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- 1. Priyadarshi Mukherjee Electronics and Telecommunication Engineering Department Indian Institute of Engineering Science and Technology. Shibpur, Howrah. West Bengal, India. priyadarshi.m004@gmail.com
- 2. Outline Introduction to Cognitive Radio Networks (CRNs) Research Issues in CRNs Resource Allocation in CRNs Power Allocation Problems in Single User CRNs Power Allocation Problems in Multiuser CRNS Joint Channel and Power Allocation Problem in Multiuser CRNS Power Allocation Problem in Relay based CRNs Joint Channel and Power Allocation Problem in Relay based CRNs Joint Channel and Power Allocation Problem in OFDM-Based CRNs with Relay Recent Trends in Resource Allocation in CRNs
- 3. Why Cognitive Radio? According to a FCC report [1], a large portion of the licensed spectrum of various agencies remains underutilized. The concept of Cognitive Radio is introduced as a method to improve the spectrum utilization. Fig 1: Spectrum Usage [2]
- 4. Introduction to Cognitive Radio Networks(CRNs) Cognitive Radio - Termed formally introduced by Joseph Mitola [3]. - “Radio that includes a transmitter in which operating parameters such as frequency range, modulation type or maximum output power can be altered by software.“ Allows the unlicensed users to dynamically and opportunistically access the “under-utilized" licensed bands.
- 5. Introduction to CRNs (Contd…) In order to access “under-utilized” licensed bands dynamically and opportunistically, Cognitive Radio has to: identify the spectrum opportunities (idle frequency bands) in spatial and frequency domain. or use the licensed spectrum with transmit power constraint so that the interference created by secondary users is below the tolerable limit.
- 6. The Basic Cognitive Cycle Fig 2: Basic Cognitive Cycle [4]
- 7. Characteristics of CRNs Cognitive capability Ability to capture or sense the information from its radio environment and allows to identify and select the portion of the spectrum that are unused at a specific time or location. Reconfigurability Dynamically programmable capability according to radio environment to transmit and receive on a variety of frequencies.
- 8. Terminology Primary user(PU): users have license to use a certain frequency spectrum. Secondary user(SU): devices/ users that able to sense and adapt licensed users allocated spectrum. Spectrum hole: a frequency band licensed to a PU but not utilized by that user at a particular time and at a speciﬁc geographic location.
- 9. Detection of Spectrum Holes In the context of detection of the presence of spectrum holes, the spectrum has been classified into three predominant types [4]: Black spaces: occupied by high-power “local” interferers some of the time. Grey spaces: partially occupied by low-power interferers. White spaces: free of RF interferers except for ambient noise, made up of natural and artificial forms of noise.
- 10. Some Research Issues on CRNs Spectrum Sensing and Dynamic Spectrum Management Transmission Power Control Spectrum Allocation Routing in Multi-hop CRNs Link Scheduling Group and Link Management OFDM in Cognitive Radio
- 11. Resource Allocation in CRNs Based on local information on the spectrum band, CR users need to determine the communication resources intelligently. Each CR user tries to utilize spectrum resource as much as possible. Two main issues in Resource Allocation: Power Allocation Channel Allocation
- 12. Resource Allocation in CRNs (Power and Channel Allocation) Without relay With relay Single Users Multiple Users Single Relay Multiple Relays Dual Hop Multi Hop Fig 3: Classification of Resource Allocation Problem in CRNs (based on network architecture)
- 13. Power Allocation Problem in Single User CRNs In power allocation, mainly the transmission power of the CR user is adjusted by considering co-channel (or inter-user) interference. Power allocation is based on the PU activities in its transmission, not to violate the interference constraints. Of late, power allocation in cognitive radio network is being related to OFDM for certain advantages.
