Читать книгу Spatial Multidimensional Cooperative Transmission Theories And Key Technologies - Lin Bai - Страница 39

The particularity of a wireless link is that it is affected by random fluctuations in signal levels across time, space, and frequency. This characteristic is fading and affects the system performance (symbol or bit error rate). Take the SISO Rayleigh fading channel transmitted by binary phase shift keying (BPSK) as an example.

When there is no fading (h = 1), in the additive white Gaussian noise (AWGN) channel, the bit error rate (SER) is

When considering the fading, the level of the received signal fluctuates with and the bit error rate is given as

where p_s(s) is the distribution function of the fading. For Rayleigh fading, the integration of the above equation yields

When the SNR is large, the bit error rate in Eq. (2.91) becomes

In order to overcome the negative impact of fading on the bit error rate, diversity techniques are often employed. The principle of diversity is to provide the receiver with multiple copies of the same transmitted signal, and each replica acts as a diversity branch. If this replication is affected by independent fading conditions, the probability that all branches will be in a fading state at the same time can be greatly reduced. Therefore, diversity stabilizes the link by channel enhancement, which improves the bit error rate performance of the system.

As fading can occur in time, frequency, and space domains, diversity techniques can be used in these domains. For example, time diversity can be obtained by coding and interleaving, and frequency diversity can exploit the time spread of the channel (in the τ domain) by equalization techniques or multi-carrier modulation. Obviously, time and frequency diversity techniques can result in a loss of time or bandwidth due to the introduction of redundancy. Conversely, because multiple antennas are used at one or both ends of the link, space or polarization diversity does not sacrifice time and bandwidth.