4.3 Proposed Channel Estimation Method
4.5.6 Average Number of Iterations
Figure 4.12 compares the average number of iterations in the ITU Veh-A channel for 16QVeh-AM modulation at ve = 240km/hr with |J| = 8 and Eb/No=20dB. Due to the use of the approximate weighting matrix, when
|Θ| is larger than 48, the method III requires one more iteration compared with the method II. However, the method III is still an attractive approach by decreasing V from 7 to 6 at the price of slight BER performance degradation when the computational complexity of matrix inverse is an issue.
0 2 4 6 8 10 12 14 16 18 20 22
−30
−28
−26
−24
−22
−20
−18
−16
−14
−12
Eb/No (dB)
NSE
Two−Path channel Veh−A channel
Figure 4.4: NSE performance of the MPIC-based decorrelation method in the initialization stage (ve = 240km/hr).
0 2 4 6 8 10 12 14 16 18 10−4
10−3 10−2 10−1
Eb/No (dB)
BER
Method I Method II Method III
STBC−Based MMSE Kalman Filtering Perfect CSI
Figure 4.5: BER performance for QPSK modulation in the two-path channel at ve = 240km/hr (|J| = 8 and |Θ| = |Q| = 192).
4 6 8 10 12 14 16 18 20 22 10−3
10−2 10−1
Eb/No (dB)
BER
Method I Method II Method III
STBC−Based MMSE Kalman Filtering Perfect CSI
Figure 4.6: BER performance for 16QAM modulation in the two-path chan-nel at ve= 240km/hr (|J| = 8 and |Θ| = |Q| = 192).
4 6 8 10 12 14 16 18 20 22 10−3
10−2 10−1
Eb/No (dB)
BER
Method I Method II Method III
STBC−Based MMSE Kalman Filtering Perfect CSI
Figure 4.7: BER performance for 16QAM modulation in the ITU Veh-A channel at ve = 240km/hr (|J| = 8 and |Θ| = |Q| = 192).
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 10−4
10−3 10−2 10−1
fd
BER
Method I Method II Method III
Without Error Propagation Perfect CSI
Figure 4.8: BER versus normalized maximum Doppler frequency in the ITU Veh-A channel for QPSK modulation (|J| = 8, |Θ| = |Q| = 192, and Eb/No=16dB).
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 10−4
10−3 10−2 10−1
fd
BER
Method I Method II Method III
Without Error Propagation Perfect CSI
Figure 4.9: BER versus normalized maximum Doppler frequency in the ITU Veh-A channel for 16QAM modulation (|J| = 8, |Θ| = |Q| = 192, and Eb/No=22dB).
2 3 4 5 6 7 8 9 10 11 10−3
10−2 10−1
|J|
BER
Method I Method II Method III
Without Error Propagation Perfect CSI
Figure 4.10: BER versus number of pilot tones used in the ITU Veh-A channel for 16QAM modulation (ve = 240km/hr, |Θ| = |Q|, and Eb/No=20dB).
192 96 48 24 12 6 3 10−3
10−2 10−1 100
|θ|
BER
Method I Method II Method III
Without Error Propagation Perfect CSI
Figure 4.11: BER versus number of data subcarriers used in the ITU Veh-A channel for 16QAM modulation (ve = 240km/hr, |J| = 8, and Eb/No=20dB).
192 96 48 24 12 6 3 1
2 3 4 5 6 7 8
|θ|
Average number of iterations
Method I Method II Method III
Figure 4.12: Average number of iterations versus |Θ| in the ITU Veh-A chan-nel for 16QAM modulation (ve = 240km/hr, |J| = 8, and Eb/No=20dB).
4.6 Summary
In this chapter, we present a two-stage channel estimation method for STBC-OFDM systems in mobile wireless channels. In the initialization stage, an MPIC-based decorrelation method is used to estimate multipath delays and multipath complex gains. In the tracking stage, two refined DF DFT-based channel estimation methods are proposed by using a few pilot tones to form an optimal gradient vector at the first iteration, and the optimal step size is directly calculated from the received signals. Further, in order to reduce computational complexity of matrix inverse in the method II, an approximate weighting matrix is proposed and used in the method III. The simulation results show that both the method II and the method III can effectively alle-viate the error propagation effect and thus significantly improve the perfor-mance of the method I (i.e., the classical DF DFT-based channel estimation method). The two refined methods also outperform the STBC-based MMSE method and the Kalman filtering method, especially when a high-level mod-ulation scheme, e.g. 16QAM, is adopted in mobile environments.
Chapter 5
EM-based Iterative Receivers for OFDM and BICM-OFDM Systems in Doubly Selective Channels
5.1 Literature Survey and Motivation
OFDM is a promising technique to realize high data rate transmission over multipath fading channels. Due to the use of a GI, it allows for a simple one-tap equalizer [52]. In addition, BICM combined with OFDM, known as BICM-OFDM, is introduced as a way to offer superior performance by exploiting frequency diversity [53]. Over the past decade, OFDM has found widespread application in several standards such as 802.16e WMAN [54].
