^{1, 2}

^{1}

^{3}

^{1}

^{2}

^{3}

Accurate channel impulse response (CIR) is required for equalization and can help improve communication service quality in next-generation wireless communication systems. An example of an advanced system is amplify-and-forward multiple-input multiple-output two-way relay network, which is modulated by orthogonal frequency-division multiplexing. Linear channel estimation methods, for example, least squares and expectation conditional maximization, have been proposed previously for the system. However, these methods do not take advantage of channel sparsity, and they decrease estimation performance. We propose a sparse channel estimation scheme, which is different from linear methods, at end users under the relay channel to enable us to exploit sparsity. First, we formulate the sparse channel estimation problem as a compressed sensing problem by using sparse decomposition theory. Second, the CIR is reconstructed by CoSaMP and OMP algorithms. Finally, computer simulations are conducted to confirm the superiority of the proposed methods over traditional linear channel estimation methods.

Two-way relay network (TWRN) has attracted great attention because it can improve spectral efficiency unlike a one-way relay network [

The MIMO-OFDM-TWRN system faces more challenges because channel estimation is required not only for data detection but also for self-data cancellation at the two terminals. Linear channel estimation methods have been proposed for MIMO-OFDM-TWRN. In [

In this study, we focus on the TWRN with multiple antennas at relay

The remainder of this paper is organized as follows. Section

Figure

MIMO-OFDM-TWRN:

The channel between the

The training signal vectors transmitted from the

The matrix

In phase II, the vector

The vector

According to the matrix theory, matrices

From (

Compressed sensing (CS) describes a new signal acquisition theory in which sparse high dimensional vectors can be accurately recovered from a small number of linear observations. CS has been applied in various areas, such as imaging, radar, speech recognition, and data acquisition. In communications, an immediate application of CS is wireless sparse multipath channel estimation. Detailed descriptions can be found in [

In this paper, we consider the linear model as (

Since the channel impulse responses

By utilizing CS recovery algorithms for compressive channel estimation, we propose CCE-OMP and CCE-CoSaMP. The two estimation methods for convoluted channels are described as follows.

Given

Given the received signal

In this section, we present the simulation results and analyze the performance of compressive channel estimation in a MIMO-OFDM two-way relay network. We compare the performance of the proposed estimators with that of an LS-based linear estimator and adopt 10,000 independent Monte Carlo runs for averaging. We consider the MIMO relay network with

MSE performance of channel estimation at

The channel estimators are evaluated via the average MSE, which is defined by

MSE performance of channel estimation at

A comparison between the simulation results in the two figures (Figures

We also compare the performance of the proposed CCE-CoSaMP estimator with that of the ECM estimator algorithm in this section. Figures

MSE performance of channel estimation at

MSE performance of channel estimation at

This paper investigated the channel estimation problem in sparse multipath MIMO two-way relay networks that adopt the OFDM technique. To address the shortcomings of conventional linear channel estimation methods, we proposed compressed channel estimation methods for MIMO-OFDM two-way relay networks under the AF protocol. The sparseness of convoluted sparse channels was demonstrated by a measure function. The proposed methods exploited the sparsity in the MIMO TWRN channel. The simulation results confirmed the superior performance of the proposed method compared with conventional linear methods, for example, LS and ECM.

This study is funded by the National Natural Science Foundation of China (Grant nos. 61071175, 61202499, 61271421, and 61152004).