Joint Frequency Offset and Channel Estimation for OFDM Systems Using Pilot Symbols and Virtual Carriers

TLDR: The receive-signal correlation structure due to the pilots and VCs is derived, the evidence of joint multivariate Gaussian distribution of the received samples is given, and an approximate maximum likelihood (ML) frequency offset estimator is derived.

Abstract: We consider joint estimation of carrier frequency offset and channel impulse response (CIR) for orthogonal frequency division multiplexing (OFDM) systems with pilot symbols and virtual subcarriers (VCs). We derive the receive-signal correlation structure due to the pilots and VCs, give the evidence of joint multivariate Gaussian distribution of the received samples, and derive an approximate maximum likelihood (ML) frequency offset estimator. We also derive the asymptotic mean-square error (MSE) and an approximate Cramer-Rao bound (CRB) and establish the asymptotic unbiasedness. Without pilots, in high signal-to-noise ratio, our estimator is equivalent to Liu and Tureli's estimator with Nv virtual carriers. When the pilot number (Np) is greater than the channel length L, our estimator acts as a subspace-based estimator with Nv + Np - L virtual carriers. A decision-directed joint ML estimator is derived to iteratively update the estimates of frequency offset, data symbols and CIR. The optimal pilot and virtual carrier placement strategies are also discussed. The resulting decision-directed joint estimator performs within 0.8 dB of the ideal case even when the frequency offset is as large as 20%

Figures

Fig. 2. NMSE versus carrier frequency offset.

Fig. 5. NMSE of the joint ML estimation of the carrier frequency offset versus SNR

Fig. 6. Bit error rate of the joint ML estimation algorithm versus SNR

Fig. 1. OFDM system with pilot-symbol-aided channel estimation

Fig. 4. NMSE of the joint ML estimation of the channel response versus SNR

Fig. 3. NMSE versus SNR. P is the number of pilot symbols used in estimation, N=64, BPSK.