The Shannon-Hartley law states that the channel capacity of a band-limited Additive White Gaussian Noise (AWGN) channel can be expressed as in Equation 1:
where B is the channel bandwidth, is the signal to noise ratio (SNR), and C is the channel capacity in bits/sec. The SNR is defined as , where S is the received signal power and N is the AWGN power within the channel bandwidth.
In most mobile radio systems, however, the channel exhibits Rayleigh fast fading, aggravated by typically log-normally distributed shadowing or slow fading, resulting in a time-variant channel capacity. Lee  derived an estimate of the channel capacity in Rayleigh fading environments and showed that when using diversity in a Rayleigh fading environment, the average channel capacity can approach that for a Gaussian channel. The normalised channel capacity can be expressed as in Equation 2:
an upper bound approximation, which has to be replaced by Lee's estimate  in case of Rayleigh channels:
where 0.577 is the Euler constant. Evaluation of this formula shows a 32% channel capacity reduction in comparison to the Gaussian channel at an SNR of 10 dB.
In a cellular re-use structure the effect of co-channel interference must be included in the channel capacity estimate. Hence the definition of in Equations 1-3 must be modified by replacing the SNR by the signal to noise-plus-interference ratio (SINR). The SINR is defined below in Equation 4, where S is the received signal power, I is the received interference power and N is the AWGN power within the channel's bandwidth:
Therefore the normalised channel capacity for a band-limited, interference-contaminated Gaussian channel is defined in Equation 5:
In a noise-limited radio system without power-control one would expect the SINR to reduce with distance from the transmitter, when using an omni-directional aerial. However in an interference-limited system the pattern of SINR is less regular. The normalised channel capacity for a typical hexagonal cell in a simulated system, with Rayleigh fast- and log-normal shadow fading having a standard deviation of 6 dB and a frequency of 1 Hz is shown in Figure 1. Let us now concentrate our attention on the effects of co-channel interference.
Figure 1: Simulated normalised channel capacity profile of a hexagonal cell, employing a reuse factor of 7, pathloss exponent of 3.5, slow-fading frequency of 1 Hz, standard deviation of 6 dB and random 4QAM video user positions within cell boundaries
The co-channel interference performance and capacity of various cellular systems was investigated for example by Lee and Steele in Reference . Our co-channel interference studies have mainly concentrated on the up-link of hexagonal cells with a reuse factor of 7, using an omni-directional antenna at the centre of each cell. This is a commonly investigated cellular cluster type, where each basestation has 6 so-called first-tier co-channel interferers. The average SINR profile of the previously used hexagonal cell characterised previously in Figure 1 in terms of normalised channel capacity is shown in Figure 2. Having characterised the propagation environment, let us now focus our attention on aspects of the proposed transceiver.
Figure 2: Simulated SINR contours of a hexagonal cell, employing a reuse factor of 7, pathloss exponent of 3.5, slow-fading frequency of 1 Hz, standard deviation of 6 dB and random 4QAM video user positions within cell boundaries