Cognitive radio is a paradigm for wireless communication in which either a network or a wireless node changes its transmission or reception parameters to communicate efficiently by avoiding interference with licensed or unlicensed users. This alteration of parameters is based on the active monitoring of several factors in the external and the internal radio environment, such as the radio frequency spectrum, user behavior, and network state. As a key technology enabling the cognitive radio, spectrum sensing plays an important role in the detection of an occurrence of an incumbent or available radio frequency [1].

Cognitive radio technology makes it possible to share the same spectrum band temporally or spatially between heterogeneous systems in order to improve the utilization of the spectrum [2]. However, the secondary system should not cause harmful interference to the primary system. Therefore, spectrum sensing is per-formed by the secondary signal to check whether the primary signal occurs or not. The performance of spectrum sensing is evaluated by using the probability of missed detection (P_MD) and the probability of false alarm (P_FA) [3, 4]. P_MD denotes the probability that the secondary signal does not detect a primary signal even though the primary signal exists. Thus, the secondary signal causes a severe interference to the primary signal. On the other hand, P_FA denotes the probability that the secondary signal detects a primary signal even though the primary signal does not exist. In this case, the utilization of the spectrum decreases as the secondary signal does not use the current band anymore. It has been known that there is a tradeoff between P_MD and P_FA according to the sensing threshold [5-7]. If the sensing threshold is increased, P_MD is increased, but P_FA is decreased. Therefore, it is important to determine a suitable value of the sensing threshold for the cognitive radio environment.

In an ad hoc network, a communication node controls its own transmit power according to the distance to its correspondent node [8]. If an ad hoc node uses the band of the primary system as the secondary system, the amount of interference from the ad hoc node to the primary system depends on the strength of the transmit power of the ad hoc node. Moreover, in spectrum sensing, the sensing threshold is a criterion to judge whether the primary system receives harmful interference or not; thus, we can expect the sensing threshold to be related to the transmit power of the secondary system. Therefore, in this study, we focus on the determination of the sensing threshold in a cognitive radio-based ad hoc network environment. First, we model a cognitive radio system in the ad hoc network and present a condition in which the primary and the secondary systems can coexist on the same channel without harmful interference from each other. Then, we derive a suitable value of the sensing threshold for efficient spectrum sharing and decide the sensing time required for reliable spectrum sensing against channel fading.

The rest of this paper is organized as follows: in Section II, the system model and the operation of the proposed sensing threshold control algorithm are presented. In Section III, the performance of the proposed scheme is analyzed. In Section IV, numerical and simulation results are presented. Section V concludes this paper.

Fig. 1 illustrates a system model for the considered cognitive radio ad hoc network. The primary system is regarded as a one-way broadcast system, such as a wireless microphone; therefore, a primary receiver (PR) always receives the signal from a primary transmitter (PT). As the secondary system, we consider a pair of ad hoc nodes. Namely, two secondary users (SU) perform peer-to-peer communication by using the same frequency band as the primary system and use a transmit power control (TPC) mechanism according to the distance between them.

We define some parameters as follows: rp: radius of PT coverage. rs: radius of SU coverage. d: distance between SU and PR. Pp: transmit power of PT. Ps: transmit power of SU. Pn: background thermal noise power. γrx: signal-to-interference-plus-noise ratio (SINR) received at PR. γreq: minimum required SINR at PR. λ: sensing threshold of SU.

Previous studies have dealt with issues of TPC for spectrum sharing in a cognitive radio system [9-13]. As a common approach, an SU first senses the power level of a PU and then controls its transmission power within a specified range such that the SU does not interfere with the PU. However, the SU sometimes cannot decrease its transmission power below a certain power level to guarantee the transmission rate required by the quality-of-service (QoS). In this case, the SU should change the currently used channel to another one in order to not interfere with the PU. Unlike the above scenario, in our approach, the SU first controls its transmission power according to the QoS requirement and then senses the PU signal. In order that the SU’s transmission has no influence on the PU, the SU decides a sensing threshold based on the predetermined transmission power and performs spectrum sensing by using the decided sensing threshold.

