Pilot symbols for channel estimation in OFDM systems

We consider superimposing pilot symbols on to data symbols for channel estimation for orthogonal frequency division multiplexing (OFDM) systems. We first derive maximum-likelihood (ML) and minimum-mean square error (MMSE) iterative channel estimators. Modeling the time domain signal as Gaussian, we derive an ML channel estimator by averaging the likelihood function for both data and channel impulse response (CIR) over the resulting Gaussian vector. Two data detectors are also proposed by eliminating the CIR from the likelihood function. The resulting integer least squares problem can be efficiently solved using a sphere decoder (SD). Furthermore, the Cramer-Rao bound (CRB) for the superimposed channel and data estimation is derived. The equispaced pilot placement is optimal in superimposed training. The ideal performance benchmarks are reached by our proposed estimators. Their performance is comparable to that of a separated training scheme, but they offer a higher data rate