- 14. System Model PU-Tx gpp PU-Rx gps gsp SU-Tx gss SU-Rx Figure 4: A simple CR network system model[4]. Assumptions: PU and SU links share the same narrow-band frequency for transmission. All channels involved are assumed to be independent block fading (BF) channels. The additive noises at PU-RX and SU-RX are assumed to be CN(0, N0). instantaneous channel power gain at fading state ν for the primary link instantaneous channel power gain at fading state ν for the secondary link instantaneous channel power gain at fading state ν for the link from PU-Tx to SU-Rx instantaneous channel power gain at fading state ν for the link from SU-Tx to PU-Rx
- 15. Objective Function Assuming that transmitted signals are Gaussian in nature [6], the ergodic capacity of the SU link is defined [5] as (1) where Pp : constant power transmitted by PU-Tx. ps: instantaneous transmit power of SU-Tx. E{.}: expectation The objective function is: (2) 0 2 1log' NPg pg EC pps sss 0 2 0 1logmax NPg pg EC pps sss ps Assuming the noise (n) to be AWGN, i.e. n ~ CN(0,N0).
- 16. Constraints in Power Allocation Mainly 2 types of power constraints [6] exist: A. Transmit power constraint. (i) peak transmit power constraint, i.e. ps≤ Ppeak (3) (ii) average transmit power constraint, i.e. E{ps}≤Pav (4) Ppeak: peak transmit power constraint. Pav : average transmit power constraint. B. Interference power constraint. (i) peak interference power constraint (PIP), i.e. gspps≤ Qpeak (5) (ii) average interference power constraint (AIP), i.e. E{gspps}≤Qav (6) Qpeak: peak interference power constraint. Qav: average interference power constraint . E{.} : expectation opn.
- 17. Problem Formulation The problem thus formulated: from equation (2) s.t C1: transmit power constraint, from equation (3)/(4) C2: interference power constraint, from equation (5)/(6) This above problem has been solved [6] by convex optimization. 0 2 0 1logmax NPg pg EC pps sss ps
- 18. Numerical Result Fig 5: Capacity under both the peak power constraints vs. transmit power constraint (Ppeak ) [6]. As can be seen in the plot, in spite of Ppeak increasing gradually, capacity does NOT increase monotonically, but saturate at some point of time in the presence of the interference constraints.
- 19. Constraint based on PU Outage Instead of applying the conventional interference power constraint, a constraint based on the maximum tolerable outage probability for the PU [5] may also be considered. Given target transmission rate ro, SU being absent, the transmission outage probability of the PU is (7) 0 0 2 1logPr r N Pg ppp p
- 20. Constraint based on PU Outage (contd…) But when SU is active, the transmission outage probability of the PU becomes (8) To protect the PU, additional outage probability of PU caused by SU transmission should not be larger than Δε. εc − εp ≤ Δε. (9) • Equation (9) is termed as the PU outage loss constraint. 0 0 2 1logPr r Npg Pg ssp ppp c
- 21. Problem Formulation The ergodic capacity of the SU can be obtained by solving the following problem: from equation (2) s.t. C1: transmit power constraint, from equation (3)/(4) C2: εc − εp ≤ Δε. from equation (9) This problem has been solved [5] by applying convex optimization. 0 2 0 1logmax NPg pg EC pps sss ps
- 22. Power Allocation Problem in Multiuser CRNs Till this point of time, the scenario where multiple CUs exist, have not been highlighted upon. Hence the quality of service (QoS) requirement of CUs could not be guaranteed. Thus, power allocation in multiuser CRNs is of much more practical importance.
- 23. System Model The uplink of a single cell of a CRN is considered [7] with N unlicensed users. A network with one licensed receiver is considered, having a maximum interference tolerance . The maximum interference tolerance (Qmax) is calculated [7] as Qmax= ξ Tmax The network is modeled as interference channels, where gi: path gain between base station (BS) and user equipment (UE) i. max mQ Boltzmann’s constant Interference temperature limit.
