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In this letter, we propose a virtual channel (VC) optimization approach with a closed-loop and adaptive scheme for overloaded MIMO systems. With this approach, each input data stream goes through a VC which is generated at the transmitter; then it is transmitted to a receiver through the actual wireless channels. The VCs are concatenated with the actual wireless channels. Through VC optimization, the values of which can be adjusted to reduce the channel correlation, leading to a much improved system performance. Compared to the conventional overloaded MIMO systems, the overloaded MIMO systems with this approach can achieve significantly better performances in terms of the system capacity and symbol error rate (SER). The method that uses genetic algorithm (GA) for finding the optimal VC vector is described. Simulation results illustrate the effectiveness of the proposed approach.

Massive multiple-input multiple-output (MIMO), also known as large MIMO, has been considered as one of the most promising candidate technologies for future 5G communications due to its ability to achieve high throughput and spectral efficiency and enhance the energy efficiency of sensor networks [

In this letter, we propose a virtual channel (VC) approach with the closed-loop and adaptive scheme for a downlink overloaded MIMO system, namely, the VC overloaded MIMO system. With this approach, each input data stream goes through a VC which is generated at the transmitter before it is transmitted to a receiver through the actual wireless channels. Since the VCs are concatenated with the actual wireless channels, the system performance not only depends on the actual wireless channels but also depends on the VCs. Therefore, by optimizing the VCs according to feedback information the channel correlation can be largely reduced. Thus, compared to the conventional overloaded MIMO systems, that is, the nonprecoded ones, an overloaded MIMO system with VCs can provide a much improved performance.

Thus, the main contributions of this letter are summarized as follows.

Consider a downlink VC overloaded MIMO system equipped with

Simplified block diagram of a downlink VC overloaded MIMO system.

The

When

From Figure

The capacity of a VC overloaded MIMO system is given as [

For arbitrary

Then from (

From (

The optimization criterion (

Suppose the total number of generations is

Set the generation counter

Calculate the fitness function value

Update the generation counter

Selection: rank all chromosomes from the best to the worst according to the fitness function values

Crossover: apply a single point crossover operator to do the crossover operation. Randomly select a crossover point (an integer between 1 and

Mutation: make a small change in the child chromosomes to lead a broader searching space, with a mutation probability

Calculate the fitness function values

If

From the above steps, it can be seen that there is no computation unmanageable in any step and the proposed algorithm is practically implementable. Furthermore, the computational complexity of GA is approximately

In this section, the simulation results are presented to compare the capacity and SER performances of the VC overloaded MIMO systems with those of the conventional overloaded MIMO systems. Here, we assume that

In Figure

Capacity comparison between the VC overloaded MIMO system and the conventional overloaded MIMO system.

Figure

SER performances of the VC overloaded MIMO systems, in comparison with those of the conventional overloaded MIMO systems and the overloaded MIMO systems with open-loop precoding for different antenna configurations.

Figure

Convergence property of GA comparison under different conditions: (a) convergence property of GA with different population sizes; (b) convergence property of GA with different crossover probabilities; (c) convergence property of GA with different mutation probabilities; (d) convergence property of GA at different SNRs.

In this paper, we propose a closed-loop and adaptive VC optimization approach that can significantly improve the performances of the downlink overloaded MIMO systems according to feedback information. Specifically, by using GA to find the optimal VC vector, the performance optimization can be achieved. Simulation results demonstrate that the VC overloaded MIMO system outperforms the conventional overloaded MIMO system as well as the overloaded MIMO systems with open-loop precoding in the system capacity and SER.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by the University Doctoral Research Foundation of China (Grant 20130181110006).