EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS LETTERS, VOL. 17, PP. 151-155, 2006 1 Maximum a posteriori decorrelating receiver for MC-CDMA systems Hatem Boujemˆaa and Mohamed Siala Higher School of Communications of Tunis, Route de Raoued Km 3.5, 2083 El Ghazala, Ariana, Tunisia boujemaa.hatem@supcom.rnu.tn, mohamed.siala@supcom.rnu.tn Abstract — In this letter, we propose a maximum a posteriori decorre- lating receiver for multicarrier code division multiple access systems. The decorrelating receiver consists in a maximum a posteriori combining of an uncorrelated version of the sig- nal demodulated over the different subcarriers. The decor- relating receiver performance is compared to that of the conventional receiver which is based on a maximum ratio combining strategy. I. Introduction The Conventional Receiver (CR) for MultiCarrier Code Di- vision Multiple Access (MC-CDMA) systems is based on a Maximum Ratio Combining (MRC) of the demodulated signal over the different subcarriers [1-2]. The MRC rule is optimum when the channel is known. However, this rule is no longer optimum when the channel is estimated and the fading characteristics on the different subcarriers are correlated. The correlation of the observed channel at the different subcarriers depends on both the multipath delay profile of the channel and the subcarriers separation. In order to improve the receiver performance, we extend in this letter the structure of the Decorrelating Receiver (DR), proposed in [3] for Direct Sequence (DS) CDMA systems, to MC-CDMA systems. The proposed receiver consists in a Maximum A Posteriori (MAP) combining of an uncorrelated version of the signal demodulated over the different subcarriers. This uncorrelated version is provided by means of the Karhunen Lo` eve (KL) orthogonal expan- sion using the channel statistics. For a precise characteri- zation and evaluation of the enhancement in performance provided by this new structure, the DR performance is in- vestigated for perfect and Maximum Likelihood (ML) esti- mated channel statistics and compared to that of the CR. Finally, note that the proposed receiver can be used for both uplink and downlink. II. System model An MC-CDMA transmitter spreads the original signal using a spreading code in the frequency domain [1-2]. In the following, the expressions of the transmitted and re- ceived signals are given in the presence of a single user, with the abstraction of serial-to-parallel conversion of the transmitted symbols [1]. Without loss of generality, the number of subcarriers, N , is assumed to be equal to the spreading factor. The equivalent base-band transmitted signal can be written as e(t)=  k s k g(t - kT s ) N-1  m=0 c kN+m e j2πfm(t-kTs) , (1) where s k is the k-th transmitted symbol, T s is the symbol period, {c kN+m } N-1 m=0 is a unit modulus spreading sequence, g(t) is a rectangular pulse response with unit useful energy and duration T s = T u s + ∆ where T u s is the useful symbol period and ∆ is the guard interval, f m = f 0 + m∆f is the m-th subcarrier frequency, f 0 is the frequency of the first subcarrier and ∆f =1/T u s is the subcarrier separation. The symbol stream is assumed to be organized in time slots containing respectively N d and N p data and pilot symbols. We denote by E s and E p respectively the useful transmit- ted energy per data and pilot symbols. If the channel delay spread is lower than the guard interval ∆, then the restriction of the received signal to the interval [kT s +∆, (k + 1)T s ] can be rewritten as r(t)= s k √ T s - ∆ N-1  m=0 c kN+m e j2πfm(t-kTs) H (f m ; t)+ n(t), (2) where H (f m ; t)=  h(τ ; t)e -j2πfmτ dτ, (3) h(τ ; t) is the impulse response of the multipath fading chan- nel at time instant t and n(t) is an additive white complex gaussian noise. An MC-CDMA receiver uses a Discrete Fourier Trans- formation (DFT) to recover the transmitted signal over the different subcarriers [1-2]. In the following, a perfect synchronization on the different subcarrier frequencies is assumed. After removing the received signal during the guard interval and compensating the modulation due to the spreading sequence, the DFT outputs for symbol s k can be written as z k =(z k,0 , ··· z k,N-1 ) T = s k H k + n k , (4) where H k = (H (f 0 ; kT s ), ··· ,H (f N-1 ,kT s )) T , n k = (n k,0 , ··· ,n k,N-1 ) T is a zero mean complex Gaussian noise with covariance matrix N 0 I N and (.) T is the transpose op- erator.