Preconditioned Iterative Inter-Carrier Interference Cancellation for OFDM Reception in Rapidly Varying Channels Andrea Ancora, Giuseppe Montalbano ST-Ericsson Business Unit Cellular Systems 505 route des Lucioles 06560 Sophia Antipolis, France Email: {Andrea.Ancora, Giuseppe.Montalbano}@stericsson.com Dirk T.M. Slock EURECOM Mobile Communications Dept. 2229 route des Crˆ etes, BP 193 06904 Sophia Antipolis Cedex, France Email: Dirk.Slock@eurecom.fr Abstract—The attractiveness of OFDM decreases with the ris- ing of inter-carrier interference in quickly time-varying channels. Classical OFDM low-complex detection is impaired and more elaborated techniques are required to mitigate the need for full matrix equalization. We present here a fresh approach to this subject, introducing novel fast-converging iterative techniques based on preconditioning. Moreover, we interpret windowing under a new perspective in association with the Basis Expansion Modeling of the time-varying channel. We discuss the complexity of the proposed methods, showing that they are still linear to the OFDM block size. We conclude by illustrating their competitive performance by means of numerical simulations. Index Terms—OFDM, Inter-Carrier Interference, Iterative Interference Cancelling, Basis Expansion Modeling I. I NTRODUCTION Orthogonal Frequency Division Multiplexing (OFDM), adopted by numerous existing wireless telecommunication standards, allows for flexible bandwidth allocation and low- complexity transmitter and receiver architectures. However the performance of classical OFDM low complexity receivers is severely impacted by fast time-varying propagation channels causing the rising of inter-carrier interference (ICI). Those circumstances occur in the presence of high Doppler spread relative to the OFDM symbol rate due to the mobile re- ceiver velocity. In practice, the increased ICI prevents classical OFDM receiver schemes from reliably detecting the desired signal. Hence, more advanced receiver equalization techniques are required to mitigate the effect of the ICI. Optimal linear ICI equalization techniques generally involve complex full channel matrix inversion. In existing OFDM telecommunication systems, the typical size of the required Discrete Fourier Transform renders such a full channel matrix inversion operation prohibitively complex for practical imple- mentation. Hence, several approaches have been adressed to reduce the complexity while maintaining acceptable perfor- mance. To this end, the use of time-domain windowing of the OFDM received signal has been shown to limit the significant span of the ICI, generating banded channel transfer matrices. In addition, iterative equalization and detection techniques have been proposed to further reduce the complexity of the receiver operating in the frequency-domain, see e.g. [1], [2] and references therein, or in the time-domain as in [3], [4]. We introduce here an alternative and original framework for iterative ICI cancellation. Our analysis of the detection performance, the convergence speed, and the complexity pro- vide guidelines to derive novel fast-converging iterative ICI cancellation algorithms. We show that proper preconditioning exploiting the inherent structure of the OFDM signal and the ICI yields to nearly optimal detection performance with very fast-converging and affordable complexity iterative algorithms. II. SIGNAL AND SYSTEM MODEL We consider the transmission over a time-varying, frequency-selective fading channel with continuous-time im- pulse response h(t,τ ) = ∑ m α m (t)ψ(τ − τ m ) assumed to obey the wide sense stationary uncorrelated scattering (WSS-US) model [5], where ψ(τ ) represents the equivalent transmit-receive front-end low-pass filter, τ m represents the p-th path delay, α m (t) is the time-varying complex channel coefficient associated with the m-th path of the propagation channel respectively. We shall refer to h[k,l] as the corre- sponding low-pass sampled discrete-time impulse response, and assume h[k,l] to be well-approximated by a finite-impulse response model with a maximum delay spread of L samples. Then we assume a classical OFDM system with cyclic- prefix (CP) of duration N cp ≥ L to avoid inter-symbol- interference. By letting N denote the number of sub-carriers the OFDM symbol duration is given by N block = N + N cp . The frequency-domain k-th OFDM transmit symbol s[k]= [s[kN ] ...s[kN − N + 1]] T , where (·) T denotes transpose, comprising the encoded symbols s[i] at the output of channel encoding, interleaving and mapping onto a finite-symbol con- stellation S assumed i.i.d. with unit energy, is modulated by an N ×N discrete-Fourier transform unitary matrix F so as to obtain x[k]= F H s[k] where (·) H denotes Hermitian operator. For the sake of the notational simplicity and without loss of generality, we shall drop the time index k in the sequel.