Hungarian-Murty Soft Decision Decoding Scheme for a MIMO-STBC-SPM Communication System

Abstract

The integration of Multiple-Input-Multiple-Output (MIMO), Space-Time Block Coding (STBC), and Spatial Permutation Modulation (SPM) has led to signifi- cant advancements in spectral efficiency and system performance. However, the decoding process in such systems can be computationally demanding. To address this challenge, a soft-decision decoding algorithm based on the Hungarian-Murty algorithm is proposed. The study aims to evaluate the impact and effectiveness of the Hungarian-Murty algorithm on the system’s performance, particularly in terms of Bit Error Rate (BER). The proposed algorithm seeks to enhance decoding efficiency while main- taining reliable error correction performance. The research reviews various low- complexity decoding algorithms and methods used to assess Space-Time Block Code performance, which have guided the development of the proposed solution. The study employs a MIMO-STBC-SPM transceiver system utilizing Quadrature Amplitude Modulation (QAM) and permutation in low-complexity schemes. The BER performance of these schemes is simulated in a Rayleigh fading multi-path channel with additional additive white Gaussian noise to support the evaluation of the proposed soft-decision decoding algorithm. The Hungarian-Murty Algorithm, a combinatorial optimization algorithm, is used to solve assignment problems within MIMO systems with STBC-generalized spa- tial permutation modulation. This algorithm optimizes the signal-to-noise ratio (SNR) at the receiver by finding the optimal permutation matrix for data bit encoding. The soft-decision decoder iteratively ranks the costs of the input sig- nal matrix until the assignment produces a valid code word, thereby improving decoding efficiency and error correction. STBC-SM (Space-Time Block Code with Spatial Modulation) and STBC-SPM are discussed, highlighting their enhancements in error rate performance through the integration of STBC techniques and the use of permutation vectors. Spatial Per- mutation Modulation (SPM) and Generalized Spatial Modulation (GSM) are also explored, demonstrating their contributions to improving diversity and reducing error rates. The findings of this study are expected to provide valuable insights into the Hungarian-Murty algorithm’s effectiveness in reducing computational complexity iv while maintaining reliable performance in MIMO-STBC-SPM systems, thereby advancing the field of wireless communications. An analysis of complexity shows that the Hungarian Murty Algorithm (HMA) con- siderably lowers computational requirements. While traditional Maximum Like- lihood (ML) Hard Decision Decoding operates with a factorial time complexity of O(K! · Nt), the HMA reduces this to a more manageable O(K4 · Nt), where K is the size of the permutation vector, and Nt denotes the number of transmit antennas. This simplification makes the HMA particularly advantageous for large MIMO systems. Regarding BER performance, the HMA-based decoder shows significant improve- ments, especially in systems utilizing 16-QAM modulation. Simulation results in- dicate that at higher SNR, the HMA can achieve up to a 2 dB improvement in BER compared to traditional ML Hard Decision Decoding. In contrast, at lower SNRs, 4-QAM systems perform better due to their resilience to noise, while the higher- order 16-QAM system benefits more from the HMA at increased SNRs, leading to better data throughput and reduced errors. Additionally, systems equipped with multiple receiving antennas (Nr = 2) experience up to a 30% decrease in BER at critical SNR levels. The results from this research underscore the potential of the Hungarian-Murty Algorithm to improve both computational efficiency and error performance in MIMO-STBC-SPM systems. By effectively balancing complexity and perfor- mance, the HMA offers a promising solution for enhancing the reliability and efficiency of wireless communication systems, particularly in challenging or high- noise conditions.