As shown in Fig. 1, when the primary and the secondary systems use the same channel, the PR receives interference from the SU. Nevertheless, if only the SINR received at the PR is greater than the minimum SINR required for decoding, the interference from the SU is tolerable for the PR. On the basis of this underlying concept [14], we suppose the worst case scenario because we do not know the location of the PR practically. The worst case corresponds to when the PR is located on the boundary of the PT coverage and the nearest position to the SU, as shown in Fig. 1. In this case, the PR has the lowest SINR and this SINR should be greater than γ_req for the primary and the secondary systems to share the same spectrum band. Therefore, the following condition is formed (there might be multiple ad hoc connections. For the sake of simplicity, in this paper, we assume that multiple ad hoc connections can use different channels through their control signaling and each ad hoc connection uses a half-duplex mode. Therefore, only one SU can be an interferer at any given point of time):

where the function of path loss is given by L(x) = x^-α where α denotes the path loss exponent and x represents the distance between the transmitter and the receiver.

From (1), we can derive the minimum distance between the SU and the PR required for them to share the same spectrum. The minimum distance, d_min, is calculated as

That is, spectrum sharing is possible only if the distance between the SU and the PR is longer than d_min. Under this optimized coexistence condition, the signal power that the SU receives from the PT becomes P_pL(d_min+r_p); thus, this value can be used as a criterion to judge whether spectrum sharing is possible or not. Therefore, the proposed sensing threshold of SU, λ_prop, is determined as

The regulation for a shared spectrum provides information about the primary system, such as P_p, r_p, and γ_req [15]. In addition, the SU can estimate the path loss exponent α and the noise power level P_n in a given channel [16]. Therefore, the sensing threshold λ_prop given by (3) depends only on the transmit power of the SU, P_s. In other words, the sensing threshold should be decreased as the transmit power is increased, which implies that the SU should detect the primary signal more sensitively as it causes more interference by increasing its transmit power.

For spectrum sensing, the overall procedure of the SU can be summarized as follows: 1) The SU decides its transmit power by TPC considering the distance with the other SU. 2) The SU decides its sensing threshold by using (3). 3) The SU performs spectrum sensing (e.g., energy detection) by using the decided sensing threshold. 4) If the detected power is greater than the sensing threshold, the SU does not use the current channel and changes to another channel immediately. 5) If the detected power is smaller than the sensing threshold, the SU continues to use the current channel and performs spectrum sensing next time. 6) Every time the SU changes its transmit power, it recalculates the sensing threshold.

For the performance evaluation, we constructed an analysis model as shown in Fig. 2. We can consider an onedimensional analysis because the algorithm depends only on the distance between the SU and the PT. Suppose that there is an X-axis and the origin is the SU; then, a PT can be located at any point on the X-axis. The detection range in which the SU can detect the primary signal varies according to its sensing threshold l. For example, when the SU sets its sensing threshold to the proposed sensing threshold (i.e., λ = λ_prop), its detection range becomes d_min+r_p, which is the minimum distance between the SU and the PT required for spectrum sharing. However, if the sensing threshold increases (i.e., λ >λ_prop), then the detection range of the SU shrinks and the SU may not detect the PT signal even though the PR receives harmful interference from the SU (i.e., the missed detection occurs).

In contrast, if the sensing threshold decreases (i.e., λ < λ_prop), the detection range extends and the SU may detect the PT signal unnecessarily although the PR is not interfered by the SU (i.e., a false alarm occurs).

If we consider a radio propagation model with lognormal slow fading (in spectrum sensing, the instantaneous received signal is averaged to decide its strength; therefore, fast fading can be neglected on average), the signal power that the SU receives from the PT is expressed as

where x denotes the distance between the SU and the PT, and Z represents a Gaussian random variable with zero mean and standard deviation σ.

Missed detection occurs when the received signal power is less than the sensing threshold in spite of the requirement that the SU must detect the PT signal. Therefore, P_MD at a distance x is defined as

Then, the average probability of missed detection is calculated as

where Q(·) represents a Q-function defined as and m denotes the number of sensing operations for decision making. On the other hand, P_FA at a distance x is defined as

Therefore, the average probability of a false alarm is obtained by

Notice that the average probabilities of missed detection and false alarm ( and ) are the function of m (i.e., the number of sensing operations for averaging). Since the channel fluctuation (i.e., fading) deteriorates the sensing performance, we need to consider temporal averaging to mitigate the fading effect. In other words, the sensing time should be increased according to the fading level in order to satisfy the requirements of missed detection and false alarm. Therefore, the total sensing time, T_S, is determined as

where ε₁ and ε₂ denote the sensing constraints of missed detection and false alarm, respectively, and t_s indicates the time needed for one sensing operation.