Spatial Multidimensional Cooperative Transmission Theories And Key Technologies. Lin Bai
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Название: Spatial Multidimensional Cooperative Transmission Theories And Key Technologies

Автор: Lin Bai

Издательство: Ingram

Жанр: Зарубежная компьютерная литература

Серия:

isbn: 9789811202476

isbn:

СКАЧАТЬ are independent. Combining signals from all antennas, the detected variable can be expressed as

figure

      where h = [h1 , . . . , hMR]T.

      (1) Equal gain combining

      The weight of equal gain combining is Wn = e−jϕn, indicating that the signals from different antennas are in phase and can be added together. This approach requires the combiner to have a complete knowledge of the known signal phase. And the post-combiner signal of Eq. (2.100) becomes

figure

      where figure is the Gaussian white noise.

      When the channel is a Rayleigh distribution, the mean value of the output SNR can be obtained.

figure

      It can be seen that the array gain increases linearly with MR, and it is greater than the array gain of selective combining. In addition, the diversity gain of equal gain combining is MR, which is similar to that of the selective combining.

      (2) Maximum ratio combining

      The selection weight of maximum ratio combining is figure, and its post-combiner signal

figure

      where n′ = hHn. Because it maximizes the output SNR ρout, this strategy is called maximum ratio combining. And

figure

      In the maximum ratio combining diversity scheme, the array gain ga is always equal to MR.

      Consider the case of transmitting with BPSK modulation. It is well known that when u = ||h||2 and different channels are independently distributed Rayleigh channels, u obeys 2MR degrees of freedom χ2 distribution.

figure

      The bit error rate can be given by

figure

      when the SNR is large, the above equation becomes

figure

      It can be seen that the diversity gain is still MR.

      For other constellations, using maximum likelihood detection,5 the error probability is

figure

      where figure and dmin are the nearest neighbor and the minimum separation distance of the constellation, respectively. The analytical solution of the above expression can be obtained by following Eq. (2.106). The upper bound of the bit error rate is usually obtained using the Chernoff bound. Equation (2.108) can also be written as

figure

      Since u is a χ2 variable, the average upper bound above is

figure

      when the SNR is large, Eq. (2.110) is simplified to

figure

      Similar to the case of BPSK, the diversity gain is equal to the number of receiving branches in an independent and identically distributed Rayleigh channel.

      (3) Minimum mean square error combining

      When the noise is spatially correlated or non-Gaussian interference occurs, the maximum ratio combining is no longer optimal. In this case, the minimum mean-squared error combining is an optimal gain combining, from which the weight is obtained by minimizing the mean square error between the transmitted symbol c and the combiner output z, namely

figure

      And it is easy to get the optimal weight vector

figure

      where Rni is the correlation matrix of noise and interference. When there is no interference, Rni = E{nnH}. If the noise across the antenna is white noise, then figure, and the minimum mean square error combining diversity is simplified to a maximum ratio combining diversity with only one coefficient difference.

      2.3.2.3Reception diversity through hybrid selection combining or gain combining

      A hybrid approach combines the selection algorithm with the maximum ratio combining. At each moment, the receiver first selects figure branches with the largest SNR among MR branches and then combines them by the maximum ratio combining algorithm. This strategy is called augmentation selection.

      Obviously, it can be concluded that the average SNR of the combiner output is the sum of the two items. The first item corresponds to the maximum ratio combining figure branches and the second item is generated from the figure branches of the MR branches, which is the extension of Eq. (2.95). Therefore, the overall array gain is

figure

      Similarly, for selective combining (figure = 1), the diversity gain of the hybrid selection combining and maximum ratio combining is equal to MR instead of figure.

      The MISO system utilizes MT transmitting antennas with pre-processing or precoding to perform diversity at the transmitting end. And the obvious difference from reception СКАЧАТЬ