- 24. Objective Function Total system capacity based on Shannon formula is described as (10) where p=(p1,…,pN)T, p1 is transmit power of user i. The objective function is: (11) N i N ijj jj ii gp gp pC 1 ,1 2 2 1log noise and the interference from the licensed users. )(max 0 pC p
- 25. Constraints in Power Allocation Peak transmit power constraint , (12) where , and : maximum transmit power of user i. Peak interference power constraint Hp ≤ Qmax, (13) where hi: path gain between user i and the PU-Rx, and pp 0 Nppp ,...,1 ip NihH 1
- 26. Problem Formulation The optimization problem thus formulated: from equation (11) s.t. C1: peak transmit power constraint from equation (12) C2: peak interference power constraint from equation (13) This problem is a concave minimization problem with linear constraints in mathematical programming. So, the branch and bound algorithm [7] has been used here to search optimal solutions. pC p 0 max
- 27. Joint Channel and Power Allocation Problems in Multiuser CRNs Till now, power allocation was being done assuming that the channels have been already allocated. But to achieve satisfactory performance from a multiuser multichannel wireless network, such as CRNs, not just power but joint channel and power allocation provides satisfactory results.
- 28. System Model A CRN is considered with K users and N channels (both K and N varying dynamically based on the number of contending users and available vacant channels) . AP CR Primary User Fig. 7: Cognitive Radio Network [8]. An access point (AP) controls the transmission of CRs lying within its range of coverage and also collects reports about the activities of primary users (PUs) that CRs may interfere with.
- 29. Assumptions The following knowledge [8] is available at the AP: (i) the set of vacant channels that are not currently utilized by PUs and are free for CRs to use. (ii) the power gains of this channel set corresponding to each of the contending users. Channels are assumed to be independent and identically distributed (IID). The strength of each is assumed to be Rayleigh distributed.
- 30. Problem Formulation Let N0: one-sided noise power spectral density B: unit bandwidth Pnk: uplink power when channel n is assigned to the user k Capacity associated with user k (depends on the number of channels assigned) is (14) The total sum capacity is: (15) The objective function is: (16) N n nk nknk nkk BN gP BC 1 0 2 1log assignment of channel n to user k,ϵ {0,1} C nknk P 0,10 max K k N n nk nknk nk K k k BN gP BCC 1 1 0 2 1 1log
- 31. Problem Formulation (contd…) Sum transmit power constraint (17) The constrained optimization problem is : from equation (16) s.t. C1: sum transmit power constraint from equation (17) The above optimization problem comprises both continuous and discrete variables and thus belongs to the class of mixed integer programming. N n knk kPP 1 available power budget C nknk P 0,10 max
- 32. Problem Formulation (contd…) To make the problem tractable, discrete nature of αnk is relaxed and channel sharing among different users is allowed, i.e. αnk is allowed to take on continuous values in the range from 0 to 1. Thus, now the optimization problem is : from equation (16) s.t. C1: sum transmit power constraint from equation (17) C2: assignment constraint, i.e. (18)n K k nk 1 1 C nknk P 0,10 max
- 33. Problem Formulation In this new formulation, channel sharing is allowed among different users under the condition stated in C2. The importance of having αnk in the denominator of C (15) becomes clear now as αnk can be a fraction (channel sharing). The methodology used here is to start solving the modified problem (with channel sharing) and then find the condition that allows for only 1 user utilization per channel. Above formulated problem being convex, convex optimization has been used to solve it. C nknk P 0,10 max
- 34. Power Allocation Problem in Relay based CRNs In the case of direct communication between SUS and SUD, transmission power requirement, sometimes, may exceed the limits of acceptable interference to the PU. It may also happen that there exists no direct link between the source(S) and the destination (D). To address such problems, the context of relay-based CRNs is of high practical importance.
- 35. System Model As shown below, a communication system with N relay nodes is considered. rN s Ia-b d Ia-b r1 r3 Ua m n Ub Ib-a r2 a b Ua, Ub : PUs, and their coverage areas are a and b respectively. s,d: 2 SUs, which use relays r1 …rN for their communication. Ia-b : Idle channel set in a, but busy in b. [Ib-a is just the reverse] Interference for PUs Secondary transmission using Cooperative scheme Fig. 8: N relay nodes used in secondary communication. Source node and relay nodes are transmit signal with different frequency sets [9].
