1536-1276 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TWC.2018.2820703, IEEE Transactions on Wireless Communications IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. XX, NO. XX, XXX 2018 1 Optimizing Performance of Co-Existing Underlay Secondary Networks Pratik Chakraborty, Student Member, IEEE, and Shankar Prakriya, Senior Member, IEEE Abstract—In this paper, we analyze sum throughput and (asymptotic) sum ergodic rate performance of two co-existing downlink multiuser underlay secondary networks employing either fixed-rate transmission (FRT) or (channel aware) adaptive rate transmission (ART). In the considered scenario in which two secondary sources may transmit simultaneously, intelligent apportioning the interference temperature limit (ITL) is vital. We consider cases when this ITL apportioning is based on statistical properties of the channels, or on full (or partial) knowledge of the channel gains. For these cases, proper network management (NM) strategies are evolved to maximize sum throughput or sum ergodic rate of the secondary networks. Each NM strategy determines whether both secondary sources should transmit concurrently or not, and also determines their transmit powers. We demonstrate that a channel aware NM (CANM) strategy is superior to an optimal fixed NM (FNM) strategy. With secondary sources employing non-opportunistic user selection, in case of FRT (ART), we demonstrate that there exists a critical target-rate (ITL) below which it is advantageous to operate both secondary networks concurrently. We present closed form expressions of critical parameters that influence sum throughput and sum ergodic rate. Computer simulations are presented to corroborate the derived expressions. Index Terms—Co-existing networks, underlay, downlink, sum throughput, sum ergodic rate, network management I. I NTRODUCTION A rapid increase in wireless devices and services in the past decade or so has led to a demand for very high data rates over the wireless medium. With prolific increase in data traffic, mitigating spectrum scarcity by more efficient utilization of the under-utilized spectrum has drawn attention of researchers both in academia and industry. Cognitive radio (CR) devices have shown promise in alleviating these problems of spectrum scarcity and low spectrum utilization efficiencies. In underlay mode of operation of cognitive radios, both secondary (unlicensed) and primary (licensed) users co-exist and transmit in parallel so that the total secondary interference caused to the primary user is below a predetermined threshold [1] referred to as the interference temperature limit (ITL). This ensures that the primary performance in terms of throughput or outage is maintained at a desired level. Most of the analysis till date in underlay CR literature is confined to one secondary node transmitting with full permissible power and catering to its own set of receivers, while maintaining This work was supported by Information Technology Research Academy through sponsored project ITRA/15(63)/Mobile/MBSSCRN/01. P. Chakraborty is with the Bharti School of Telecommunication Tech- nology and Management, IIT Delhi, New Delhi 110016, India (e-mail: bsz128380@dbst.iitd.ac.in). S. Prakriya is with the Department of Electrical Engineering, IIT Delhi, New Delhi 110016, India (e-mail: shankar@ee.iitd.ac.in). service quality of the primary network. For such secondary networks, performance improvement is achieved by exploiting diversity techniques [2], [3], intelligent resource allocation [4], increasing the number of hops [5], etc. However, there still remains scope to further exploit spatial reuse using underlay transmissions, that can lead to improved network coverage and result in higher data rates. A. Related Work: The idea of concurrent secondary transmissions has been proposed by researchers for enhancing physical layer security [6], or further improving spectrum utilization efficiency [7], [8]. In [7], two or more cognitive femtocells reuse the spectrum of a macrocell either in a overlay, interweave or underlay manner for better spectrum utilization. It is emphasized that [7] uses transmit power control 1 , and focuses on estimating the maximum permissible density of femtocells in a macro- cell. The authors in [8] solve a multi-objective optimization problem that maximizes secondary sum rate, while minimizing the total interference caused to the primary receiver. Perfor- mance study of randomly distributed underlay heterogeneous networks can be found in [9]–[11]. In heterogeneous networks, interferences influence overall performance and also determine feasibility of practical implementation. In situations when secondary networks reuse white spaces of the macro base station, unwanted interferences may arise either due to sensing error or primary user return. While the former arises due to faulty sensing of the primary spectrum, causing excessive in- terference to the primary receiver from secondary transmitters, the latter depends on primary traffic pattern and can have detrimental effect on network performance. Ways of mitigating such interferences have been addressed in [12]–[14]. However, to implement an underlay scheme with concurrent secondary transmissions in a cellular framework, the major issue not only lies in mitigating interferences among other heteroge- neous users, but also careful handling of interferences from heterogeneous transmitters to maintain QoS of the macro cell [15]. Thus, radio resource allocation [16], [17] and interference management [18] play key roles in deployment of such het- erogeneous networks. Radio environment maps [19] have been proposed to serve as databases for dynamic spectrum access. For the purpose of implementation, their system architectures and models [20], [21] have been a major subject of study over recent years. A comprehensive survey of heterogeneous 1 In this paper, we focus exclusively on receive power control, which is more appropriate for small primary coded packets.