However, in mobile radio environments, multipath channels are usually time-variant. The channel time variation destroys the orthogonality among
sub-carriers, and thereby yields ICI. The effect of ICI on the BER performance has been intensively studied in [55, 56]. As the maximum Doppler frequency increases, the one-tap equalizer is no longer sufficient to conquer this chan-nel distortion. It is shown in [56] that if the maximum Doppler frequency is larger than 8% of the subcarrier spacing, the signal-to-ICI plus noise ratio is less than 20dB. Hence, in order to obtain reliable reception, there is a need for efficient algorithms to combat the ICI effect in a mobile OFDM receiver.
A wide variety of schemes for ICI mitigation have been proposed, mainly consisting of ICI self-cancellation, blind equalization, and ICI cancellation-based equalization [56–69]. At the expense of reduced bandwidth efficiency, the ICI self-cancellation scheme is simple and effective to provide good BER performance [57, 58]. The scheme, however, is not suitable for existing stan-dards as modification to transmit formats is required. In contrast, the blind equalization scheme is efficient in saving bandwidth but it involves high com-putation complexity [59]. Among the three ICI mitigation schemes, the ICI cancellation-based equalization scheme is the most common [60–69]. Based on zero-forcing or MMSE criterion, two optimal frequency-domain equaliz-ers are derived in [60–62]. To enhance the performance, successive interfer-ence cancellation with optimal ordering can be incorporated with the MMSE equalizer [63]. Several works, like [56] and [64–66], are targeted toward re-ducing the complexity of frequency-domain equalizers. By ignoring small ICI terms, a partial MMSE equalizer is proposed in [64] to avoid the inversion of a large-size matrix, while a recursive algorithm is developed in [56] for calcu-lation of equalizer coefficients. Moreover, [65] incorporates a partial MMSE
equalizer with successive interference cancellation, and [66] combines the par-tial MMSE equalizer with BICM. Both methods benefit greatly from time diversity gains induced by mobility. We also find two DF equalizers in [67,68], which make use of power series expansion on time-variant frequency response.
Apart from using frequency-domain equalizers, [60] and [69] consider time-domain equalizers which first achieve ICI shortening, followed by MMSE detection and parallel interference cancellation, respectively, to remove the residual ICI.
For successful implementation of the ICI cancellation-based equalization, it is essential to obtain an accurate estimate of channel variation or the equiv-alent ICI channel matrix. In general, this can be accomplished through the use of embedded reference signals such as pilot symbols or pilot tones. In [63], an MMSE estimator, which demands frequent pilot symbols inserted among OFDM data symbols, is proposed to estimate time-variant CIR. As complex-ity is concerned, most studies model the time variation of each channel tap as a polynomial function. By assuming CIR varies in a linear fashion within an OFDM symbol, [64] and [67] exploit pilot symbols for parameter estima-tion, whereas [68] and [70] belong to the category which uses pilot tones.
It is concluded that a first-order polynomial is adequate to capture channel dynamics with the normalized maximum Doppler frequency up to 0.1. When normalized maximum Doppler frequency is larger than 0.1, a 2-D polynomial surface function is suggested in [61] to model time-varying channel frequency response and to gain better performance.
The EM algorithm can facilitate solving the ML estimation problem in
an iterative manner which alternates between an E-step, calculating an ex-pected complete log-likelihood (ECLL) function, and an M-step, maximizing the ECLL function with respect to some unknown parameters [71, 72]. Re-cently, a few EM-based methods have been proposed for channel estimation and data detection in OFDM systems [73–75]. The major difference among these methods lies whether they formulate the original ML problem into a data sequence detection problem or a channel variable estimation problem.
Yet, the wireless channel is assumed to be quasi-static in all these works, i.e., channel gain remains constant over the duration of one OFDM symbol.
In this chapter, we investigate two EM-based iterative receivers for OFDM and BICM-OFDM systems in doubly selective fading channels. By assuming channel varies in a linear fashion, we first analyze the ICI effect in frequency domain and derive a data detection method based on the EM algorithm using the ML criterion. In an effort to reduce complexity, groupwise processing is adopted for the two EM-based receivers. For OFDM systems, we implement an ML-EM receiver which iterates between a groupwise ICI canceller and an EM detector. Based on this receiver structure, a TURBO-EM receiver for BICM-OFDM systems is then proposed to successively improve the perfor-mance by applying the turbo principle. Finally, for the initial setting of the two receivers, MMSE-based channel estimation is first performed by using a few pilot tones and it is later improved via the DF methodology.
The rest of this chapter is organized as follows. In Section 5.2, we de-scribe the OFDM and BICM-OFDM systems, followed by the analysis of ICI in frequency domain. According to the frequency domain ICI model, an
[ ] [ ] X k
c k x n[ ]
Figure 5.1: BICM-OFDM systems.
EM-based data detection method is developed in Section 5.3. In Section 5.4, an ML-EM receiver and a TURBO-EM receiver are proposed. Afterwards, we describe the initialization procedure of the two receivers and discuss their computational complexity. In Section 5.5, we present our computer simula-tion results. Finally, some conclusions are drawn in Secsimula-tion 5.6.