Resource Allocation in Spectrum-Sharing Cognitive Heterogeneous Networks

Haijun Zhang; Theodoros A. Tsiftsis; Julian Cheng; Victor C. M. Leung

doi:10.1007/978-981-10-1389-8_19-1

Handbook of Cognitive Radio pp 1-46 | Cite as

Resource Allocation in Spectrum-Sharing Cognitive Heterogeneous Networks

Authors
Authors and affiliations

Haijun ZhangEmail author
Theodoros A. Tsiftsis
Julian Cheng
Victor C. M. Leung

Living reference work entry

First Online: 26 May 2017

Received: 04 December 2016

Accepted: 12 January 2017

39 Downloads

Abstract

Cognitive radio-enabled heterogeneous networks are an emerging technology to address the exponential increase of mobile traffic demand in the next-generation mobile communications. Recently, many technological issues such as resource allocation and interference mitigation pertaining to cognitive heterogeneous networks have been studied, but most studies focus on maximizing spectral efficiency. This chapter introduces the resource allocation problem in cognitive heterogeneous networks, where the cross-tier interference mitigation, imperfect spectrum sensing, and energy efficiency are considered. The optimization of power allocation is formulated as a non-convex optimization problem, which is then transformed to a convex optimization problem. An iterative power control algorithm is developed by considering imperfect spectrum sensing, cross-tier interference mitigation, and energy efficiency.

Keywords

Cognitive heterogeneous networks Fairness Imperfect spectrum sensing Orthogonal frequency division multiple access (OFDMA) Power control Resource allocation Sensing time optimization

This is a preview of subscription content, to check access.

Appendix

The proof of Theorem 1.

Proof.

(1) Suppose that $\eta {_{13,n}}^{{\ast}}$ is the optimal solution of (22), the inequality can be obtained

$$\displaystyle{ \begin{array}{l} \eta _{13,n}^{{\ast}} = \dfrac{P(\mathcal{H}_{n}^{v})(1 - q_{n}^{f}(\varepsilon _{n},\hat{\tau }))R_{1,n}(\hat{\tau },\tilde{P}_{s,n}^{v}) + P(\mathcal{H}_{n}^{o})q_{n}^{m}(\varepsilon _{n},\hat{\tau })R_{3,n}(\hat{\tau },\tilde{P}_{s,n}^{v})} {\tilde{P}_{s,n}^{v} + P_{c}} \\ \geq \dfrac{P(\mathcal{H}_{n}^{v})(1 - q_{n}^{f}(\varepsilon _{n},\hat{\tau }))R_{1,n}(\hat{\tau },P_{s,n}^{v}) + P(\mathcal{H}_{n}^{o})q_{n}^{m}(\varepsilon _{n},\hat{\tau })R_{3,n}(\hat{\tau },P_{s,n}^{v})} {P_{s,n}^{v} + P_{c}}\end{array} }$$

(79)

$$\displaystyle{ \begin{array}{*{20}{l}} \mathop{\max }\limits _{P_{s,n}^{v}}\left \{P(\mathcal{H}_{n}^{v})(1 -q_{n}^{f}(\varepsilon _{n},\hat{\tau }))R_{1,n}(\hat{\tau },P_{s,n}^{v}) + P(\mathcal{H}_{n}^{o})q_{n}^{m}(\varepsilon _{n},\hat{\tau })R_{3,n}(\hat{\tau },P_{s,n}^{v}) -\eta _{13,n}^{{\ast}}(P_{s,n}^{v} + P_{c})\right \} \\ = P(\mathcal{H}_{n}^{v})(1 -q_{n}^{f}(\varepsilon _{n},\hat{\tau }))R_{1,n}(\hat{\tau },P_{s,n}^{v}) + P(\mathcal{H}_{n}^{o})q_{n}^{m}(\varepsilon _{n},\hat{\tau })R_{3,n}(\hat{\tau },P_{s,n}^{v}) -\eta _{13,n}^{{\ast}}(P_{s,n}^{v} + P_{c}) = 0.\end{array} }$$

(80)

Hence, we have (81)

$$\displaystyle{ \left \{\begin{array}{*{20}{l}} P(\mathcal{H}_{n}^{v})(1 -q_{n}^{f}(\varepsilon _{n},\hat{\tau }))R_{1,n}(\hat{\tau },\tilde{P}_{s,n}^{v}) + P(\mathcal{H}_{n}^{o})q_{n}^{m}(\varepsilon _{n},\hat{\tau })R_{3,n}(\hat{\tau },\tilde{P}_{s,n}^{v}) -\eta _{13,n}^{{\ast}}\left (\tilde{P}_{s,n}^{v} + P_{c}\right ) = 0 \\ P(\mathcal{H}_{n}^{v})(1 -q_{n}^{f}(\varepsilon _{n},\hat{\tau }))R_{1,n}(\hat{\tau },P_{s,n}^{v}) + P(\mathcal{H}_{n}^{o})q_{n}^{m}(\varepsilon _{n},\hat{\tau })R_{3,n}(\hat{\tau },P_{s,n}^{v}) -\eta _{13,n}^{{\ast}}\left (P_{s,n}^{v} + P_{c}\right ) \leq 0. \end{array}\right. }$$

