Transport Throughput of Secondary Networks in Spectrum Sharing Systems Chengzhi Li and Huaiyu Dai Department of Electrical and Computer Engineering North Carolina State University, Raleigh, NC email: {cli3, hdai}@ncsu.edu Abstract—Spectrum sharing systems such as cognitive radio networks have drawn much attention recently due to their potential to resolve the conflict between increasing demand for spectrum and spectrum shortage. Such systems are typically composed of primary and secondary networks; the configuration of the latter depends on spectrum opportunity unexploited in the former. In this paper we explore the characteristics of the single hop transport throughput (STT) of the secondary network with outage constraints imposed on both networks. STT is a new metric that inherits the merits of both the traditional transport capacity and another popular metric, transmission capacity, incorporating transmission distance and outage probability into a uniform framework. We first derive the limit of STT, single hop transport capacity (STC), together with a practical upper bound for it. Then we investigate STT with secondary receivers randomly located in the field of interest. Three models regarding the selection of receivers are considered: optimally selected, ran- domly selected, or the nearest. Study on these models provides a comprehensive view of achievable secondary network throughput, and offers insights into the configuration of secondary networks. In addition, the broadcast transport throughput (BTT) of the secondary networks is also investigated as an extension of STT, and its similarity with STT in the nearest neighbor model is revealed. I. I NTRODUCTION Spectrum sharing systems have tremendous potential to alle- viate the spectrum shortage problem and achieve remarkable spectrum efficiency; the inherent spectrum sharing mechanism also provides a flexible way of spectrum management. One prominent example is cognitive radio networks, where sec- ondary (unlicensed) users are allowed to temporarily access spectrum that is not currently used by primary (licensed) users. It is generally preferable that the operation of the secondary network is transparent to the primary network, which requires that the interference incurred by secondary operations be constrained within an acceptable level. It is of great interest to understand to what extent the sec- ondary network can gain in transmission of its own useful data, without harming the regular operation of the primary network significantly. In literature, relevant research is dominated by the study of either the scaling law of transport capacity [1]– [3] or transmission capacity with outage consideration [4]– [7]. The former was proposed in the seminal work [8] and defined as the maximum bit·meters per second the network can achieve in aggregate; recent works in the capacity study This work was supported in part by the National Science Foundation under Grant CNS-0721825, CCF-0830462 and ECCS-1002258. of CR networks or ad-hoc overlaid networks [1]–[3], [9] show that there is no performance loss for the secondary network in terms of scaling law of transport capacity. Nonetheless, asymptotic analysis on the scaling law only characterizes the (rough) relationship between capacity and network size, ne- glecting the effect of many important system parameters. As an alternative, transmission capacity [10] quantifies the maximum spacial density under some outage probability constraint, and sparks an enormous interest recently (see [11] for its latest de- velopment). The outage probability of the secondary networks is studied in [4], [5]. In [6] it is shown that the spectrum effi- ciency of the whole overlaid networks can be improved if extra outage is allowed for the primary network. The achievable transmission capacity 1 of the secondary network is studied in [7], and maximized with respect to its transmitter density. Transmission capacity admits quantitative system analysis, but leaves out the consideration (and optimization) of transmission distance, a key parameter for wireless networks. To offer a comprehensive view of network throughput of decentralized overlaid networks, we study a new metric in this paper: single hop transport throughput (STT), which quantifies the total number of one-hop reliable transmissions in a unit area, weighted by corresponding transmission rates and distances. STT inherits the merits of both traditional transport capac- ity and transmission capacity, and incorporates transmission distance and outage probability into a uniform framework. STT deserves thorough investigation in the secondary network in that single hop transmissions may be preferred due to its inferior role in the spectrum access; it will also serve as a basis for extension to the multi-hop case. Note that our metric is similar in spirit to the random access transport capacity (RTC) recently proposed in [12]. Their difference is that in RTC the transmission distance is pre-determined while in STT it is dynamic across the network. On the one hand, we would like to determine the achievable network throughput when links are activated by specific network protocols (such as nearest neighbor routing). On the other hand, it is desired to explore the limiting performance of the network with transmission distance optimized. In this work we study STT of the secondary network in a decentralized setting, subject to outage constraints for both the 1 defined as the product of the spatial density and the actual outage probability