Spatial Multidimensional Cooperative Transmission Theories And Key Technologies. Lin Bai

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      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 M_T antennas. Obviously, this technique yields a full-diversity gain M_T, but reduces the transmit array gain.

      2.3.3.2Space–time coded transmit diversity

      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.

      2.3.3.3Indirect transmit diversity

      The technique of obtaining space diversity by combining or space–time coding described above belongs to the direct transmit diversity technique. By using well-known SISO techniques, converting space diversity to time or frequency diversity can also be realized.

      Assuming M_T = 2, the phase shift is achieved by delaying the signal on the second transmit branch by one symbol period or by selecting the appropriate frequency shift. СКАЧАТЬ