(81)

Therefore, $\mathop{\max }\limits _{P_{s,n}^{v}}\left \{\begin{array}{*{20}{l}} P(\mathcal{H}_{n}^{v})(1 - q_{n}^{f}(\varepsilon _{n},\hat{\tau }))R_{1,n}(\hat{\tau },P_{s,n}^{v}) \\ \begin{array}{l} +\ P(\mathcal{H}_{n}^{o})q_{n}^{m}(\varepsilon _{n},\hat{\tau })R_{3,n}(\hat{\tau },P_{s,n}^{v}) \\ -\ \eta _{13,n}^{{\ast}}(P_{s,n}^{v} + P_{c}) \end{array} \end{array} \right \} = 0$ can be concluded. That is, eq. (80) is achieved.

(2) Suppose that $\widetilde{P}_{s,n}^{v}$ is a solution to the problem of (80). The definition of (80) implies that (82)

$$\displaystyle{ \begin{array}{l} \begin{array}{*{20}{l}} P(\mathcal{H}_{n}^{v})(1 - q_{n}^{f}(\varepsilon _{n},\hat{\tau }))R_{1,n}(\hat{\tau },P_{s,n}^{v}) + P(\mathcal{H}_{n}^{o})q_{n}^{m}(\varepsilon _{n},\hat{\tau })R_{3,n}(\hat{\tau },P_{s,n}^{v}) \\ -\ \eta _{13,n}^{{\ast}}\left (P_{s,n}^{v} + P_{c}\right )\leq P(\mathcal{H}_{n}^{v})(1 - q_{n}^{f}(\varepsilon _{n},\hat{\tau }))R_{1,n}(\hat{\tau },\tilde{P}_{s,n}^{v}) \\ +\ P(\mathcal{H}_{n}^{o})q_{n}^{m}(\varepsilon _{n},\hat{\tau })R_{3,n}(\hat{\tau },\tilde{P}_{s,n}^{v}) -\eta _{13,n}^{{\ast}}\left (\tilde{P}_{s,n}^{v} + P_{c}\right ) = 0\end{array}\\ or \\ \left \{\begin{array}{*{20}{l}} P(\mathcal{H}_{n}^{v})(1 - q_{n}^{f}(\varepsilon _{n},\hat{\tau }))R_{1,n}(\hat{\tau },P_{s,n}^{v}) + P(\mathcal{H}_{n}^{o})q_{n}^{m}(\varepsilon _{n},\hat{\tau })R_{3,n}(\hat{\tau },P_{s,n}^{v}) \\ -\ \eta _{13,n}^{{\ast}}\left (P_{s,n}^{v} + P_{c}\right ) \leq 0 \\ P(\mathcal{H}_{n}^{v})(1 - q_{n}^{f}(\varepsilon _{n},\hat{\tau }))R_{1,n}(\hat{\tau },\tilde{P}_{s,n}^{v}) + P(\mathcal{H}_{n}^{o})q_{n}^{m}(\varepsilon _{n},\hat{\tau })R_{3,n}(\hat{\tau },\tilde{P}_{s,n}^{v}) \\ -\ \eta _{13,n}^{{\ast}}\left (\tilde{P}_{s,n}^{v} + P_{c}\right ) = 0.\end{array} \right. \end{array} }$$

(82)

Therefore, we obtain

$$\displaystyle{ \frac{\left \{\begin{array}{l} P(\mathcal{H}_{n}^{v})(1 - q_{n}^{f}(\varepsilon _{n},\hat{\tau }))R_{1,n}(\hat{\tau },\tilde{P}_{s,n}^{v}) \\ + P(\mathcal{H}_{n}^{o})q_{n}^{m}(\varepsilon _{n},\hat{\tau })R_{3,n}(\hat{\tau },\tilde{P}_{s,n}^{v}) \end{array} \right \}} {\tilde{P}_{s,n}^{v} + P_{c}} =\eta _{ 13,n}^{{\ast}} }$$

(83)

and

$$\displaystyle{ \frac{\left \{\begin{array}{l} P(\mathcal{H}_{n}^{v})(1 - q_{n}^{f}(\varepsilon _{n},\hat{\tau }))R_{1,n}(\hat{\tau },P_{s,n}^{v}) \\ + P(\mathcal{H}_{n}^{o})q_{n}^{m}(\varepsilon _{n},\hat{\tau })R_{3,n}(\hat{\tau },P_{s,n}^{v}) \end{array} \right \}} {P_{s,n}^{v} + P_{c}} \leq \eta _{13,n}^{{\ast}}. }$$

(84)

□

Lemma 1.

