# DFT-Based Channel Estimation with Symmetric Extension for OFDMA Systems

- Yi Wang
^{1, 2}Email author, - Lihua Li
^{1, 2}, - Ping Zhang
^{1, 2}and - Zemin Liu
^{1, 2}

**2009**:647130

**DOI: **10.1155/2009/647130

© Yi Wang et al. 2009

**Received: **3 February 2008

**Accepted: **10 November 2008

**Published: **18 January 2009

## Abstract

A novel partial frequency response channel estimator is proposed for OFDMA systems. First, the partial frequency response is obtained by least square (LS) method. The conventional discrete Fourier transform (DFT) method will eliminate the noise in time domain. However, after inverse discrete Fourier transform (IDFT) of partial frequency response, the channel impulse response will leak to all taps. As the leakage power and noise are mixed up, the conventional method will not only eliminate the noise, but also lose the useful leaked channel impulse response and result in mean square error (MSE) floor. In order to reduce MSE of the conventional DFT estimator, we have proposed the novel symmetric extension method to reduce the leakage power. The estimates of partial frequency response are extended symmetrically. After IDFT of the symmetric extended signal, the leakage power of channel impulse response is self-cancelled efficiently. Then, the noise power can be eliminated with very small leakage power loss. The computational complexity is very small, and the simulation results show that the accuracy of our estimator has increased significantly compared with the conventional DFT-based channel estimator.

## 1. Introduction

The orthogonal frequency-division multiplexing (OFDM) is an effective technique for combating multipath fading and for high-bit-rate transmission over mobile wireless channels. In OFDM system, the entire channel is divided into many narrow subchannels, which are transmitted in parallel, thereby increasing the symbol duration and reducing the ISI.

Channel estimation has been successfully used to improve the performance of OFDM systems. It is crucial for diversity combination, coherent detection, and space-time coding. Various OFDM channel estimation schemes have been proposed in literature. The LS or the linear minimum mean square error (LMMSE) estimation was proposed in [1]. Reference [2] also proposed a low-complexity LMMSE estimation method by partitioning off channel covariance matrix into some small matrices on the basis of coherent bandwidth. However, these modified LMMSE methods still have quite high-computational complexity for practical implementation and require exact channel covariance matrices. Reference [3] introduced additional DFT processing to obtain the frequency response of LS-estimated channel. In contrast to the frequency-domain estimation, the transform-domain estimation method uses the time-domain properties of channels. Since a channel impulse response is not longer than the guard interval in OFDM system, the LS and the LMMSE were modified in [4, 5] by limiting the number of channel taps in time domain. References [6, 7] showed the performance of various channel estimation methods and yielded that the DFT-based estimation can achieve significant performance benefits if the maximum channel delay is known. References [8–11] improved upon this idea by considering only the most significant channel taps. Reference [12] further investigated how to eliminate the noise on the insignificant taps by optimal threshold.

However, in many applications such as OFDMA system, only the estimates of partial frequency response are available, and the estimate of channel impulse response in time domain cannot be obtained from the conventional DFT method. After IDFT of partial frequency response, the channel impulse response will leak to all taps in time domain. As the noise and leakage power are mixed up, the conventional DFT method will not only eliminate the noise, but also lose the useful channel leakage power and result in MSE floor. We have proposed the novel symmetric extension method to reduce the leakage power. The mathematic expression of the MSE of the conventional DFT estimator and the upper bound of the MSE of our proposed estimator are derived in this paper.

The rest of the paper is organized as follows. Section 2 describes the system model and briefly introduces the statistics of mobile wireless channel. Section 3 proposes the novel channel-estimation approach for OFDMA systems. Section 4 presents computer simulation results to demonstrate the effectiveness of the proposed estimation approach. Finally, conclusion is given in Section 5.

## 2. System and Channel Model

where are the pilot subcarriers, for simplicity, it is assumed that , represents the channel frequency response on the th subcarrier. is the AWGN with zero mean and variance of .

where , and in the above expression are the block length and the symbol duration, respectively. In (3), , for , are WSS narrowband complex Gaussian processes. is the number of multipath taps. The average power of and depends on the delay profile and dispersion of the wireless channels.

## 3. Channel Estimation Based on Symmetric Extension

### 3.1. Conventional DFT Method

### 3.2. Partial Frequency Response by Conventional DFT

where . From (10), it can be seen that the channel impulse response will leak to all taps of . The conventional DFT method is no longer applicable as will be nonzero due to the power leakage; the noise and leakage power are mixed up. The elimination of noise will also cause the loss of useful channel impulse response leakage.

### 3.3. Partial Frequency Response Estimation by Symmetric Extension Method

### 3.4. Performance Analysis

### 3.5. Estimator Complexity

The conventional DFT-based channel estimator is very attractive for its good performance and low complexity. Its main computation complexity is point IFFT and FFT. Our proposed symmetric extension method also inherits the low complexity of the DFT estimator, and its main computation complexity is point IFFT and FFT. As the complexity of FFT and IFFT is significantly reduced nowadays, our proposed method can provide a good tradeoff between performance and complexity.

## 4. Performance Results

We investigate the performance of our proposed estimator through computer simulation. An OFDMA system with subcarriers is considered the guard interval . The sampling rate is 7.68 MHz, and subcarrier frequency space is 15 kHz. A six-path channel model is used. The power profile is given by dB, and the delay profile after sampling is . Each path is an independent zero-mean complex Gaussian random process.

## 5. Conclusion

A simple DFT-based channel estimation method with symmetric extension is proposed in this paper. In order to increase the estimation accuracy, the noise is eliminated in time domain. As both the noise and the channel impulse leakage power will be eliminated, we have proposed the novel symmetric extension method to reduce the channel leakage power. The noise can be efficiently eliminated with very small loss of channel leakage power. The simulation results show that, compared with the conventional DFT method, the MSE of our proposed method is significantly reduced.

## Authors’ Affiliations

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## Copyright

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