Tsai-Wei Wu∗ and Hung-Yun Hsieh∗†
∗Graduate Institute of Communication Engineering
†Department of Electrical Engineering National Taiwan University
Taipei, Taiwan, 106 Email: hyhsieh@cc.ee.ntu.edu.tw
Abstract—In this paper, we investigate the problem of pri-mary user detection in cognitive radio networks. Compared with related work that aims to propose techniques at different layers of the network protocol stack for detecting primary users, we aim to investigate the capabilities and limitations of different primary user detection techniques from the perspective of network optimization. The goal is to understand fundamental performance tradeoffs of these techniques without being limited by existing cognitive radio software and hardware platforms.
To proceed, we first identify several dimensions for designing primary transmitter detection techniques in cognitive radio net-works, including transmitter side vs. receiver side detection, and collaborative vs. non-collaborative detection. We then formulate primary transmitter detection techniques along these dimensions using mixed-integer nonlinear programming (MINLP). Evalua-tion results show the benefits of using the proposed optimizaEvalua-tion framework to profile the fundamental characteristics of primary transmitter detection techniques, thus motivating future research along this direction.
I. INTRODUCTION
The concept of cognitive radio is an “intelligent” radio that can first perceive its radio environment through wide-band spectrum sensing and then adapts its transmission or reception parameters such as operating frequency, modulation scheme, code rate, and transmission power in real time. An important goal of performing such parameter adaptation is to allow cognitive radio to coexist with conventional radio for dynamic spectrum access. Frequency bands allocated to licensed users (primary users) that are rarely used can be accessed by non-licensed users (secondary users) equipped with cognitive radio in an opportunistic fashion so spectrum utilization can be maximized while minimizing interference to primary users.
A key enabler of the cognitive radio technology is the detection of the spectrum holes (i.e., absence of primary users) through spectrum sensing. As secondary users (CR nodes) may not have accurate knowledge about the whole spectrum at all times, techniques for detecting primary users (PR nodes) need to be employed before spectrum access. Several techniques for detecting primary transmitters and/or receivers have hence been proposed in this context [1]–[5]. Detection of primary transmitters through matched filter detection, energy detection, and cyclostationary feature detection has been investigated by
This work was supported in part by funds from the National Science Council under grant NSC-96-2219-E-002-027.
related work [1]–[3]. Detection of primary receivers based on the concept of interference temperature [6] has also been proposed [4], [5].
Due to the problem of channel fading/shadowing and the existence of hidden terminals, detection of primary users based only on local observation of a CR node may result in poor detection performance [2]. A conceivable approach therefore is for a group of CR nodes to cooperate and the concerned CR node incorporates information from other CR nodes, instead of completely relying on local observation, for a more accurate detection of primary users. Related work has proposed architecture and network protocols for collab-orative sensing in cognitive radio networks using centralized or distributed approaches [7]–[9]. In centralized approaches, a central control entity is required to gather all sensing information from participating CR nodes through the common control channel. In distributed approaches, on the other hand, CR nodes self-organize to exchange information using local common channels through distributed coordination.
While cognitive radio is a promising technology for max-imizing spectrum utilization, there are still many problems to be overcome before it becomes a reality. An objective evaluation and comparison on the capabilities and limitations of different primary user detection techniques, for example, is yet to be investigated due to the lack of well-established hardware and software platforms. In this paper, we focus on the problem of primary transmitter detection in cognitive radio networks. Instead of jumping into proposing network architec-ture and protocols for detection of primary transmitters, we aim to investigate the fundamental capabilities, limitations, and performance tradeoffs of existing detection techniques.
We consider an approach based on network optimization for an objective evaluation of different techniques without being limited by existing software and hardware platforms for cognitive radio technology.
To proceed, we start by characterizing and comparing different primary transmitter detection techniques, and identify several dimensions for designing primary transmitter detection techniques in cognitive radio networks, including transmitter side vs. receiver side detection, and collaborative vs. non-collaborative detection. We then formulate primary transmitter detection techniques along these dimensions using mixed-integer nonlinear programming (MINLP). Based on the pro-This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2008 proceedings.
posed optimization framework for spectrum sharing among CR and PR nodes, we present numerical results to show the performance tradeoffs of different primary transmitter detection techniques. We discuss the results with the goal to provide solution perspectives for addressing the problem in future work.