Let $\boldsymbol{A}$ be an N × N symmetric matrix, $\boldsymbol{A}$ is negative semidefinite if and only if all the kth order principal minors of $\boldsymbol{A}$ are no larger than zero if k is odd, and not less than zero if k is even, where 1 ≤ k ≤ N.

The proof of Theorem 2.

Proof.

First, define the element $\tau _{k,i,n}\widehat{R}_{k,i,n}^{\mathrm{F}}$ in (59) as $f(\tau _{k,i,n},\widehat{p}_{k,i,n}) = \tau _{k,i,n}\widehat{R}_{k,i,n}^{\mathrm{F}}$. The objective function in (59) is the sum of $f(\tau _{k,i,n},\widehat{p}_{k,i,n})$ over all possible values of k, i, and n. Substituting $\widehat{R}_{k,i,n}^{\mathrm{F}} = \log _{2}\left (1 + \frac{\widehat{p}_{k,i,n}\hslash _{k,k,i,n}^{\mathrm{FF}}} {\tau _{k,i,n}I_{k,i,n}} \right )$ into $f(\tau _{k,i,n},\widehat{p}_{k,i,n})$, so we have

$$\displaystyle{ f(\tau _{k,i,n},\widehat{p}_{k,i,n}) = \tau _{k,i,n}\log _{2}\left (1 + \frac{\widehat{p}_{k,i,n}\hslash _{k,k,i,n}^{\mathrm{FF}}} {\tau _{k,i,n}I_{k,i,n}} \right ). }$$

(85)

Based on (85), one obtains

$$\displaystyle{ \frac{\partial ^{2}f} {\partial \tau _{k,i,n}^{2}} = -\frac{1} {\ln 2} \frac{(\widehat{p}_{k,i,n}\hslash _{k,k,i,n}^{\mathrm{FF}})^{2}} {\tau _{k,i,n}(\tau _{k,i,n}I_{k,i,n} + \widehat{p}_{k,i,n}\hslash _{k,k,i,n}^{\mathrm{FF}})^{2}}, }$$

(86)

$$\displaystyle{ \frac{\partial ^{2}f} {\partial \tau _{k,i,n}\partial \widehat{p}_{k,i,n}} = \frac{\partial ^{2}f} {\partial \widehat{p}_{k,i,n}\partial \tau _{k,i,n}} = \frac{1} {\ln 2} \frac{\widehat{p}_{k,i,n}(\hslash _{k,k,i,n}^{\mathrm{FF}})^{2}} {(\tau _{k,i,n}I_{k,i,n} + \widehat{p}_{k,i,n}\hslash _{k,k,i,n}^{\mathrm{FF}})^{2}}, }$$

(87)

$$\displaystyle{ \frac{\partial ^{2}f} {\partial \widehat{p}_{k,i,n}^{2}} = -\frac{1} {\ln 2} \frac{\tau _{k,i,n}(\hslash _{k,k,i,n}^{\mathrm{FF}})^{2}} {(\tau _{k,i,n}I_{k,i,n} + \widehat{p}_{k,i,n}\hslash _{k,k,i,n}^{\mathrm{FF}})^{2}}. }$$

(88)

Consequently, the Hessian matrix of $f(\tau _{k,i,n},\widehat{p}_{k,i,n})$ can be written as

$$\displaystyle{ \boldsymbol{H} = \left [\begin{array}{*{20}{c}} \frac{\partial ^{2}f} {\partial \tau _{k,i,n}^{2}} & \frac{\partial ^{2}f} {\partial \tau _{k,i,n}\partial \widehat{p}_{k,i,n}} \\ \frac{\partial ^{2}f} {\partial \widehat{p}_{k,i,n}\partial \tau _{k,i,n}} & \frac{\partial ^{2}f} {\partial \widehat{p}_{k,i,n}^{2}} \end{array} \right ]. }$$

(89)

Substituting (86), (87), (88) to (89), we can show that the first-order principal minors of $\boldsymbol{H}$ are negative, and the second-order principal minor of $\boldsymbol{H}$ is zero. Therefore, $\boldsymbol{H}$ is negative semidefinite according to Lemma 1, and $f(\tau _{k,i,n},\widehat{p}_{k,i,n})$ is concave. The objective function of (59) is concave because any positive linear combination of concave functions is concave [23, 33]. As the inequality constraints in (59) are convex, the feasible set of the objective function in (59) is convex, and the corresponding optimization problem is a convex problem. This completes the proof . ⊓ ⊔

