# Optimal Resource Allocation Policies for Multi-User Backscatter Communication Systems
## 1 Introduction  
With the emergence of the Internet-of-Things (IoT), the sustainable energy supply of electronic equipment has become an important issue. However, the lifetime of wireless devices with fixed sources (e.g., batteries) is limited, as periodically replacing or recharging batteries may be inconvenient or infeasible. Recently, radio frequency (RF) signals--which can charge devices by energy harvesting (EH) techniques--have become a potential energy source [1]. RF signals based on EH techniques have been extensively exploited in simultaneous wireless information and power transfer (SWIPT) systems [2; 3] and wireless-powered communication networks (WPCNs) [4; 5; 6; 7]. However, in either SWIPT systems or WPCNs, devices require oscillators for carrier signal generation and analog-to-digital converters (ADCs) for signal modulation, which causes high energy consumption. To solve this problem, backscatter communication (BackCom) techniques [8] that do not require oscillators and ADCs have received significant attention in recent years, and can be extensively used in wireless sensor networks [9; 10; 11; 12]. BackCom systems normally include a transceiver, often known as a reader, and multiple nodes, known as tags. The reader transmits excitation signals to activate the tags in forward channels and receives backscattered signals from the tags in backward channels. Tags can be classified as three types: active, passive, and semi-passive. Active tags can radiate signals, while the latter two types communicate with readers based on reflection [8]. Throughout this paper, tags refer to passive or semi-passive tags without specific declaration. For an activated tag,there are typically two states--i.e., sleep and active states. In the sleep state, each tag's antenna input impedance is matched, and all input energy will be harvested. In the active state, a portion of excitation signals is backscattered to the reader, and the remainder is harvested for circuit operation. However, only semi-passive tags can store energy during the sleep state, due to the availability of batteries. In [13], ambient backscatter was introduced to enable ubiquitous communication where devices communicate by backscattering environment signals (e.g., TV broadcast signals). However, communication based on environmental power sources may not be stable. To fix this problem, fixed energy sources were introduced in [14]. In [15], a novel network architecture--i.e., a wirelessly powered BackCom network--was modeled using stochastic geometry, and the network coverage probability and transmission capacity were analyzed. In [16] and [17], the authors investigated the security problems of signal-input single-output (SISO) and multiple-input multiple output (MIMO) BackCom systems, respectively. To improve the transmission rate of the secondary user, the BackCom was introduced in cognitive radio networks [18]. To boost the deployment of BackCom systems, the reader collision problem was studied in [19]. The resource allocation problem is usually an important issue in wireless networks. In [20], the authors investigated the resource allocation schemes for two-tier networks, including spectrum-sharing femtocells and macrocells. In [21], the authors used cooperative Hash bargaining game theory to study the joint uplink subchannel and power allocation problem in cognitive small cells. Note that the time resource allocation of both the sleep and active states has an important effect on the performance of BackCom systems. However, this key factor was not investigated in the works [13; 14; 15; 16; 17]. Although this time allocation was considered in [18], the transmission rate was fixed such that the significant link reliability was not investigated. To account for the link reliability, the time allocation control for maximizing the system goodput with fixed reader transmission power in a single-user BackCom system including a semi-passive tag was studied in our previous work [22]. In practical deployment of a BackCom system, a reader usually serves multiple tags.