Complexity Reduction by Using QR-Based Scheme in Computing Capacity for Optimal Transmission

Chien-Hung Pan

Research output: Contribution to journalArticlepeer-review


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 low-complexity 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 simplify the calculation of the optimal transmission rate constrained constellation, we propose a simplistic multiplication of the resulted simple triangular matrix and a transmitted signal vector. Then, we also propose a modified mutual information calculation (MMIC) to achieve a quite low-complexity via the divided calculation. By using computer simulation and field- programmable gate array (FPGA) implementation, simulation results show that the proposed QRD-based schemes are capable of achieving conventional performance, but at a low-complexity level.
Original languageEnglish
Pages (from-to)391-405
Number of pages15
JournalWireless Personal Communications
Issue number2
StatePublished - May 2011


  • Multiple-input multiple-output
  • Channel capacity
  • QR decomposition
  • Eigenvalues
  • Mutual information
  • Field-programmable gate array


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