The rest of this paper is organized as follows. Section II dis-cusses related work and background information of this paper.
Section III presents the detection model and the optimization framework of the target problem. Section IV shows numerical results of a given network topology, and finally Section V concludes the paper.
II. RELATEDWORK
In this section, we first categorize related work on primary transmitter detection into non-collaborative and collaborative detection. We then describe related work based on network optimization that addresses different problems in cognitive radio networks.
A. Primary Transmitter Detection
The process of detecting primary transmitters starts by clas-sifying and determining the signal from primary transmitters based on local measurements of CR nodes. Several related work has been proposed for detecting primary transmitters [1], [3], [7]–[9]. Detection of signals from primary transmitters through matched filter detection, energy detection, and cyclo-stationary feature detection has in particular attracted attention and under investigation by many research endeavors [1]–
[3]. Depending on how local observations are processed in the detection hypothesis model, primary transmitter detection techniques can be categorized into non-collaborative and col-laborative detection as discussed in the following:
1) Non-Collaborative Detection: Non-collaborative detec-tion of primary transmitters [1] refers to the case where spectrum sensing information is measured and maintained by individual CR nodes alone to determine the presence of primary transmitters. Local observations based on matched filter detection, energy detection, or cyclostationary feature detection are used without exchanging information with other CR nodes. Since these techniques are based entirely on the local observation of a CR node, the problem of hidden terminals due to channel shadowing or insufficient information cannot be avoided.
2) Collaborative Detection: Collaborative detection [7]–[9]
refers to the case where information from multiple CR nodes are incorporated for detecting primary transmitters. Exchange of local observations from individual CR nodes can be imple-mented either in a centralized or distributed manner [7], [8].
In centralized approaches, a central control entity is required to gather all sensing information from CR nodes through the common control channel. In distributed approaches, on the other hand, CR nodes self-organize to exchange information using local common channels through distributed coordination.
CR Transmitter Primary Transmitter
r r
CR Receiver Primary Receiver Figure 1. Network Scenario
B. Network Optimization
Several studies exist in the literature that use the approach of network optimization to investigate the capabilities of software defined radio (SDR) networks or cognitive radio (CR) net-works. For example, the authors in [10] investigate spectrum sharing in multi-hop SDR networks. They consider spectrum sensing with sub-band division, scheduling, interference con-straints, and flow routing, and then formulate the problem of minimizing the total radio bandwidth used in cognitive radio networks as mixed integer non-linear programming (MINLP).
They develop a near optimal algorithm based on a novel sequential fixing procedure to this MINLP problem.
In [11], the authors propose a spectrum auction framework for spectrum allocation with interference constraints to max-imize auction revenue and spectrum utilization. Their design includes a compact and highly expressive bidding language, various pricing models to control tradeoffs between revenue and fairness, and fast auction-clearing algorithms to compute revenue-maximizing prices and allocations.
In [12], the authors formulate an optimization problem by jointly considering power control, scheduling, and flow routing constraints in multi-hop SDR networks. The objective is to minimize the bandwidth-footprint product (BFP), which characterizes the spectrum and space occupancy for a SDR network. They also develop a solution procedure based on branch-and-bound technique and convex hull relaxation to solve the proposed MINLP problem.
While these studies pave the foundation of our work, they do not consider the optimization problem of primary transmitter detection for spectrum sharing. We discuss in the following how we characterize the capabilities and limitations of different primary transmitter detection techniques in cellular cognitive radio networks.
III. FRAMEWORK
We consider a network with |Vcr| cells of CR nodes and
|Vpr| cells of primary nodes distributed in the same region as illustrated in Figure 1. In a CR cell, CR users communicate with the CR base station for utilizing spectrum holes left by This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2008 proceedings.
TABLE I
PRIMARYTRANSMITTERDETECTIONMODELS
Model Participating Entities A Transmitter only B Receiver only
C Transmitter and receiver
D Transmitter and its neighbors within ranger E Receiver and its neighbors within ranger
F Transmitter, receiver and their neighbors within ranger
primary users. We assume that transmission parameters (e.g.
transmission powers and operating channels) of individual primary users have already been decided through external mechanisms in absence of the CR users. Transmission pa-rameters of individual CR users, on the other hand, are to be determined by solving the network optimization problem that we present in this section.
