Spatial Multidimensional Cooperative Transmission Theories And Key Technologies. Lin Bai

       Fig. 2.11. The MIMO system model.

2.4.2Uncoded MIMO signal detectionb

      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 ^M, where 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

      Since the maximum likelihood detection requires exhaustive retrieval and the number of all possible transmitted signal vectors is ^M, 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

      And the corresponding ZF signal is estimated as

      With and , 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 (H^HH)⁻¹H^Hn 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.

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

      

      Therefore, the MMSE hard decision 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

      where s_i and h_i 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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