IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 1 Hybrid Active/Passive Wireless Network Aided by Intelligent Reflecting Surface: System Modeling and Performance Analysis Jiangbin Lyu, Member, IEEE, and Rui Zhang, Fellow, IEEE Abstract—Intelligent reflecting surface (IRS) is a new and cation technologies that would achieve higher spectral/energy promising paradigm to substantially improve the spectral and efficiency (SE/EE) yet at an affordable deployment/operational energy efficiency of wireless networks, by constructing favorable cost. Among others, some prominent wireless technologies communication channels via tuning massive low-cost passive reflecting elements. Despite recent advances in the link-level per- proposed in the last decade include ultra-dense network formance optimization for various IRS-aided wireless systems, it (UDN), massive multiple-input multiple-output (MIMO), and still remains an open problem whether the large-scale deployment millimeter wave (mmWave) communication [1]. Although of IRSs in wireless networks can be a cost-effective solution these technologies significantly enhanced the wireless network to achieve their sustainable capacity growth in the future. To SE, they also incurred increasingly more energy consumption address this problem, we study in this paper a new hybrid wireless network comprising both active base stations (BSs) and and higher hardware cost, due to the deployment of more base passive IRSs, and characterize its achievable spatial throughput stations (BSs) and/or relays in the network as well as mounting in the downlink as well as other pertinent key performance them with more active antennas requiring costly radio fre- metrics averaged over both channel fading and random locations quency (RF) chains, especially when operating at mmWave of the deployed BSs/IRSs therein based on stochastic geometry. frequency bands. Therefore, it is doubtful whether the existing Compared to prior works on characterizing the performance of wireless networks with active BSs only, our analysis needs to paradigm by adding more and more active nodes/components derive the power distributions of both the signal and interference in the wireless network would be a cost-effective solution to reflected by distributed IRSs in the network under spatially cor- achieve its sustainable capacity growth in the future. related channels, which exhibit channel hardening effects when To tackle this challenge, intelligent reflecting surface (IRS) the number of IRS elements becomes large. Extensive numerical has recently emerged as a promising solution based on the new results are presented to validate our analysis and demonstrate the effectiveness of deploying distributed IRSs in enhancing the concept of reconfiguring the wireless propagation environment hybrid network throughput against the conventional network that is traditionally deemed to be random and uncontrollable without IRS, which significantly boosts the signal power but [2]–[5]. Specifically, IRS is a planar surface consisting of results in only marginally increased interference in the network. a massive number of low-cost passive reflecting elements Moreover, it is unveiled that there exists an optimal IRS/BS density that can be tuned dynamically to alter the amplitude and/or ratio that maximizes the hybrid network throughput subject to a total deployment cost given their individual costs, while the phase of the signal reflected by them, thus collaboratively conventional network without IRS (i.e., zero IRS/BS density ratio) reconfiguring the signal propagation to achieve various desired is generally suboptimal in terms of throughput per unit cost. functions such as three-dimensional (3D) passive beamform- Index Terms—Intelligent reflecting surface, hybrid ac- ing, spatial interference nulling and/or cancellation. Compared tive/passive wireless network, spatial throughput, stochastic ge- to the conventional active relaying/beamforming, IRS does not arXiv:2004.13318v4 [cs.IT] 15 May 2021 ometry, performance analysis. require any active RF chain for signal transmission/reception but simply leverages passive wave reflection, thus leading to I. INTRODUCTION much lower hardware cost and energy consumption yet operat- ing spectral efficiently in full-duplex (FD) without the need of The proliferation of mobile applications and explosive costly self-interference cancellation (SIC) [2]. Moreover, IRS growth of wireless data have been continually spurring en- can be easily attached to or removed from the existing objects thusiasm in inventing new and innovative wireless communi- in the environment (e.g., walls and ceilings), and seamlessly This work was supported in part by the National Natural Science Foundation integrated into cellular or WiFi systems without the need to of China (No. 61801408 and No. 61771017), the Natural Science Foundation modify their current infrastructure and operating standards [2]. of Fujian Province (No. 2019J05002), the Fundamental Research Funds for As such, IRS can be densely deployed in wireless networks the Central Universities (No. 20720190008), and the National University of Singapore under Research Grant R-261-518-005-720 and R-263-000-E86-112. at a low and scalable cost as well as with high flexibility and J. Lyu is with the School of Informatics, and Key Laboratory of compatibility. Underwater Acoustic Communication and Marine Information Technol- The appealing advantages of IRS have attracted a great deal ogy (Ministry of Education), Xiamen University, China 361005 (e-mail: [email protected]). R. Zhang is with the Department of Electrical and Computer of interest recently in investigating IRS-aided wireless systems Engineering, National University of Singapore, Singapore 117583 (email: from various aspects and/or under different setups, such as [email protected]). passive beamforming design [6]–[12], IRS-aided orthogonal Copyright ©2021 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from frequency division multiplexing (OFDM) system [13] [14], the IEEE by sending a request to [email protected]. non-orthogonal multiple access (NOMA) [15]–[17], physical IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2 layer security [18]–[21], wireless information and power trans- fading effect. To our best knowledge, the modeling of a general fer [22]–[24], and so on. The above works on IRS-aided wire- multi-cell hybrid wireless network aided by randomly located less systems mainly aim to optimize the system performance IRSs and the characterization of the distribution of the users’ at the link level with one or more IRSs at fixed locations, achievable signal-to-interference-plus-noise ratio (SINR) as which show that the IRS-aided system can achieve significant well as the spatial throughput of the hybrid network have not energy efficiency [12] and/or spectral efficiency improvement been investigated yet in the literature. over the traditional system without IRS, with optimized IRS Motivated by the above, in this paper, we model a hybrid reflection coefficients. In [25], the authors investigate a multi- active/passive wireless network under the general multi-cell user system aided by multiple intelligent surfaces (equivalent setup and derive the distributions of the signal power, inter- to a single large IRS) co-located at a random location in ference power, and thereby the users’ achievable SINR in the the network. However, since IRS typically serves users in its network, with the ultimate goal of characterizing the spatial proximity, distributed IRSs should be deployed in the network throughput of the network, defined as the achievable rate per to serve distant groups of users and thereby boost the network user equipment (UE) averaged over both the wireless channel throughput. Motivated by this, in our prior work [26], the fading and the random BS/IRS locations. Thus, this work is a spatial throughput of a single-cell multi-user system aided by substantial extension of our prior work [26] under the single- distributed IRSs located at random locations is characterized, cell setup to the more general multi-cell setup. We focus on which is compared favorably with the conventional system the downlink communication from the BSs to the UEs while aided by distributed relays but with significantly reduced active the proposed analytical framework can be similarly extended antennas, under their respectively optimized deployment. to the uplink communication, which is left for our future Furthermore, for large-scale deployment of IRSs in future work. Compared to other prior works on characterizing the wireless systems, one critical issue is the modeling, design performance of wireless networks with active BSs only (see, and performance characterization of the IRS-aided multi-cell e.g., [33] and references therein), our analysis needs to derive hybrid wireless network comprising both distributed active the power distributions of both the signal and interference BSs and passive IRSs subjected to the inter-cell interference. reflected by distributed IRSs in the network under spatially There have been some recent works (e.g., [27]–[32]) along correlated channels, which exhibit channel hardening effects this line. Considering a finite number of co-channel/interfering when the number of IRS elements becomes large. Our main BSs, joint active/passive beamforming design with a cell-edge contributions are summarized as follows. IRS is investigated for the users’ weighted-sum-rate maximiza- tion [27]