A novel approach for beamforming based on adaptive combinations of vector projections

Highlights

• A new framework for deriving adaptive beamforming algorithms is proposed.

• The proposed framework is based on a linear combination of vector projections.

• A new adaptive beamforming algorithm is devised from the proposed framework.

• The new algorithm outperforms other competing algorithms from the literature.

• Simulation results show the effectiveness of the proposed beamforming algorithm.

Abstract

Multi-antenna systems have emerged as a key technology to meet the growing demand for capacity in mobile communications. The spatial filtering capability of these systems can be exploited to enhance the signal-to-interference-plus-noise ratio (SINR) in wireless communication channels, allowing to reduce transmission power and increase data rates. However, this is not an easy task due to computational and spatial-selectivity limitations, requiring the use of effective beamforming algorithms to provide adequate balance between signal-of-interest maximization and interference minimization. In this context, a new framework for developing beamforming algorithms is proposed in this paper. Such a framework, termed adaptive combination of vector projections (ACVP), is derived from a geometric analysis of stochastic algorithms and is based on a linear combination of vectors belonging to the subspaces spanned by signals available at the array input. The proposed framework is used to devise a new beamforming algorithm, which applies a sigmoid function along with the stochastic gradient method for dynamically adjusting the linear combination of vector projections. The resulting algorithm, named sigmoid-based ACVP algorithm, exhibits low computational burden and provides higher SINR levels than competing techniques from the open literature. Numerical simulation results are shown aiming to confirm the effectiveness of the proposed approach.

Introduction

The growing demand for spectrum and energy efficiency in mobile communications has motivated a continuous research effort towards improving system capacity while keeping power consumption at low levels. In this context, adaptive beamforming has shown promise, since the real-time spatial filtering capability provided by this technique can be used for enhancing the signal-to-interference-plus-noise ratio (SINR) in both uplink and downlink channels [1], [2], [3]. Such an enhancement, in turn, allows improving system capacity by means of reducing frequency reuse [4], as well as through more efficient modulation and coding schemes [5], [6]. Moreover, the enhanced SINR levels obtained by using beamforming algorithms can be exploited to develop power control schemes that reduce the energy consumption while maintaining acceptable link quality [7], [8], [9].

Beamforming algorithms can be designed to operate in either the uplink or downlink channel of base stations. Some important aspects distinguish uplink beamforming from downlink beamforming. For instance, in the uplink case, the SINR of each user does not depend on the beamformer obtained for the other users (i.e., the SINR of all users are decoupled) [10]. As a consequence, the implementation of uplink beamforming algorithms can be carried out in a distributed manner. In contrast, the downlink beamformer of each user affects the crosstalk experienced by the remaining users [10], [11]. Thereby, centralized processing is usually required to fully coordinate the downlink beamforming of multiple base stations [12], [13], [14], [15], [16], which entails high-capacity backhaul links [16] and constitutes a single point of failure for the system [12]. To cope with these problems, several approaches have been discussed in the open literature aiming to achieve global optimality without the need for inter-cell communication [12], [14], [15], [16], [17], [18], [19], [20].

In order to implement downlink beamforming algorithms in either coordinated or distributed fashion, estimation of the channel state information (CSI) is usually required [4], [21]. Obtaining this information is not a straightforward task, since it depends on the downlink signals arriving at the mobile terminals, which are not readily available at the base station. To circumvent this problem in time-division duplexing (TDD) systems, the downlink CSI is generally acquired considering the reciprocity assumption [22], [23], [24], which allows obtaining accurate estimates of downlink covariance matrices from uplink measurements. In contrast, frequency-division duplexing (FDD) systems usually rely on feedback-based approaches [23], [24], [25] for obtaining the downlink CSI, particularly due to the uncorrelated nature of the frequency-separated uplink and downlink channels [25]. Thus, uplink pilot (training) signals [26], [27], [28], angle-of-arrival estimation [29], [30], [31], or feedback schemes [23], [24], [25] are required for obtaining the downlink CSI [32], [33], implying a significant allocation of system resources specially in non-stationary scenarios. As shown in [34], [35], [36], the requirement for pilot signals or angle-of-arrival estimation can be avoided in code-division-multiple-access (CDMA) systems by using both spread and despread signals to obtain covariance matrices that can be exploited to implement effective beamforming algorithms. Moreover, in non-CDMA systems, the space-time equalization structure discussed in [37] can be used for separating the signal of interest (SOI) from the interferences, which allows the development of beamforming algorithms that do not rely on pilot signals or angle-of-arrival estimation. Examples of these algorithms are the constrained stochastic gradient (CSG) and the improved CSG (ICSG) from [17] and [18], respectively. Another example is the adaptive-projection CSG (AP-CSG) from [38], which allows overcoming implementation challenges present in both the CSG and ICSG algorithms. Such an approach is also exploited in [39] to derive the adaptive-projection quadratically-constrained stochastic gradient (AP-QCSG) algorithm.

In this paper, a new framework is discussed for developing adaptive beamforming algorithms for mobile communication systems. Such a framework, named adaptive combination of vector projections (ACVP), is based on a geometric interpretation of CSG-type algorithms [38], [39], consisting of a linear combination of vectors belonging to subspaces spanned by the signals from the array input. The proposed ACVP framework paves the way for development of a new family of beamforming algorithms that can be used in mobile communication systems, requiring neither pilot signals nor angle-of-arrival estimation. An algorithm of this family, termed here sigmoid-based ACVP (SB-ACVP), is derived in this paper, representing a first practical outcome of the proposed framework. Numerical simulation results are shown, aiming to validate the proposed ACVP framework as well as to confirm the effectiveness of the proposed SB-ACVP algorithm.

The main contributions of this paper can be summarized as follows:

• A new vector-projection-based framework is proposed for developing beamforming algorithms that neither requires estimating the angle-of-arrival of the involved signals nor relies on using pilot signals.

• A novel effective adaptive beamforming algorithm is formulated by using the proposed ACVP framework.

The remainder of this paper is organized as follows. Section 2 presents the system model and problem formulation considered for developing beamforming algorithms. Section 3 is dedicated to a review of CSG-type algorithms. Section 4 presents the main contributions of this research, namely a unifying view on the behavior of adaptive-projection CSG-type algorithms, the proposed ACVP framework, and the proposed SB-ACVP algorithm. Simulation results are shown in Section 5. Finally, Section 6 presents concluding remarks.