1 Coexistence of tactical cognitive radio networks Vincent Le Nir, Bart Scheers Abstract—In this paper, we consider the scenario in which N different cognitive radio networks can not cooperate with each other and wish to broadcast a common information to their network by sharing the same Nc parallel sub-channels. This scenario is particularly adapted to tactical radio networks in which N different networks coexist in a given area and broadcast a common information (voice, data...) to their group. In this context, we propose a novel distributed power allocation for power minimization subject to a minimum rate constraint based on the iterative water-filling principle in which each network updates its power allocation autonomously. The novel algorithm generalizes the iterative waterfilling algorithm to the coexistence of multiple tactical radio networks. Index Terms—Coexistence of tactical radio networks, broadcast chan- nels, parallel multicast channels, iterative water-filling. I. INTRODUCTION When several coalition nations coexist in the same area, cur- rent technologies do not permit reconfigurability, interoperability nor coexistence of the radio terminals. Software defined radio has been developed for reconfigurability of the terminals with software upgrades and for portability of the waveforms. Cognitive radio has been developed for spectrum availability recognition, reconfigura- bility, interoperability and coexistence between terminals by means of software defined radio technology, intelligence, awareness and learning [1], [2]. Therefore, cognitive radio enables the adaptation of the transmission parameters (transmit power, carrier frequency, modulation strategy) to these scenarios. Tactical radio networks are networks in which information (mostly voice, but also packet based data) are conveyed from one transmitter to multiple receivers. When several tactical radio networks are set up in the same area and transmit in the same band, the coexistence of these networks is critical. The coexistence of multiple tactical radio networks calls for distributed algorithms implemented in the cognitive terminals. Indeed, although distributed algorithms are sub- optimal, they are preferred to centralized algorithms because of their scalability and robustness. Therefore, each terminal must be equipped with spectrum sensing and management functions to detect the spectrum holes and to find the transmit powers improving the performance of the network as a whole (capacity, stability, delay). The broadcast channel has been introduced by Cover in 1972 as a communication channel in which there is one transmitter and two or more receivers [3]. The broadcast channel with only independent information (unicast channel) belongs to the class of degraded chan- nels in which one user’s signal is a degraded version of the other signals. Its capacity region is fully characterized and can be achieved by superposition coding [4]. Contrary to a single unicast channel, the sum of unicast channels as well as MIMO broadcast channels are non-degraded [5], [6]. Previous studies on parallel broadcast channels have focused on scenarios in which independent messages are sent to the receivers (parallel unicast channels) [7], [8], [9], [10], or in which simultaneous common and independent messages are sent to the receivers [5], [11], [12]. Contrary to an unicast channel, a tactical radio network can be thought as a broadcast channel with only common information (also referred to as a multicast channel). V. Le Nir and B. Scheers are with the Royal Military Academy, Dept. Communication, Information Systems & Sensors (CISS), 30, Avenue de la Renaissance B-1000 Brussels BELGIUM. E-mail: vincent.lenir@rma.ac.be bart.scheers@rma.ac.be This research work was carried out in the frame of the Belgian Defense Scientific Research & Technology Study C4/19 funded by the Ministry of Defense (MoD). The scientific responsibility is assumed by its authors. The capacity of a single multicast channel is limited by the capacity of the worst receiver [4], [13]. However, less work has been done on multicast channels with Nc parallel sub-channels (parallel multicast channels) [14]. In this paper, we propose some solutions for the power allocation of parallel multicast channels, focusing on the power minimization subject to a minimum rate constraint for all receivers. These solutions can be used in a tactical radio network equipped with cognitive terminals, i.e in which the transmitter knows the channel state infor- mation (CSI) and noise variances of its receivers. Although the initial problem is difficult to solve, we compare different algorithms inspired from Gallager’s water-filling strategy [15] associating an inner loop for rate maximization and an outer loop for power minimization. We then consider the scenario in which N different cognitive radio networks can’t cooperate with each other and wish to broadcast a common information to their network by sharing the same Nc parallel sub-channels. In this context, we propose a novel distributed power allocation for power minimization subject to a minimum rate constraint based on the iterative water-filling principle [16] in which each network updates its power allocation autonomously. The novel algorithm generalizes the iterative waterfilling algorithm to the coexistence of multiple tactical radio networks. II. COEXISTENCE OF MULTIPLE TACTICAL RADIO NETWORKS The considered scenario is shown on Figure 1, where N different networks coexist in a given area. In each network j , the Tj receivers are within the transmission range of the transmitter which broadcasts a common information. The transmission range is represented by the gray area around the transmitter. Moreover, the transmitter and the receivers of each network are mobile. This mobility is represented by arrows at the cardinal directions of the gray circles. In each network, a receiver can also become a transmitter to broadcast a common information, causing the initial transmitter to be another receiver. Due to this mobility, the different networks can interfere with each other, causing transmission losses if dynamic spectrum management techniques are not implemented. Our goal is to alleviate this problem by equipping each terminal with an algorithm which gives the possibility to optimize its transmission power for each sub- channel. The received signals yj,it can be modeled as yj,it = hjj,it xij + N P k=j h jk,it x ik + nj,it i =1 ...Nc, j =1 ...N, t =1 ...Tj (1) where nj,it represents a complex noise with variance σ 2 j,it and h jk,it corresponds to the channel from network k to j on receiver t and tone i. We are interested in the power minimization subject to a minimum rate constraint for each network. In the following, we first derive the power allocation for a single tactical radio network. A. Single tactical radio network Considering a single tactical radio network, we assume that each transmitter has knowledge of the fading channels hit in its network. The power minimization subject to a minimum rate constraint R min for all T receivers is given by min (φ i ) i=1...Nc Nc P i=1 φi subject to Nc P i=1 log2(1 + |h it | 2 φ i Γσ 2 it ) ≥ R min ∀t . (2)