Deep learning based adaptive bit allocation for heterogeneous interference channels

Abstract

This paper proposes an adaptive bit allocation scheme by using a fully connected (FC) deep neural network (DNN) considering imperfect channel state information (CSI) for heterogeneous networks. Achieving an accurate CSI has a crucial role on the system performance of the heterogeneous networks. Different quantization techniques have been employed to reduce the feedback overhead. However, the system performance cannot increase linearly with the number of bits increasing exponentially. Since optimizing the total number of bits is too complex for the entire network, an initial step is performed to distribute the bits to each cell in the conventional method. Then, the distributed bits are further allocated to each channel optimally. In order to enable direct allocation for the entire network, a FC-DNN based method is presented in this study. The optimized number of bits can be directly obtained for a different number of bits and scenarios by the proposed approach. The simulations are performed by using various scenarios with different allocation schemes. The performance results show that the DNN based method achieves a closer performance to the conventional approach.

Introduction

Multiple input multiple output (MIMO) systems in heterogeneous networks are widely studied as a major technology for future wireless communication systems. By equipping a base station (BS) with multiple antennas in a centralized [1] or distributed [2] manner, co-channel interference can be reduced. As a result the total cell throughput can be increased [3]. This potential benefit is mainly obtained by obtaining the channel state information (CSI) at the base stations (BSs).

In frequency division duplexed (FDD) MIMO systems, CSI is acquired at the receiver using feedback methods in which the CSI is sent to the transmitters through feedback channels [4]. In feedback systems, receivers estimate the forward channels by using the pilot signals. After the estimation of the forward channels, receivers quantize the CSI, and feedback it to the transmitters. In order to reduce the feedback overhead, vector quantization approaches have been studied [5], [6]. The distortion caused by the quantizaton process can be decreased by increasing the size of the codebook, however this results with the exponentially growth in the feedback overhead. Therefore, the number of bits should be optimized depending on the channel conditions [7].

In the context of heterogeneous networks, there are different studies on the optimization of the bit allocation for limited feedback schemes. The performance of the feedback schemes can be increased by benefiting from the heterogeneous features of the considered network, which are different transmit power levels and unequal number of antennas [8], [9]. However, optimizing the total number of bits for the whole network is too complex to fulfill the requirements [10]. In order to find a local optimum, the optimization problems are handled for each cell. In the study of Aycan Beyazit et al. [11], a two-step solution is studied for the adaptive bit allocation scheme in heterogeneous networks. First the total number of feedback bits is shared to each cell considering the transmit powers and the interference levels, then the shared bits are adaptively and locally allocated to each channel in the considered cell. However, as the number of antenna and user increases as in massive MIMO multi-user systems, the complexity of the mentioned technique will even increase.

In this paper, we address the above problem and we propose a data-driven solution for the limited feedback systems through artificial neural networks which is also called deep learning. Recently, deep learning (DL) algorithms have a great attraction in communication systems due to their potentials in pointing out the wireless communication challenges which are nonlinear complex problems. As the data volume increases with the increasing number of users, antennas and base stations, more strict requirements have to be considered for the next generation communication systems. In order to fulfill these complex requirements, research studies have been focused on artificial intelligence [12], [13]. Deep learning based solutions have been studied for different research areas of the communication systems, such as Massive MIMO [14], heterogeneous network [15], [16], interference management [17] and mm-Wave [7]. Also some other studies employing DL approaches can be found in the literature, such as radio signal classification [18], resource allocation [19] and compression of the CSI [20], [21]. It is worthy of DNN-based FDD networks with limited feedback has been studied in some recent works. For the feedback channels, an extended recurrent neural network (RNN) to jointly optimize the encoding and decoding in the study of Kim et al. [22]. As another study on feedback channels, a joint DNN-based solution is performed to produce both the quantization and the beamforming vectors for homogeneous networks [23].

The main idea of this study is to achieve the direct allocation of the feedback bits to the users so that the initial step which is sharing the bits to each cell first can be eliminated. Since there are many output variables in the training set, supervised learning that learn to affiliate the input data with the output data for a given training set algorithms are suitable for this study [24].

Another property of the training data set of the handled problem is that both the input and output variables are continuous. Therefore, a regression algorithm is trained with a higher number of data obtained with the conventional bit allocation (CBA) scheme as in Aycan Beyazit et al. [11] for several different scenarios. In this study, a fully connected deep neural network (FC-DNN) is used as a regression method since there are multiple number of output variables due to the nature of the MIMO systems.

The main contributions of this study can be listed as follows.

• We propose a DNN based bit allocation learning method for a limited feedback in heterogeneous networks. In particular allocation of the feedback bits can be achieved for the entire network at once by training the DNN. So that the initial step which is the sharing of the bits among the cells can be skipped and the total computational time can be decreased. As a result, the total number of feedback bits can be directly and adaptively allocated to each user equipment (UE) by the proposed DNN based model.

• By exploiting the training data set, the proposed DNN model learns to mimic the system. So that the prediction of the number of bits for each feedback link can be achieved for different total number of bits and also for different heterogeneous network scenarios.

• Extensive simulations are performed in order to evaluate the performance of the proposed method. The obtained results are compared through three different bit allocation schemes considering different scenarios.

The rest of the paper is organized as follows. The system model is explained in Section 2. The proposed DNN-based adaptive bit allocation approach is presented in Section 3 including its structure and training phase. The performance evaluations are given in Section 4. Finally, the study is concluded in Section 5.

Notations: Sets are represented with Capital Greek letters. The transpose conjugate of the matrix $\mathbf{X}$ is given as ${\left(\mathbf{X}\right)}^H$ and the determinant of square matrix is shown as $\mathbf{X}$.