Читать книгу Spatial Multidimensional Cooperative Transmission Theories And Key Technologies - Lin Bai - Страница 27

The signal combining technologies we discussed above are all based on the assumption that the channel transmission vector h is known. However, in some cases, the channel transmission vector h is difficult to accurately measure, or h is a random variable and there is no accurate value. In this case, when it is necessary to perform a mathematical estimate of the channel transmission vector, the channel transmission vector is regarded as a random variable by considering of the inevitable estimation error.

In the following, the MMSE combining method where the channel transmission vector is a random variable is further analyzed.

Assuming that the expectation and variance of the channel transmission vector h are known, they are given as

When estimating the channel transmission vector h, we can replace its mean vector with the estimated value of h and replace its covariance matrix C with the estimated error covariance of h. In this case, the MMSE combining vector is

If = 0, the MMSE combining vector is also 0, and this indicates the failure of the MMSE combining method. In order to avoid such problems, we need to correct the MMSE combining method, and the correction methods are different based on different applications.

In the following, we will illustrate the correction of the MMSE combining method.

Assume that the channel transmission vector h = e^jϕh₀, where ϕ is a random phase vector and h₀ is a non-zero constant vector. If ϕ is uniformly distributed, = 0, then the amplitude of the channel transmission vector gain is also constant, but its phase is time-varying. If the time-varying phase changes slowly, some conventional signal modulation technologies can be used to detect the received signal with an unknown phase estimation.

If the received signal is expressed as

and c = e^jϕs is regarded as a new detection signal, then the MMSE combining vector is

However, it should be noted that the MMSE combining vector here is not time-varying. The output of the MMSE combiner is

According to , the receiver can detect the signal.

In general, if the time-varying random channel transmission vector can be decomposed into the known constant and the random variable, then we can realize the application of MMSE in the actual production process by modifying the known signals.