OFDM Communications System with Channel Estimation and LS and MMSE Equalization

Abstract

Channel estimation and subsequent equalization are key building blocks in OFDM (Orthogonal Frequency-Division Multiplexing) receivers, since each subcarrier undergoes a complex multiplicative distortion and equalization accuracy directly impacts the bit error rate (BER). This paper compares two channel estimation approaches based on the incorporation of pilot carriers: Least Squares (LS) with frequency-domain reconstruction using pchip interpolation, and a Linear Minimum Mean Square Error (LMMSE/MMSE) estimator consistent with the channel power delay profile (PDP), implemented as a Wiener filter in the frequency domain. A baseband OFDM system with a 16-sample cyclic prefix is considered under a multipath Rayleigh fading channel whose maximum delay is contained within the cyclic prefix (), enabling the per-subcarrier multiplicative model and one-tap equalization. Two Wi-Fi-inspired OFDM numerologies are evaluated:  subcarriers (802.11a/g/n/ac-like) and  subcarriers (802.11ax-like). To relate the study to practical wireless scenarios, modulation formats representative of MCS schemes used across the IEEE 802.11 family are assessed: BPSK, QPSK, 16-QAM, 64-QAM, 256-QAM, and 1024-QAM. Performance is assessed through Monte Carlo simulations of BER versus SNR for different pilot counts () and complemented with constellation diagrams. Results show that LS improves as pilot density increases, but may exhibit a BER floor when interpolation fails to track significant frequency selectivity between pilot tones. Conversely, the PDP-based LMMSE/MMSE estimator achieves lower BER across the full SNR range—particularly with sparse pilots—by exploiting the frequency correlation structure induced by multipath propagation.