Complexity Reduction by Using Triangular Matrix Multiplication in Computing Capacity for an Optimal Transmission

Multiple-input-multiple-output (MIMO) technique is often employed to increase capacity in comparing to systems with single antenna. However, the computational complexity in evaluating channel capacity or transmission rate (data rate) grows proportionally to the number of employed antennas at both ends of the wireless link. Recently, the QR decomposition (QRD) based detection schemes have emerged as a lowcomplexity solution. After conducting QRD on a full channel matrix that results in a triangular matrix, we claim that computational complexity can be simplified by the following ways. First, to simplify channel capacity calculation, we prove that eigenvalues of the full channel matrix multiplication equals eigenvalues of the triangular channel matrix multiplication. Second, to simply evaluate optimal transmission rate constrained constellation, we propose a simplified multiplication of the resulted simple triangular matrix and a transmitted signal vector. Then, we also propose a modified mutual information calculation (MMIC) to reduce the multiplication complexity in combinational multiplication processes via the divided calculation. This divided calculation is employed in the parallel architecture for the field-programmable gate array (FPGA) implementation. That is, the number of multiplications can be reduced via increasing the number of additions in the FPGA implementation. By using the computer and FPGA implementation, simulation results show that the proposed QRD-based schemes are capable of achieving conventional performance, but at a low-complexity level. Key-Words: Multiple-input multiple-output, channel capacity, QR decomposition, eigenvalues, mutual information, field-programmable gate array.