OFDM channel estimation and data detection with superimposed pilots

We propose three iterative superimposed-pilot based channel estimators for Orthogonal Frequency Division Multiplexing (OFDM) systems. Two are approximate maximum-likelihood, derived by using a Taylor expansion of the conditional probability density function of the received signal or by approximating the OFDM time signal as Gaussian, and one is minimum-mean square error. The complexity per iteration of these estimators is given by approximately O(NL^2), O(N^3) and O(NL), where N is the number of OFDM subcarriers and L is the channel length (time). Two direct (non-iterative) data detectors are also derived by averaging the log likelihood function over the channel statistics. These detectors require minimising the cost metric in an integer space, and we suggest the use of the sphere decoder for them. The Cramer–Rao bound for superimposed pilot based channel estimation is derived, and this bound is achieved by the proposed estimators. The optimal pilot placement is shown to be the equally spaced distribution of pilots. The bit error rate of the proposed estimators is simulated for N = 32 OFDM system. Our estimators perform fairly close to a separated training scheme, but without any loss of spectral efficiency.