An upper bound on the performance of K-best detection for MIMO systems

K-best detection is known to be a useful breadth first tree search detection technique for multiple input multiple output (MIMO) systems. In the process of the tree search a number of possible transmitted symbols are searched and the error performance of the K-best detection depends on this number. More the number of visited symbols, better the error performance. However this relationship is not straightforward and needs to be analyzed. In this paper, a tight upper bound on the error performance of K-best detection for MIMO systems with linear modulation scheme has been derived. In particular upper bounds for M-ary pulse amplitude modulation (M-PAM) and for 4-ary quadrature amplitude modulation (4-QAM) with Rayleigh fading channel have been established. This upper bound requires the K-best error performance for single-input singleoutput (SISO) systems. Hence we first derive an exact expression for M-PAM as well as for 4-QAM with K-best detection for SISO systems and use this to establish the upper bound. Finally we compare the derived upper bound with the simulations. It is found that the upper bound is close to the results obtained through simulations.