EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS Eur. Trans. Telecomms. 2011; 22:125–136 Published online 4 March 2011 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/ett.1461 TRANSMISSION SYSTEMS OFDM channel estimation and data detection with superimposed pilots Tao Cui 1 and Chintha Tellambura 2∗ 1 Department of Electrical Engineering, California Institute of Technology, Pasadena, CA 91125, USA 2 Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2C5 ABSTRACT 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 Cram´ er--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. Copyright © 2011 John Wiley & Sons, Ltd. * Correspondence Chintha Tellambura, Department of Electrical and Computer Engineering, University Alberta, Edmonton, Alberta, Canada T6G 2C5. E-mail: chintha@ece.ualberta.ca Received 20 July 2009; Revised 23 July 2010; Accepted 13 October 2010 1. INTRODUCTION Orthogonal Frequency Division Multiplexing (OFDM) has recently attracted much interest because of its high spec- tral efficiency and simple single-tap equalisation. However, since OFDM requires accurate channel estimates, pilot schemes has thus been widely studied [1]. Conventionally, pilots and data symbols are multiplexed in time and/or fre- quency. In rapid time varying mobile radio environments, closely spaced pilot symbols may be needed, resulting in a significant bandwidth loss. One potential solution is to use semi-blind or blind channel estimators. Those tech- niques however may exhibit both high complexity and phase ambiguities. Superimposed pilots involve arithmetically adding pilot tones to scaled data symbols. This approach enables chan- nel estimation, but incurs no spectral efficiency loss. This idea was first proposed for analogue communication in Ref. [2] and was later extended to digital single carrier sys- tems in Ref. [3]. Recently, this idea has received much renewed attention [4--17]. Reference [4] considers power allocation and system capacity of OFDM with superim- posed pilots. The use of first order statistics is considered in Ref. [5]. Reference [6], an early version of this paper, and [7, 8] provide iterative estimators. Additional topics of superimposed pilots can be found in Refs. [9--14]. In Ref. [15], a two-dimensional Wiener filter is employed to obtain channel estimates using second order statistics. However, this scheme is sensitive to the pilot-to-signal power ratio (PSR). To prevent the increase of the peak-to- average power ratio (PAPR), superimposed pilots must be carefully chosen. Redundant precoded block transmission [16] shows that in OFDM systems pilot and data super- imposed in time becomes separated in frequency, which turns out to be the separated training scheme in Ref. [1]. Iterative coded OFDM channel estimation is considered in Ref. [17]. In this paper, we derive three iterative superimposed pilot based channel estimators and two non-iterative data detectors for OFDM systems. The first one is an approximate maximum-likelihood (ML) iterative estimator, which is obtained by using a Taylor series approximation Copyright © 2011 John Wiley & Sons, Ltd. 125