This paper introduces an expectation-maximization (EM) algorithm within a wavelet domain Bayesian framework for semi-blind channel estimation of multiband OFDM based UWB communications. A prior distribution is chosen for the wavelet coefficients of the unknown channel impulse response in order to model a sparseness property of the wavelet representation. This prior yields, in maximum a posteriori estimation, a thresholding rule within the EM algorithm. We particularly focus on reducing the number of estimated parameters by iteratively discarding ``unsignificant'' wavelet coefficients from the estimation process. Simulation results using UWB channels issued from both models and measurements show that under sparsity conditions, the proposed algorithm outperforms pilot based channel estimation in terms of mean square error and bit error rate and enhances the estimation accuracy with less computational complexity than traditional semi-blind methods.
A UWB radio signal is defined as any signal whose bandwidth is larger than 20% of its center frequency or greater than 500 MHz [1]. In recent years, UWB system design has experienced a shift from the traditional "single-band" radio that occupies the whole 7.5 GHz allocated spectrum to a "multiband" design approach [2]. That consists in dividing the available UWB spectrum into several subbands, each one occupying approximately 500 MHz.
Multiband Orthogonal Frequency Division Multiplexing (MB-OFDM) [3] is a strong candidate for multiband UWB which enables high data rate UWB transmission to inherit all the strength of OFDM that has already been shown for wireless communications (ADSL, DVB, 802.11a, 802.16.a, etc.). This approach uses a conventional coded OFDM system [4] together with bit interleaved coded modulation (BICM) and frequency hopping over different subbands to improve diversity and to enable multiple access.
Basic receivers proposed for MB-OFDM [3], estimate the channel by using pilots (known training symbols) transmitted at the beginning of the information frame, implicitly assuming a time invariant channel within a single frame. Thus, for an accurate channel acquisition, one must send several pilot patterns resulting in a significant loss in spectral efficiency.
Recent works [5], [6] have reported promising results on the combination of channel estimation and data decoding process by using the Expectation-Maximization (EM) algorithm [7] . Though the latter scheme outperforms pilot based receivers, it has a higher complexity that may be of a critical concern for its practical implementations. This complexity is mainly dominated by the number of estimated parameters for channel updating and the decoding algorithm within each iteration.
In this work, we consider a semi-blind joint channel estimation and data detection scheme based on the EM algorithm, with the objective of minimizing the number of estimated parameters and enhancing the estimation accuracy. This is achieved by expressing the unknown channel impulse response (CIR) in terms of its discrete wavelet series, which has been shown to provide a parsimonious representation [8], [9]. Thus, we choose a particular prior distribution for the channel wavelet coefficients that renders the maximum a posteriori (MAP) channel estimation equivalent to a hard thresholding rule at each iteration of the EM algorithm. The latter is then exploited to reduce the estimator computational load by discarding “unsignificant” wavelet coefficients from the estimation process. Moreover, since the probability of encoded bits are involved in the EM computation, we naturally combine the iterative process of channel estimation with the decoding operation of encoded data.
This paper is organized as follows. Section II introduces MB-OFDM and its wavelet domain channel estimation observation model. In section III, we first describe a MAP version of the EM algorithm for channel estimation and then show how the number of estimated parameters can be reduced through the EM iterations. The combination of the channel estimation part with the decoding operation and implementation issues are also discussed. Section V illustrates, via simulations, the performance of the proposed receiver over a realistic UWB channel environment and section VI concludes the paper.
Notational conventions are as follows: D x is a diagonal matrix with diagonal elements x = [x 1 , . . . , x N ] T , E x [.] refers to expectation with respect to x, I N denotes an (N × N ) identity matrix; . , (.) * , (.) T and (.) H denote Frobenious norm, matrix or vector conjugation, transpose and Hermitian transpose, respectively.
FORMULATION MB-OFDM system divides the spectrum between 3.1 to 10.6 GHz into several non-overlapping subbands each one occupying 528 MHz of bandwidth [3]. The transmitter architecture for the MB-OFDM system is very similar to that of a conventional wireless OFDM system. The main difference is that MB-OFDM system uses a time-frequency code (TFC) to select the center frequency of different subbands which is used not only to provide frequency diversity but also to distinguish between multiple users (see figures 1 and 2). Here, we consider MB-OFDM in its basic mode ie. employing the three first subbands. We consider the multiband OFDM transmission of figure 2 using N data subcarriers. At the receiver, assuming a cyclic prefix (CP) longer than the channel maximum delay spread and perfect synchronization, OFDM converts a frequency selective channel into N parallel flat fading subchannels [4] for each subband as
where (1 × N ) vectors y i,n , s i,n and h i,n denote received and transmitted symbols, and the channel frequency response respectively; the noise block z i,n is assumed to be a zero mean white complex Gaussian noise with distribution CN (0, σ 2 I N ) ; i is the subband index and n refers to the OFDM symbol index inside the frame. The observation model corresponding to all three subba
This content is AI-processed based on open access ArXiv data.