We formulate the constraints for spectrum sharing among CR and primary nodes from two aspects: CR spectrum sharing and primary transmitter detection. The CR spectrum sharing constraint ensures that network resource is shared properly among neighboring CR users either in the same cell or across different cells. The primary transmitter detection constraint ensures that CR users maximize spectrum utilization while following the primary transmitter detection technique in con-sideration. In the following, we first describe various primary transmitter detection models that we consider in this paper, and then present constraints for CR spectrum sharing and primary transmitter detection.
A. Detection Models
As shown in Table I, we compare 6 different detection tech-niques (models) in this paper. Model A refers to the technique where the CR transmitter performs detection based only on its local observation. Model D, on the other hand, involves the transmitter as well as its collaborators. We introduce the parameterr to model the degree of collaboration exhibited by different detection techniques. Model C can also be considered as a form of collaboration, where both the CR transmitter and receiver are involved to detect the primary transmitter.
To model these different techniques in one framework, we introduceUuvas the set of CR nodes that collaborate to detect primary transmitters before communication between the CR pair {uv} takes place. For example, Uuv= {u} for Model A since only the transmitter u of the pair {uv} is involved to detect primary transmitters. For Model D, the setUuvincludes the transmitteru and its neighbors within the circle of radius r.
Therefore, through proper setting of the setUuv, it can be used to represent different primary transmitter detection techniques considered in this paper.
B. CR Spectrum Sharing Constraint
1) Single Cell Constraint: We first consider spectrum sharing in a single CR cell (i.e., one serving CR BS and corresponding CR users). We use s(q) to denote the base
station for a CR cell with index q ∈ Vcr, and we assume that spectrum available in the cell consists of a set of |M|
unequal-sized frequency bands. If thekth channel is used by node u for communication with its serving BS s(q), then Xus(q)k = 1; otherwise, Xus(q)k = 0. We assume that a communication between a CR user u and its serving base stations(q) is successful if no other users within the same cell are simultaneously transmitting in the same channel. In other words, we assume that a BS can communicate with multiple CR users in different channels, but not if the channels overlap.
The interference constraint within a single CR cell thus can be formulated as Equation (b) in Table II, whereCR(q) denotes the CR users within CR cellq excluding BS s(q).
2) Multi-Cell Constraint: We use the physical interference model to determine whether a CR useru can use a spectrum holek if there exist multiple CR cells in the network. Denote Puvk as the received power at nodev on channel k from the signal with powerPutransmitted by node u. We use the log-normal shadowing model for modeling the propagation gain from node u to node v as follows: where d0 is a close-in distance, duv is the distance between nodes u and v, XG is a Gaussian random variable with zero mean and standard deviation σG, and K is a constant accounting for the antenna gain and wavelength of radio propagation. As shown in Equation (1), the path loss exponent up to the close-in distance d0 is denoted as α, whereas that beyond isβ.
We assume that a transmission from node u to v is suc-cessful only if the SINR at receiver v exceeds the receiving threshold ∆. DenotePuas nodeu’s transmission power, then transmission from nodeu to node v on channel k is successful if and only if
Puvk
N +
w∈V
Pwvk ≥ ∆ (2)
where N is the background noise, V is the set of nodes that are transmitting simultaneously on channel k, and ∆ is a parameter that depends on the desired data rate and the modulation scheme. We thus formulate the interference constraint as Equation (c) in Table II, whereVprt denotes the set of all primary transmitters and Xwk is a parameter that denotes whether primary transmitter w transmits on channel k or not. T is a dummy parameter introduced to handle the case when Xus(q)k = 0.
C. Primary Transmitter Detection Constraint
As shown in Table I, we consider different primary transmit-ter detection models based on the set of participating entities (observers) involved. Note that the signal received by each observer consists of three components including signal from CR transmitters, signal from primary transmitters and back-ground noise. Different signal classification techniques such as matched filter detection, energy detection, and cyclostationary This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2008 proceedings.
