Diversity
The main idea
behind “diversity” is to provide different replicas of the transmitted signal
to the receiver. If these different replicas fade independently, it is less
probable to have all copies of the transmitted signal in deep fade
simultaneously. Therefore, the receiver can reliably decode the transmitted
signal using these received signals. This can be done, for example, by picking
the signal with the highest SNR or by combining the multiple received signals.
As a result, the probability of outage will be lower in the case that we
receive multiple replicas of the signal using diversity. To define diversity
quantitatively, we use the relationship between the received SNR, denoted by γ ,
and the probability of error, denoted by Pe. A tractable definition
of the diversity, or diversity gain, is Gd = − limγ→∞log(Pe)/log(γ ) where Pe is
the error probability at an SNR equal to γ . In other words,
diversity is the slope of the error probability curve in terms of the received
SNR in a log-log scale. There are two important issues related to the concept
of diversity. One is how to provide the replicas of the transmitted signal at the
receiver with the lowest possible consumption of the power, bandwidth, decoding
complexity and other resources. The second issue is how to use these replicas
of the transmitted signal at the receiver in order to have the highest
reduction in the probability of error.
In : Theory