On Optimizing the CP Length for MISO-OFDM in 6G Industrial Networks

Current orthogonal frequency division multiplexing (OFDM) standards specify limited options for cyclic prefix (CP) duration, regardless of the wireless channel characteristics. These fixed options can result in significant overhead when the channel delay spread is very short. To address this, a more flexible approach to CP selection is needed, allowing for CP lengths that may be shorter than the delay spread. In this paper, we revisit the classical issue of waveform optimization for channels with short delay spreads, and investigate the potential to reduce the CP duration in OFDM. Building on our prior work in [1], we extend the analysis to multi-antenna systems and assess the impact of number of antennas on multiple-input single-output (MISO)-OFDM system with reduced CP durations. We first derive closed-form expressions for the desired signal power and inter-symbol interference (ISI) power in MISO-OFDM where the CP duration is shorter than the length of channel impulse response (CIR). Then, conditioned on the radio link reliability, defined by the link outage probability, we formulate an optimization problem to jointly determine the minimum CP duration and SNR values required for the system to satisfy that reliability condition. To solve the optimization problem, we use a weighted-sum approach combined with the Bisection method. Our analysis demonstrates that energy efficiency comparable to conventional OFDM systems can be maintained, while achieving increased spectral efficiency (SE) due to the reduced CP duration.