- 36. Objective Function In general, the objective function [9] is: (19) where Pout: outage probability of the communication system. Mathematical expression of Pout is different for different relay based CRNS, depending on whether it is regenerative or non-regenerative. For instance, for single relay transmission with regenerative relay [vtc 2010], where (20) γth: threshold SNR. p1, p2: SU and relay transmit power. G1, G2: parameters independent of power. outPmin 2211 11 1 pGpG out th eP
- 37. Constraints in Power Allocation Sum power constraint [9] (21) Transmit power constraint [9] pn ≤ Pmax : n=1,2,…N (22) ps ≤ Pmax Interference power constraint [9] pshsn ≤ Tb (23) N n Tns Ppp 1 transmit power of source s transmitted power of n th relay available power budget a N n mrn Thp n 1 Ta, Tb: interference power threshold levels on m and n, respectively. hij: the link gain between node i and j. transmit power constraint
- 38. Problem Formulation The constrained optimization problem [9] is : min Pout from equation (19) s.t. C1: sum power constraint from equation (21) C2: transmit power constraint from equation (22) C3: interference power constraint from equation (23) Above formulated problem being convex in nature, convex optimization has been applied to solve it [9].
- 39. Numerical Result As can be seen in the plot, in spite of Total power increasing gradually, outage probability does NOT decrease monotonically, but saturate at some point of time in the presence of interference constraints. Fig 9: Outage Probability vs. Total power [9].
- 40. Joint Channel and Power Allocation Problem in Relay based CRN Just like multiuser CRNs, in relay based CRNs too only power allocation on the assumption of the channels being already allocated, does not provide satisfactory result always. So to improve performance, in terms of guaranteed QoS for instance, joint channel and power allocation IS important in relay based CRNs too.
- 41. System Model The system model shown in figure 10 [10] includes a N-hop CRNs with linear network topology. PUS PUD Source and the relaying nodes (R n) are operating in full-duplex mode. Underlay scenario is considered, where CUs share their spectra with PUs SU-Tx R 1 RN SU-Rx simultaneously. Available spectrum is divided into N orthogonal channels to be used by CUs. The channels are AWGN, subject to quasi-static fading, i.e. channel gains are random, although remain constant during a transmission suite from source to destination. PUS: primary source, PUD: primary destination. SU-Tx: cognitive transmitter, SU-Rx: cognitive receiver. Fig 10: System model of relay based multi-hop CR network [10].
- 42. Objective Function End to end outage probability in Rayleigh fading channel with ‘N’ regenerative relays can be written [10] as (24) where γth: predetermined SNR threshold N0: average noise power at each relay : transmission power of the m th relay over channel Ωm . : channel gain between two consecutive relays, when channel Ωm is allocated. Minimizing outage probability is equivalent to minimizing Thus, the objective function [10] is: (25) N m ss mm th out mm gP N P 1 ,, 0 exp1 ss mm g , mm P , N m ss mm th mm gP N 1 ,, 0 N m ss mm th P mm mm gP N 1 ,, 0 0, min
- 43. Constraints in Joint Channel and Power Allocation Sum power constraint (26) PT: maximum transmission power. Sum interference power constraint (27) TPU: Accumulated interference power threshold (AIPT) at PU. N m Tm PP m 1 , N m PU sp mm TgP m 1 , channel gain from the mth relay to the PU
- 44. Problem Formulation The optimization problem is: from equation (25) s.t. C1 :sum power constraint. from equation (26) C2: sum interference power constraint from equation (27) The objective function is convex and two constraints are linear. So, the minimization problem is solved by convex optimization [10]. N m ss mm th P mm mm gP N 1 ,, 0 0, min
- 45. Numerical Result Transmission Power (dB) As can be seen in the plot, this scheme [10] is comparatively better than the scheme proposed in [9] Figure 11: Outage Probability vs. Transmission Power [10]
- 46. Joint Channel and Power Allocation Problem in OFDM-Based CRNs with Relay In a cognitive radio environment, spectrum holes come and go, depending on the availability of subbands as permitted by licensed users. To deal with this phenomenon and thereby provide the means for improved utilization of the radio spectrum, a cognitive radio system must have the ability to fill the spectrum holes rapidly and efficiently. In other words, cognitive radios have to be frequency-agile radios with flexible spectrum shaping abilities. The orthogonal frequency-division multiplexing (OFDM) modulation scheme can provide the required flexibility, and is therefore being considered as a good candidate for cognitive radio.
