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How Does Beamforming Improve Network Service
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Received: 4 March 2021 / Revised: 23 March 2021 / Accepted: 6 April 2021 / Published: 8 April 2021
To address the limitations of centralized resource allocation, i.e. high computational complexity and signaling overhead, a distributed beamforming and power allocation strategy is proposed for heterogeneous networks with multiple-input-single-output (MISO) interference channels. In the proposed scheme, each secondary user transceiver pair (SU TP) determines the beamforming vector and transmission power to maximize its own spectral efficiency (SE), while keeping primary user interference below a predetermined threshold, and such resource management TP for each SU is continuously updated without information sharing until the strategies for each SU TP converge. Simulations confirm that the proposed scheme can achieve performance comparable to a centralized approach with greatly reduced computation time, for example, less than 5% drop in SE while improving computation time by more than 10 times.
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With the explosive growth of mobile data traffic and wireless devices, various networks have emerged as a promising mechanism to provide high data rates and increase communication coverage [ 1 , 2 , 3 ]. Unlike homogeneous networks, secondary users (SUs) opportunistically share the same spectrum resources as primary users (PUs) in heterogeneous networks, which improves spectral efficiency (SE), but at the same time leads to severe cross-tier interference. The reason is interference.
Given that system performance can be effectively improved with dynamic resource allocation , many studies have been conducted on strategies to efficiently share spectrum between different networks with suppression of co-channel interference. are [5, 6, 7, 8, 9]. In particular, interference management techniques have been investigated in [5, 6] to improve the SE of heterogeneous networks. In , resource allocation was proposed to jointly maximize energy efficiency and SE in multicell heterogeneous networks, and in  to maximize total throughput of cooperative device-to-device (D2D) heterogeneous networks. therefore proposed. , moreover, the authors of  formulated robust resource management for heterogeneous networks under channel uncertainty.
To further improve the performance of heterogeneous networks while reducing cochannel interference, several efforts have implemented multiantenna techniques, including multiple-input-multiple-output (MIMO) precoding  and coordinated scheduling and a beamforming scheme  is included. Analytical expressions of the capacity limit for dense massive MIMO in line-of-sight propagation environments have been obtained , and array antennas for MIMO applications have been discussed [13, 14, 15, 16, 17, 18]. Moreover, optimal transmission beamforming, power allocation, and bandwidth partitioning were jointly developed in  to maximize the reception rate of small cells while protecting the performance of macrocells. In multiuser and multichannel underlay multiple-input-single-output (MISO) heterogeneous networks, combined beamforming and resource allocation have been studied to find the maximum possible number of SUs  and to maximize the total rate of SUs while satisfying For  ] Interference requirements for PU. In [ 22 , 23 , 24 ], a distributed beamforming or power allocation was proposed to improve the performance of cooperative relay networks.
Some previous studies have considered joint optimization for beamforming and resource allocation for heterogeneous networks with multiantenna configurations [11, 19, 20, 21], but they solved non-convex optimization problems with a centralized approach, which requires a large signaling overhead to correctly get channel. State information (CSI) and high computational complexity. Although a distributed approach has been discussed [22, 23, 24], it cannot be directly applied to heterogeneous networks. Therefore, it is necessary to design a distributed approach that can be operated with practical heterogeneous networks.
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In this paper, heterogeneous networks with MISO interference channels are considered, in which different SU transceiver pairs (TPs) share the same spectrum with PUs. In such networks, an optimization problem is formulated to find optimal beamforming vectors and transmit powers to the SU TPs to maximize their sum SE while ensuring acceptable interference requirements for the PUs. Given that a centralized approach requires a large signaling overhead and high computational complexity to determine a suboptimal solution from a formulated non-convex problem, a distributed beamforming and power allocation strategy is proposed that does not require any information sharing, where each SU TP determines the beamforming vector with maximum ratio transmission (MRT) and transmitted power recursively with dual modes. Simulations in different environments confirm that the proposed scheme performs comparable to centralized power allocation with MRT in terms of sum SE and violation probability, with a significant reduction in computation time.
The rest of the article is organized as follows. In Section 2, a system model is presented along with the formulation of the problem. In Section 3, the distributed beamforming and power allocation strategy is proposed. In Section 4, the performance of the proposed scheme is evaluated in different environments, and finally, the conclusions are presented in Section 5.
Figure 1 shows the system model of a heterogeneous network with MISO interference channels, where there are N SU TPs, each consisting of a transmitter (Tx) equipped with M antennas and a receiver (Rx) equipped with M antennas. SU TP and set of antennas are shown as
, SU TPs share the same spectrum as long as the amount of interference in a single antenna equipped PU is less than a predefined threshold. The channel between Tx of SU TP I and Rx of SU TP J for antenna M is represented by
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SU for antenna M is the channel between Tx of TP I and Rx of PU. it is assumed that
SU is available on TP I to ensure the need for interference caused by Rx of PU .
On the other hand, the interference from Tx of SU TP I to Rx of PU is expressed as
The optimization problem can be formulated to find the optimal beamforming vectors and to transmit the power of the SU TPs in such a way as to maximize their sum SE while maintaining the interference level that each SU TP will give less than the permissible interference level to the PU can transfer. K causes Rx.
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Is the maximum transmission power for each SU TP. However, problem (4) is not convex due to co-channel interference; Therefore, it is difficult to find the optimal resource allocation strategy analytically. However, through painstaking search, the optimal solution can be found
With isotopic values quantified and all possible combinations evaluated, it cannot be used in practical systems due to the high computational complexity and signaling overhead for accurate CSI.
To overcome the impractical limitations in adopting a centralized approach, a distributed beamforming and power allocation strategy is proposed. Given that the optimal beamforming strategy to maximize the SE of each SU TP is MRT when the interference channels for SU TP i are unknown, the beamforming vector for SU TP i can be determined as
For a fixed beamforming vector, an optimization problem is formulated to find the optimal transmit power of the SU TPI to maximize its own SE, as follows:
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Dual methods are implemented for distributed power allocation, which works in an iterative manner . First, the Lagrangian function of (7) is defined as:
(15) shows the sum of the noise power and interference power from PU and other SU TPs; Therefore, it can be calculated by subtracting the signal power received by SU Tx I from the total received signal power without information sharing. In other words, SU TP I does not need to know the individual value of the parameter
The procedures for the proposed distributed beamforming and power allocation are summarized in Algorithm 1. Specifically, each SU initializes the TP transmission power and Lagrange multipliers, and then determines its beamforming vector using the MRT. Then it calculates the transmit power according to (15) and iteratively updates the Lagrange multipliers according to (16) and (17) until the transmit power for all SU TPs is aggregated. Given that it is not necessary to share any information with other SU TPs to find each SU TP
To evaluate performance, the following
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