A joint channel estimation and detection for frequency-domain equalization using an approximate EM algorithm☆
Introduction
Generally, the performance degradation of communications over a bandlimited channel is caused by the inter-symbol interference (ISI) [11]. To overcome the ISI, the orthogonal frequency division multiplexing (OFDM) has been widely employed for various broadband communication systems [1]. There is no ISI and only simple one-tap channel equalizer in the frequency-domain is required. It is certainly the advantage over single-carrier transmission schemes which generally suffer from the ISI and require a complicated multi-tap equalizer in the time-domain. However, OFDM has some disadvantages. One is the high peak-to-average power ratio [12]. Another disadvantage, as pointed out in [13], [7], is that the multipath diversity is not achieved over a multipath fading channel (in [13], this drawback has been explained in the frequency-domain). In order to take advantage of both single- and multi-carrier transmission schemes, the frequency-domain equalization for single-carrier transmission has been investigated in [13], [4], [7]. It can provide better performance over a frequency-selective fading channel and its equalization in the frequency-domain can be easily implemented.
In this paper, we consider the joint detection and channel estimation for the OFDM and single-carrier transmission with cyclic prefix (SCCP) in the frequency-domain. Since the detection performance depends on the accuracy of the channel estimate, the joint processing is employed with the expectation-maximization (EM) algorithm [6] to improve the accuracy of the channel estimate. In [9], the EM algorithm is also utilized for the joint processing in OFDM. Although the EM algorithm can be directly used for the SCCP, its complexity is generally prohibitively high when the size of signal block is large. To avoid this difficulty, we propose an approximate EM algorithm for the joint processing. It is noteworthy that the proposed approximate EM algorithm can be used for OFDM and it becomes the standard EM algorithm in this case.
It can be seen that the proposed approach is a semi-blind method since the known and unknown symbols are simultaneously used to estimate the channel. Note that a similar approach has been considered in [2]. However, the proposed approximate EM algorithm differs from that in [2] as follows: the joint processing is carried out in the time-domain and the unconstrained maximum-likelihood (ML) detection is considered in [2], while the EM algorithm is used in the frequency-domain and the constrained ML detection is employed in the paper.
The rest of the paper is organized as follows. In Section 2, the background is presented. The EM algorithm is considered and some approximations are used to reduce the complexity for single-carrier transmission in Section 3. Simulation results are presented in Section 4 and we conclude the paper with some remarks in Section 5.
Section snippets
Background
In this section, we consider two different transmission schemes: multi-carrier transmission (especially OFDM) and SCCP with the channel estimation and frequency-domain equalization. It will be shown that a single expression for the received signal can be used for both OFDM and SCCP. Hence, if a joint processing method has been derived with the expression for the received signal, it can be used for both OFDM and SCCP.
A joint channel estimation and detection using EM algorithm
In this section, we propose a method for the joint channel estimation and data detection by using the EM algorithm. There would be approximations to reduce the computational complexity.
If the channel estimate and data detection are jointly carried out, we can obtain better channel estimate. From (11) and the probability density function (pdf) of conditioned on , , and , the joint ML estimation of the channel vector and data symbol vector can be formulated as
Simulation results
In this section, simulation results to see the performance of the joint channel estimation and data detection using the approximate EM algorithm are presented. Throughout the paper, we assume that BPSK or QPSK is used for signaling and the data rate is symbols per second (sps). The coefficients of the CIR are assumed to be independent circular complex Gaussian random variables with zero mean (i.e., the channel is modeled as L-tap multipath Rayleigh fading channel). For each signal block,
Concluding remarks
In this paper, block-based transmission schemes with CP have been considered including OFDM and SCCP. A unified representation of the received signal in the frequency-domain has been derived in terms of pilot and data symbols. Based on the unified representation, we investigate the joint channel and data detection with the ML approach over the constrained domain. Due to a high computational complexity in SCCP, an approximate EM algorithm is proposed and its performance has been demonstrated
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This work was supported by HY-SDR Research Center at Hanyang University, Seoul, Korea, under the ITRC Program of MIC, Korea.