Читать книгу Spatial Multidimensional Cooperative Transmission Theories And Key Technologies - Lin Bai - Страница 45
2.3.3.1Transmit diversity formed by matched beamforming
ОглавлениеThis beamforming technique is also known as transmitting maximum ratio combining and it assumes that the transmitter knows all the information about the channel. In order to use diversity, signal c is appropriately weighted before being transmitted to each antenna. At the receiving end, the signal can be expressed as
where h = [h1 , . . . , hMR] denotes the MISO channel vector and W is the weight vector. And the weight vector that maximizes the received SNR is
where the denominator guarantees that the average total transmitting power remains unchanged and is equal to ES. This vector makes the transmission in the direction of the matched channel and is therefore also called the matched beamforming or conventional beamforming. Similarly, for reception maximum ratio combining, the average output SNR is ρout = MTρ, and therefore, the array gain is equal to the number of transmitting antennas MT. If the bit error rate has the following upper bound at a high SNR, the diversity gain is also equal to MR.
Therefore, the matched beamformer exhibits the same performance as the reception maximum ratio combining. It requires knowledge of the complete information of the transmitting channel, which means there is feedback from the receiver in the time duplex system. If frequency duplexing is adopted, the interchangeability of the upper and lower channels is no longer guaranteed, and the understanding of the channel information at the transmitting end is greatly reduced. In addition, the matched beamformer is optimal in the absence of interfering signals but cannot cancel the interference.
Similar to the aforementioned augmented selection algorithm for SIMO systems, the matched beamformer can be combined with the selective combining algorithm. In the beamformer, the transmitter selects antennas out of MT antennas. Obviously, this technique yields a full-diversity gain MT, but reduces the transmit array gain.
