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 [1] 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 [1] 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 [2]. 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

Wed Sep 4 14:30:51 BST 1996