Space-time coding techniques can be used to achieve very high spectral efficiencies in highly scattering environments using multiple transmit and receive antennas. At the remote station, there is usually a more limited space allotted to the antenna array than at the base station. Since the spectral efficiency improves with the number of antennas, one is interested in how many antennas can be crammed into the limited space on the remote station. This paper addresses some of the issues which affect the allowable density of antennas in the remote station. In particular, the mutual impedance between antenna elements in the remote array, the correlation between the signal and noise fields received by these elements, and amplifier noise contributions impact on the channel capacity achievable by such arrays. In particular, we assume the transmitter is radiating from nT elements of uncoupled half wave dipoles and knows nothing of the channel. A formula is given for the maximum channel capacity to a receiving array of nR elements, coupled to each other in the presence of ambient noise or interference with a uniform angle of arrival distribution. This formula neglects amplifier noise in the receivers. It is shown that the channel capacity is already determined at the terminals of the receiving array and can not be improved by internal coupling networks following the receiving array. When the propagation is by means of full three dimensional scattering, the channel capacity is unaffected by mutual coupling in the receiving array.
It is of interest to find compare optimum beamforming communications between a random antenna array of sensors and a uniform antenna array base station to MIMO communications between the two arrays. For these purposes we examine a specific example. Channel capacity is compared for various versions of MIMO communications. Channel state information is assumed to be known a.) at the receiving array only, and b) at both the transmitting and receiving arrays. When the signal to noise ratio is high, the blind transmitter and the knowledgeable transmitter MIMO provides higher channel capacity than the beamformer, but for very low signal to noise ratio only the knowledgeable transmitter MIMO equals the beamformer channel capacity.