- 47. System Model An OFDM-based relay CRN is considered, as shown in figure 10 [11] The CR relay system coexists with the primary system in the same geographical location. There is no direct link between S and D. So, S tries to communicate with D through R. The CR system’s frequency spectrum is divided into N subcarriers each having a Δf bandwidth. The relay is assumed to be half-duplex, thus receiving and transmitting in two different time slots. cognitive relay R cognitive source S primary receiver cognitive destination D obstacle Fig. 12: Cooperative relay cognitive radio network [11].
- 48. Objective Function Let In 1st time slot, S connects to R via jth subcarrier and in 2nd slot, R connects to D via kth subcarrier. Ps (PR): maximum total transmission powers that can be used in S (R). noise power (σ2)is assumed to be same for all subcarriers. Transmission rate of jth subcarrier in the source coupled with kth subcarrier in the relay [11], R(j, k) is (28) where :power transmitted over the jth (kth) subcarrier in the S-R(R-D) link. : jth (kth) subcarrier fading gain over S-R(R-D) link. 2222 1log,1logmin 2 1 ),( k RD k RD j SR j SR HPHP kjR )( k RD j SR PP )( k RD j SR HH
- 49. Objective Function (contd…) Our aim is to maximize the CR system throughput by: Optimization of subcarrier pairing. Distribution of the available power budgets in S and R between the subcarrier pairs. The objective function [11] is: (29) N j N k kj tPP kjRt kj k RD j SR 1 1 , ,0,0 ),(max , assignment variable. tj,k= 1, when jth subcarrier is selected in 1st time slot and kth subcarrier in the 2nd time slot. 0, otherwise. total number of subcarriers
- 50. Constraints in Joint Channel and Power Allocation Source power constraint [11] (30) Relay power constraint [11] (31) Interference power constraint at the 1st and 2nd time slot [11] ; (32) Subcarrier pairing constraint [11] (33) : subcarrier interference factor to the PU band from S (R). N j s j SR PP 1 N j R k RD PP 1 N j th j SP j SR IP 1 N j th k RP k RD IP 1 N j kj N k kj ktjt 1 , 1 , ,1;,1 )( j RP j SP
- 51. Problem Formulation The optimization problem [11] is formulated as: from equation (29) s.t. C1: source power constraint from equation (30) C2: relay power constraint from equation (31) C3: interference power constraint at the 1st and 2nd time slot from equation (32) C4: subcarrier pairing constraint from equation (33) This problem has been solved [11] by applying convex optimization. N j N k kj tPP kjRt kj k RD j SR 1 1 , ,0,0 ),(max ,
- 52. Numerical Result As can be seen in the plot, in spite of interference threshold (Ith) increasing gradually, capacity does NOT increase monotonically, but saturate at some point of time in the presence of the interference constraints. Fig 13: Capacity under both the power constraints vs. interference threshold (Ith) [11].
- 53. Recent Trends in Resource Allocation in CRNs In a highly dynamic environment (as in CRN), finding a reasonably good solution (i.e., a suboptimal solution) fast enough is the only practical goal. Otherwise, spectrum holes may disappear before they can be utilized for communication. In such a situation, the concept of equilibrium is very important, and here comes the advantage of using Game Theory in this context. Due to this advantage of the very idea of Game Theory , it is now being quite interestingly used to solve the Resource Allocation Problems in CRNs. For instance, [12] shows the investigation of distributed power control for CRNs, based on a cooperative game-theoretic framework.
