Читать книгу Spatial Multidimensional Cooperative Transmission Theories And Key Technologies - Lin Bai - Страница 46

The beamforming technique described previously requires channel information for the transmitter to obtain optimal weights. Conversely, Alamouti proposes a particularly simple but original diversity approach for the two transmit antenna systems, called the Alamouti algorithm, which does not require information on the transmit channel. Considering that in the first symbol period, two symbols c₁ and c₂ are simultaneously transmitted from antenna 1 and antenna 2, and then two symbols – and are transmitted from antenna 1 and antenna 2 in the second symbol period, it is assumed that the flat fading channel remains unchanged during these two symbol periods, which is expressed as h = [h₁, h₂] (the subscript indicates the antenna number rather than the symbol period). The symbol received in the first symbol period is

The symbol received in the second symbol period is

where each symbol is divided by , and then the vector has a unit average energy (assuming that c₁ and c₂ are obtained from the unit average energy constellation). n₁ and n₂ are the corresponding terms of additive noise in each symbol period (in this case, the subscript represents the symbol period rather than the antenna number). Combining Eq. (2.118) with Eq. (2.119), we get

It can be seen that the two symbols are extended on two antennas over two symbol periods. Therefore, H_eff represents a space–time channel. Adding the matched filter to the received vector y can effectively decouple the transmitted symbols, such as

where n′ satisfies . The average output SNR is

It shows that the Alamouti algorithm cannot provide array gain due to a lack of information about the transmitting channel (note E{||h||²} = M_T = 2).

However, for independent and identically distributed Rayleigh channels, the average bit error rate of the above problem has the following upper bound at high SNR.

It means that despite the lack of transmit channel information, the diversity gain is equal to M_T = 2, which is the same as the transmit maximum ratio combining. From a global perspective, the Alamouti algorithm has a lower performance than the transmit or receive maximum ratio combining due to its zero array gain.