Spatial Multidimensional Cooperative Transmission Theories And Key Technologies. Lin Bai
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СКАЧАТЬ 2.4.1System model

      The MIMO system model is shown in Fig. 2.11. Consider the system with two transmitting antennas and two receiving antennas as an example. Since each receiving antenna can receive signals from different transmitting antennas, the received signals from the two receiving antennas can be expressed as

figure

      where hij, sj, and ni represent the channel gain from the jth transmitting antenna to the ith receiving antenna, the transmitted signal of the jth transmitting antenna, and the additive noise of the ith receiving antenna, respectively. Defining y = [y1 y2]T, the received signal vector can be expressed by the matrix multiplication.

figure

      where channel matrix figure, transmitted signal vector figure, and noise vector figure. The corresponding system model can be extended to any MIMO system with M transmitting antennas and N receiving antennas. The system model expression can still be expressed by Eq. (2.145), and the channel can be assumed to be an additive white Gaussian noise channel. In the AWGN channel, the received noise vector n is assumed to be a zero-average CSCG random vector,8, 9 whose mean value is E(nnH) = N0I, covariance matrix is R, namely figure.

figure

       Fig. 2.11. The MIMO system model.

      2.4.2.1Maximum likelihood MIMO signal detection

      It can be seen from Eq. (2.145) that the purpose of detecting the MIMO signal is to estimate the unknown transmitted signal vector s when the received signal vector y and the channel matrix H are known. Although we are unable to obtain accurate information of the noise vector n, all possible cases of transmitting the signal vector s can be obtained in advance according to the modulation method. For an MIMO system with M transmitting antennas, if the transmitted symbols are taken from a constellation symbol set, then the number of all possible transmitted signal vectors is figureM, where figure denotes the number of symbol elements in the set. For example, when the modulation method adopts 4-quadrature amplitude modulation (QAM) and the number of transmit antennas M is 2, the number of all possible transmitted signal vectors s is 42 = 16. It can be easily found that the number of possible transmitted signal vectors increases exponentially with M.

      In summary, maximum likelihood MIMO signal detection can be accomplished by retrieving all possible transmitted signals and calculating the corresponding likelihood function values. Defining f(y|s) as a likelihood function that transmits signal vector s when signal y is received, the transmitted signal vector of maximum likelihood can be expressed as

figure

      Since the maximum likelihood detection requires exhaustive retrieval and the number of all possible transmitted signal vectors is figureM, the computational complexity of the ML detection algorithm increases exponentially with the number of transmit antennas M.

      2.4.2.2Linear MIMO signal detection

      In order to reduce the complexity of detection, we can also consider using the linear filtering method to complete the detection process. In the linear MIMO signal detection, each transmitted signal can be detected separately after the received signal y is filtered by a linear filter. Therefore, the function of a linear filter is to separate the interference signals.

      First, we consider zero forcing (ZF) detection. The ZF detection linear filter is defined as

figure

      And the corresponding ZF signal is estimated as

figure

      With figure and figure, the hard decision of the transmitted signal vector s can be made by the symbol-level estimation.

      It should be noted that since the noise term, namely the effect of (HHH)−1HHn in Eq. (2.148), will be amplified, the equivalent noise will be amplified when the channel matrix H is nearly singular. Therefore, the performance of the ZF detection cannot be well guaranteed. In order to reduce the influence caused by the equivalent noise being amplified in the ZF detection, the MMSE detection utilizes the statistical property of the noise to improve the ZF detection method. The calculation of the MMSE filter matrix is based on the minimum mean square error criterion.

figure

      where Es represents the signal energy. The corresponding estimate of the transmitted signal vector can be expressed as

figure

      

      Therefore, the MMSE hard decision figure of the signal vector s can be obtained.

      2.4.2.3Successive interference cancellation (SIC) detection

      With the consideration of the existence of interference signals, how to realize high-performance signal detection has become a key issue that modern wireless communication needs to solve. For example, assume that the signal received by the receiver is

figure

      where si and hi represent the ith signal and the channel gain experienced by the signal, respectively, and n represents the background noise. When detecting the signal s1, the signal-to-interference plus noise ratio can be expressed as

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