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

Abstract

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 single- output (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. the error performance of K-best detection depends on the choice of K and this dependency of error performance over K needs to be analyzed. In this paper an upper bound on the symbol error rate (SER) of K-best detection for MIMO systems with linear modulation has been derived. This upper bound is found to be a function of SER performance of K- best detection for SISO systems. Though K-best detection is meaningless for SISO systems but to establish the upper bound it is necessary to find its error performance. Therefore we first derive an exact expression for one dimensional constellation i.e. M-PAM with K-best detection for SISO systems over AWGN as well as Rayleigh channel and use it to establish the upper bound. We have also analyzed the two dimensional constellation geometries for different values of K. Particularly for 4-QAM, we first derive the expressions for different values of K and then use these expressions to derive the upper bound. The trend of SER performances for different values of K has been investigated and it shows that the derived upper bound is close to the simulation results. The rest of this paper is structured as follows: Section II describes the system model and Section III first describes the K-best detection and then a general upper bound on the error performance of K-best is established. To derive the upper bound for specific cases such as M-PAM and 4-QAM the exact expressions for K-best detection with SISO systems have been established in Section IV and V respectively. Section VI compares the theoretical results with simulations and finally Section VII concludes the paper.