- 54. Recent Trends in Resource Allocation in CRNs (contd…) Joint spectrum sensing and throughput
- 55. References [1] Federal Communications Commission, “Spectrum Policy Task Force ,” Rep. ET Docket no. 02-135, Nov. 2002. [2] I. F. Akyildiz, W. Y. Lee, M. C. Vuran, and S. Mohanty, “Next generation/ dynamic spectrum access/cognitive radio wireless networks: A survey,” Computer Networks, Vol. 50, pp. 2127–2159, May 2006. [3] J. Mitola, “Cognitive radio: An integrated agent architecture for software defined radio,” Ph.D. dissertation, KTH Royal Inst. of Technol., Stockholm, Sweden, 2000. [4] S. Haykin, “Cognitive Radio: Brain-empowered Wireless Communications”, IEEE Journal on Selected Areas in Communications (JSAC), Vol. 23, No. 2, Feb. 2005, pp. 201-220. [5] Xin Kang, Rui Zhang, Ying-Chang Liang, and Hari Krishna Garg, “Optimal Power Allocation for Cognitive Radio under Primary User’s Outage Loss Constraint, ” IEEE International Conference on Communication( ICC), pp.1-5, June 2009. [6] Xin Kang, Ying-Chang Liang, Arumugam Nallanathan, “Optimal Power Allocation for Fading Channels in Cognitive Radio Networks under Transmit and Interference Power Constraints, ” IEEE International Conference on Communication( ICC), pp. 3568 - 3572, May 2008. [7] Wei Wang, Tao Peng, Wenbo Wang, “Optimal Power Control under Interference Temperature Constraints in Cognitive Radio Network,” IEEE Wireless Communications and Networking Conference(WCNC), pp. 116– 120, March 2007.
- 56. References (contd…) [8] F. F. Digham, “Joint Channel and Power Allocation for Cognitive Radios” IEEE Wireless Communications and Networking Conference(WCNC), pp. 882 – 887, April 2008. [9] L.K. Saliya Jayasinghe and Nandana Rajatheva, “Optimal Power Allocation for Relay Assisted Cognitive Radio Networks ,” IEEE 72nd Vehicular Technology Conference (VTC’10- Fall), pp. 1-5, September 2010. [10] Tamaghna Acharya, Swagata Mandal and Santi P. Maity, “Joint Power and Channel Allocation in Cognitive Radio Ad Hoc Networks,” 5th International Conference on Communication Systems and Networks (COMSNETS), pp. 1-7, January 2013. [11] Musbah Shaat and F. Bader, “Asymptotically Optimal Subcarrier Matching and Power Allocation for Cognitive Relays With Power and Interference Constraints,” IEEE Wireless Communications and Networking Conference(WCNC), pp. 663-668, April 2012. [12] Chun-Gang Yang, Jian-Dong Li and Zhi Tian, “Optimal Power Control for Cognitive Radio Networks Under Coupled Interference Constraints: A Cooperative Game-Theoretic Perspective,” IEEE Transactions on Vehicular Technology, Vol. 59, Issue 4, pp. 1696-1706, May 2010. [13] Timo Weiss, Joerg Hillenbrand, Albert Krohn Friedrich K. Jondral , “Mutual interference in OFDM-based spectrum pooling systems,” in Vehicular Technology Conference (VTC’04- Spring), Vol. 4, pp. 1873-1877, May 2004.
- 57. Questions
- 58. PU-Rx CU Base Station CR Interference link System Model Fig. 6: System Model with 1 PU and N CRs
- 59. Subcarrier interference factor Assuming an OFDM based CR, the power spectrum density of the ith subcarrier is [13] where Pi: total transmit power in the ith subcarrier. Ts: symbol duration. The mutual interference introduced by the ith subcarrier to PU [11] is The term Ωi is defined as the INTERFERENCE FACTOR of the ith subcarrier to the PU band. 2 sin s s sii fT fT TPf i i Bd Bd iiiii PdffGPdI i i 2/ 2/ )(, spectral distance between ith subcarrier and the PU band bandwidth occupied by PU Channel gain between ith subcarrier and PU