error for a 4

Channel capacity with esitmation error

MMSE channel estimation MSE versus SNR

In this paper, the effect of mutual coupling on MIMO channel estimation accuracy and the resulting channel capacity has been investigated. The mathematical analysis and simulation results have shown that when the antenna element spacing at either transmitter or receiver is within 0.2