Over the last few years, the mobile communication technology develops rapidly, and
so do the wireless techniques. The wideband transmission became an inevitable trend because of the data rate demanded by users. The wireless network has the advantage of the mobility, the convenience and the high-coverage. Limits of time and place do not restrain the
communication among people. However, the channel of the wireless communication is interfered with by severe noise, and the multipath effect is also a problem which should be overcome. The multipath propagation causes the frequency selective fading and the
inter-symbol interference (ISI), and thus harms the quality of transmission and degrades the system performance. It would be significant to choose an appropriate system model according to the channel conditions and the requirements for transmission.
There are many techniques invented for raising the utility rate and mitigating the influence of the multipath effect, and orthogonal frequency division multiplexing (OFDM) is one of the most famous schemes. In OFDM, subcarrier frequencies are chosen to be
orthogonal to each other; namely, the crosstalk between the sub-channels is eliminated. The orthogonality also provides high spectral efficiency since almost the whole available
frequency band can be utilized. The duration of each symbol is long enough to put in a guard interval to eliminate the ISI, and the cyclic prefix (CP) used as the guard interval consists of a copy of the end of the OFDM symbol. Besides, OFDM is equipped for coping with
attenuation of high frequencies in a long copper wire and narrowband interference. The effect of frequency selective fading can be considered as flat over an OFDM sub-channel if its band is sufficiently narrow. This makes the equalizer simpler at the receiver compared with
conventional single-carrier modulation.
OFDM requires accurate frequency synchronization between the receiver and the transmitter. The subcarriers are no longer orthogonal if there is frequency deviation, inducing the inter-carrier interference (ICI). Frequency offsets are typically caused by mismatched transmitter and receiver oscillators, or by Doppler shift due to movement, and this effect worsens as speed increases or as the length of a symbol gets longer. In communication systems, the transmission often proceeds in the high- mobility condition, but the time-variant channels damage the orthogonality, cause the ICI effect and then lower the system
performance. As a result, the ICI suppression is a significant issue for research in mobile communication, and it is also the main study in this paper.
There have been many techniques suggested for the ICI suppression; for example, minimum mean square error (MMSE) [3], minimum mean square error with successive detection (MMSE-SD) [3], polynomial cancellation coding (PCC) [4] and self-cancellation coding [5]. The method in [3] is efficient but with high computational complexity. The schemes in [4] and [5] provide good bit error rate (BER) performance at the expense of sacrificing bandwidth efficiency. In [6] and [7], the piece-wise linear model is proposed to
approximate the channel variation, helping the analysis of properties of the channel. It is explained that energy of a sub-carrier leaks to the adjacent sub-carriers owing to Doppler shift in [8] and [9]. The expectation-maximization (EM) algorithm can be utilized to solve the maximum-likelihood (ML) estimation problem in an iterative manner. Recently, some EM-based methods have been proposed for channel estimation and data detection in OFDM systems. But the wireless channel is assumed to be quasi-static, i.e., channel gain remains constant over the duration of one OFDM symbol.
In this paper, we propose an EM-based receiver for OFDM systems in doubly selective fading channels. By assuming channel varies in a linear fashion, we analyze the ICI effect in frequency domain and derive a channel estimation method based on the EM algorithm in [10]
and [11] under the ML criterion. A Gibbs sampler (a Markov chain Monte Carlo procedure) is used for the calculation of Bayesian estimates and also for data detection in the EM algorithm.
Moreover, we combine the EM-based receiver with a group-wise ICI cancellation scheme for the sake of reducing the computational complexity. The ML-EM receiver is implemented to iterate between a group-wise ICI canceller and an EM detector (including the Gibbs samplers inside). The MMSE estimator is employed in the receiver for the initial setting by exploiting the pilot tones in each frame, and the accuracy of initialization can be refined successfully through the mechanism of decision feedback.
The rest of this paper is organized as follows. In Chapter 2, the system under study is
described and the ICI effect is analyzed in frequency domain. And the basic idea of the Gibbs sampling method is briefly introduced in Chapter 3. In Chapter 4, a channel estimation method is derived from the EM algorithm combined with a Gibbs sampler using the ML criterion, and accordingly, we propose an ML-EM receiver for OFDM systems. And the ML-EM receiver is further united with the group-wise method in chapter 4.The problem of computing the ICI power (or the variance of ICI) for the Gibbs sampling is treated in Chapter 5. Results of computer simulation are presented and discussed in Chapter 6. In the final part of the paper, Chapter 7, we draw some conclusions for the study.
The following are some interpretations of notations used in the paper. Boldface capital letters denote matrices, whereas boldface lowercase letters denote column vectors. The superscripts and stand for the transpose and the Hermitian transpose of a matrix, respectively. The column vector can be explicitly expressed by
( )
⋅ T( )
⋅ Hx x x1, 2,…,xx or
{ }
: 1, ,
x ii ∈ …
x
, where x is the dimension of the vector x. The notation{ }
…represents a set, e.g. a set x=