In this paper, we give statistical results for the channel capacity (spectral efficiency) of a transmit/receive array. We show that the capacity is approximately normal for Ricean and Rayleigh channels, and that this holds for correlated and uncorrelated antennas. The starting point is the extension of Shannon's theorem given by Foschini (1996) and Foschini and Gans (1998) for the capacity in a Rayleigh fading environment for transmit/receive arrays. Foschini et al.'s results assume that:
The total power transmitted is constant;
The average power of each transmit antenna is the same;
The noise power at each receiver is the same;
The radio link comprises Rayleigh faded channels and uncorrelated antennas.
Here, we consider the more general case:
The total transmitted power may vary, for example be constant or increase with N;
The average power of each transmitting antenna can be different;
The noise power at each receiver can be different;
The radio link can have Ricean (including Rayleigh) fading and correlated antennas.
For these conditions, we give expressions for the distribution and percentiles of the capacity of a link with N transmit antennas and M receive antennas for the cases of M fixed or M/N fixed. These expressions are power series in and for these cases respectively. The series arise by noting that the expression for capacity is a smooth function of the weighted sample mean, so that the expansions of Cornish and Fisher can be applied. The first three terms of these expansions will be given. The capacity is shown to be asymptotically normal, so for large arrays, simple outage estimates are possible, and this applies for a variety of conditions.
G.J. Foschini (1996), "Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas," Bell Labs Technical Journal, Autumn 1996, pp. 41- 59.
G.J. Foschini, M.J. Gans (1998), "On limits of wireless communications in a fading environment when using multiple antennas," Wireless Personal Communications, Vol. 6, 1998, pp. 311-335.
Kit Withers gained his PhD in statistics at Stanford on a Fulbright Scholarship. After working at UC and HEW in San Francisco he returned to the New Zealand Department of Scientific and Industrial Research, later restructured as Industrial Research Ltd., where he is the senior statistician. He has developed theoretical tools and applied them to a number of areas including problems for electrical engineers, climate change problems, and the spread of HIV. He is now working full-time on wireless communications problems. He has published about 50 papers.