TABLE II
FORMULATION FORPRIMARYTRANSMITTERDETECTION
maximize
feature detection have been proposed in related work for detecting the presence of primary signals. In this paper, we introduce three parametersα, β and γ to model the capability of different detectors in separating the three components from the received signal. For example, an energy detector that simply measures the energy of the received signal hasα = 1, β = 1 and γ = 1 since the detector does not distinguish the signal of primary users from that of CR users. If a CR node can perfectly distinguish the signal of primary users from other signal (e.g. through the use of the pilot signal), then α = 1, β = 0 and γ = 1.
Note that the pair of us(q) in a cell q cannot be active if the presence of primary users is detected. In other words, u can use the channel k if and only if no one in Uus(q) detects the presence of primary transmitters. We thus formulate the constraint for different primary transmitter detection models as listed in Table I using Equation (d) in Table II.
D. Objective Function
We consider an objective function that maximizes the total CR throughput (capacity) subject to the aforementioned con-straints as follows:
where the link capacity is calculated based on Shannon’s theorem using the following equation:
Cuvk = BWklog2
INDEX OFSYMBOLS USED IN THEFORMULATION
Symbols Definition Vcr set of CR cells Vpr set of primary cells Vprt set of primary transmitters
Uuv set of collaborative CR users for pair{uv}
s(q) base station for a CR cell with indexq ∈ Vcr
Xus(q)k whether link{us(q)} on channel k is active or not Xwk whether primary transmitterw transmits on channel k or
not
CR(q) CR users (not including BS) in CR cellq
Puvk received power at node v on channel k of the signal transmitted by nodeu
duv distance between nodesu and v Pu transmission power of nodeu Cuvk capacity of link{uv} on channel k BWk bandwidth of channelk
N background noise M set of channels
∆ SINR threshold
Θ detection threshold
Overall, the objective function together with different con-straints for modeling spectrum sharing and primary transmit-ter detection in cognitive radio networks are formulated as a mixed-integer nonlinear programming problem shown in Table II. Table III lists the symbols used in the formulation.
IV. SIMULATIONRESULTS
In this section, we present numerical results to compare the performance of different primary transmitter detection techniques using the proposed optimization framework. The MINLP formulation as shown in Table II is solved through the NEOS optimization server [13].
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2008 proceedings.
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A. Topology and Parameters Setting
We consider a network scenario consisting of five primary cells and two CR cells as shown in Figure 2. A CR cell includes one CR base station and several CR users, whereas a primary cell has an active pair of primary transmitter and receiver. Capacity of each link is determined based on the SINR at the receiver using Equation (4). The transmission power of each primary transmitter is set to 10 units, and the maximum transmission power of CR transmitters is limited to 50 units. (Note that the actual transmission power of each CR transmitter is to be determined by the optimization problem.) We assume that the channel bandwidth BWk = 50 for each channel. We vary the range of collaboration r and detection threshold Θ and observe the performance of each detection technique in terms of interference at primary transmitters.
B. Results and Discussion
We consider both the energy detector and feature detector for detection of primary transmitters, with the former using α = β = γ = 1 and the latter using α = γ = 1 and β = 0.
Note that the objective function of the optimization problem is to maximize the CR throughput while following the primary transmitter detection constraints. To compare the performance of each primary transmitter detection model as we showed in Table I, we measure the average interference incurred at primary transmitters caused by CR users in the network.
In Figure 3, we vary the range of collaboration r and observe the performance of different primary transmitter de-tection models. As shown in Figure 3(a), Models A, B, and C involve only the CR transmitter and/or the receiver, and hence their performance is insensitive to the collaboration range r.
Models D, E, and F, on the other hand, involve neighbors within the collaboration range, and hence as r increases (more participating entities for detecting primary transmitters), their interference on primary transmitters is reduced. It can also be observed from Figure 3(a) that the transmitter based model (Model A) incurs slightly higher interference than the receiver based model (Model B). The reason is because the CR receiver (CR base station) can potentially receive from multiple CR transmitters (CR users). Since the energy
Models D, E, and F, on the other hand, involve neighbors within the collaboration range, and hence as r increases (more participating entities for detecting primary transmitters), their interference on primary transmitters is reduced. It can also be observed from Figure 3(a) that the transmitter based model (Model A) incurs slightly higher interference than the receiver based model (Model B). The reason is because the CR receiver (CR base station) can potentially receive from multiple CR transmitters (CR users). Since the energy