A Closed-Form Minimum BER Precoder for Orthogonal Time Frequency Space Systems

• Published in: IEEE communications letters Vol. 26; no. 8; pp. 1898 - 1902
• Main Authors: Sun, Jinjing, Wang, Zulin, Huang, Qin
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bit error rate; Closed form solutions; Convexity; Errors; Exact solutions; Interference; Lower bounds; Manganese; Minimization; minimum BER precoder; minimum mean square error; Optimization; Orthogonal time frequency space; Signal to noise ratio; Symbols; Time-frequency analysis; zero-forcing
• ISSN: 1089-7798; 1558-2558
• DOI: 10.1109/LCOMM.2022.3175474

This letter devises a closed-form precoder for Orthogonal Time Frequency Space (OTFS) systems with linear equalization to minimize the bit error rate (BER). The precoder is developed by optimally allocating the power to adapt to the equivalent channel in the delay-Doppler domain. To achieve the minimum BER precoder design, we convert the minimization of the average BER into the minimization of its lower bound subject to a transmission power constraint. By exploiting the convexity, a closed-form minimum BER precoder is designed, which actually achieves the lower bound. As such, the unified bit error probability function for both the zero-forcing (ZF) and minimum mean square error (MMSE) equalizations is derived and verified with their numerical counterparts. Simulation results demonstrate that the designed precoders can provide lower BER than the existing linear equalizations without precoding.