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Transmit antenna selection plays an important role in large-scale multiple-input multiple-output (MIMO) communications, but optimal large-scale MIMO antenna selection is a technical challenge. Exhaustive search is often employed in antenna selection, but it cannot be efficiently implemented in large-scale MIMO communication systems due to its prohibitive high computation complexity. This paper proposes a low-complexity interactive multiple-parameter optimization method for joint transmit antenna selection and beamforming in large-scale MIMO communication systems. The objective is to jointly maximize the channel outrage capacity and signal-to-noise (SNR) performance and minimize the mean square error in transmit antenna selection and minimum variance distortionless response (MVDR) beamforming without exhaustive search. The effectiveness of all the proposed methods is verified by extensive simulation results. It is shown that the required antenna selection processing time of the proposed method does not increase along with the increase of selected antennas, but the computation complexity of conventional exhaustive search method will significantly increase when large-scale antennas are employed in the system. This is particularly useful in antenna selection for large-scale MIMO communication systems.

Large-scale multiple-input multiple-output (MIMO) with a very large number of antennas has been an active research topic in wireless communication and navigation systems [

However, the price to pay for large-scale MIMO is increased radio frequency (RF) hardware complexities. Antenna selection is an elegant solution to such problems [

Large-scale MIMO brings also signal processing complexities. Transmitter-based processing techniques are commonly employed to transfer the processing complexity from the mobile units to the base station, thus facilitating cheap and energy efficient mobile units. To reduce signal processing complexity, beamforming is necessary for large-scale MIMO systems [

This paper considers low-complexity and joint transmit antenna selection and beamforming for large-scale MIMO communication systems. Joint antenna selection and beamforming have not only great theoretical interest, but also good practical useness [

To avoid exhaustive search in antenna selection, we present a low-complexity interactive multiple-parameter optimization approach for joint transmit antenna selection and beamforming for large-scale MIMO communication systems. Our objective is to jointly maximize the channel outrage capacity and SNR performance and minimize the mean square error in transmit antenna selection and minimum variance distortionless response (MVDR) beamforming without exhaustive search. The proposed method first selects an initial transmit antenna subset and estimates the weight vector using the MVDR beamformer. Next, the transmit antenna subset is updated by the optimization algorithm. The final antenna subset and weight vector are determined after several repeated optimization steps.

The remaining sections of this paper are organized as follows. Section

In this paper, we consider a large-scale MIMO communication system model, as shown in Figure

Large-scale MIMO communication system model.

The MIMO channel between the

The signal received at the receive side can be expressed as [

Without regard to coding and modulation, the MIMO system capacity using all antennas is given by [

Similar to the method used in [

For calculating

Exhaustive search is widely used in current antenna selection literature. However, to select the transmit antennas in the optimal way, we have to be computed for

When the variables

This problem is still nonconvex due to nonconcavity of the objective function. As the cost function is concave when two of the three variables are known, [

The first optimization object of our method is to minimize the least squares (LS) estimation error. This LS-based formulation necessitates a pilot-aided transmission protocol and thus provides better performance than the method of [

The second optimization object of our method is to maximize the output SNR. Let the equivalent

Using the optimum

Therefore, the joint transmit antenna selection and beamforming can be processed in the following procedure: at first, we solve the P1 optimization problem with an initial value for

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(24) Finally, the antennas are chosen corresponding to the

The cumulative distribution function (CDF) and pairwise error probability (PEP) are analyzed in this section.

Even for the exhaustive search method, it is noted in [

The SNR of one transmit-receive link can be represented by

Consider the signal model (

Since

The lower bound is [

In this section, we provide extensive simulations to evaluate our proposed method. To compare the different approaches, we use the measures of CDF versus the achievable rates, channel capability, SNR improvement, and optimization processing time. Unless stated otherwise, the CDF curves and each point on the simulation graphs are determined by averaging over the results obtained from

First, we simulate the advantages of large-scale antennas in MIMO communications. Figure

Impact of MIMO system size on CDF.

Comparison of simulated and theoretical CDFs.

Next, we consider a large-scale MIMO system with

CDFs of rates for various

Output SNR versus input SNR.

Furthermore, we compare our method with the conventional exhaustive search and [

Comparison of CDF versus achievable rates of our proposal with exhaustive search method and [

Comparison of CDF versus achievable rates of our proposal with [

Comparison of CDF versus achievable rates of our proposal with [

Using the simulation computer is with the following configuration parameters: the computer processor is “Inter(R) Core (TM) i7-2600 CPU

Comparison of optimization processing time of our method with exhaustive search method and [

Finally, we simulate the conditional PEP. Consider also a MIMO system with

Large-scale MIMO communication has received much attention in recent years, but antenna selection for large-scale MIMO communication system is a technical challenge because the conventional exhaustive search method cannot be efficiently implemented in large-scale MIMO systems. This paper proposes a low-complexity interactive multiple-parameter optimization for large-scale MIMO communication systems. The proposed method first selects the initial transmit antenna subset and estimates the weight vector using the MVDR beamformer. Next, the transmit antenna subset is updated by the joint optimization algorithm. The final antenna subset and weight vector are determined after several repeated optimization steps. Extensive simulation results are provided. It is shown that the proposed method significantly outperforms the conventional exhaustive search method in optimization processing time, without significant degradation of CDF versus the achieved rates, system capacity, and SNR improvement. Therefore, the proposed method is particularly useful in designing joint transmit antenna selection and beamforming for large-scale MIMO communication systems. In this paper, the performance of our proposal is compared with the classic exhaustive search method because it is the most optimal antenna selection method excluding computation complexity in existing methods. We plan to perform more performance comparisons with some other advanced tools in future work.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported in part by the National Natural Science Foundation of China under Grant no. 41101317 and the Program for New Century Excellent Talents in University under Grant no. NCET-12-0095.