Читать книгу Spatial Multidimensional Cooperative Transmission Theories And Key Technologies - Lin Bai - Страница 54

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.