References

1.
Zhang H, Chu X, Guo W, Wang S (2015) Coexistence of Wi-Fi and heterogeneous small cell networks sharing unlicensed spectrum. IEEE Commun Mag 22(3):92–99Google Scholar
2.
Samarakoon S, Bennis M, Saad W, Debbah M, Latva-aho M (2016) Ultra dense small cell networks: turning density into energy efficiency. IEEE J Sel Areas Commun 34(5):1267–1280CrossRefGoogle Scholar
3.
Zhang H, Dong Y, Cheng J, Hossain Md J, Leung VCM (2016) Fronthauling for 5G LTE-U ultra dense cloud small cell networks. IEEE Wirel Commun 23(6):48–53CrossRefGoogle Scholar
4.
Bennis M, Simsek M, Czylwik A, Saad W, Valentin S, Debbah M (2013) When cellular meets WiFi in wireless small cell networks. IEEE Commun Mag 51(6):44–50CrossRefGoogle Scholar
5.
Zhang H, Jiang C, Beaulieu NC, Chu X, Wen X, Tao M (2014) Resource allocation in spectrum-sharing OFDMA femtocells with heterogeneous services. IEEE Trans Commun 62(7):2366–2377CrossRefGoogle Scholar
6.
Bennis M, Perlaza SM, Blasco P, Han Z, Poor HV (2013) Self-organization in small cell networks: a reinforcement learning approach. IEEE Trans Commun 12(7):3202–3212Google Scholar
7.
Zhang H, Jiang C, Beaulieu NC, Chu X, Wang X, Quek T (2015) Resource allocation for cognitive small cell networks: a cooperative bargaining game theoretic approach. IEEE Trans Wirel Commun 14(6):3481–3493CrossRefGoogle Scholar
8.
Hong X, Wang J, Wang C, Shi J (2014) Cognitive radio in 5G: a perspective on energy-spectral efficiency trade-off. IEEE Commun Mag 52(7):46–53CrossRefGoogle Scholar
9.
Huang L, Zhu G, Du X (2013) Cognitive femtocell networks: an opportunistic spectrum access for future indoor wireless coverage. IEEE Wirel Commun 20(2):44–51CrossRefGoogle Scholar
10.
Chen X, Zhao Z, Zhang H (2013) Stochastic power adaptation with multiagent reinforcement learning for cognitive wireless mesh networks. IEEE Trans Mob Comput 12(11):2155–2166CrossRefGoogle Scholar
11.
Wang W, Yu G, Huang A (2013) Cognitive radio enhanced interference coordination for femtocell networks. IEEE Commun Mag 51(6):37–43CrossRefGoogle Scholar
12.
Hu D, Mao S (2012) On medium grain scalable video streaming over femtocell cognitive radio networks. IEEE J Sel Areas Commun 30(3):641–651CrossRefGoogle Scholar
13.
Urgaonkar R, Neely MJ (2012) Opportunistic cooperation in cognitive femtocell networks. IEEE J Sel Areas Commun 30(3):607–616CrossRefGoogle Scholar
14.
Cheng S, Ao W, Tseng F, Chen K (2012) Design and analysis of downlink spectrum sharing in two-tier cognitive femto networks. IEEE Trans Veh Technol 61(5):2194–2207CrossRefGoogle Scholar
15.
Wang X, Ho P, Chen K (2012) Interference analysis and mitigation for cognitive-empowered femtocells through stochastic dual control. IEEE Trans Wirel Commun 11(6):2065–2075CrossRefGoogle Scholar
16.
Xie R, Yu FR, Ji H, Li Y (2012) Energy-efficient resource allocation for heterogeneous cognitive radio networks with femtocells. IEEE Trans Wirel Commun 11(11):3910–3920CrossRefGoogle Scholar
17.
Le L, Niyato D, Hossain E, Kim DI, Hoang DT (2013) QoS-aware and energy-efficient resource management in OFDMA femtocells. IEEE Trans Wirel Commun 12(1):180–194CrossRefGoogle Scholar
18.
Zhang H, Jiang C, Mao X, Chen H (2016) Interference-limit resource allocation in cognitive femtocells with fairness and imperfect spectrum sensing, accepted. IEEE Trans Veh Technol 65(3):1761–1771CrossRefGoogle Scholar
19.
Zhang H, Nie Y, Cheng J, Leung VCM, Nallanathan A (2017) Sensing time optimization and power control for energy efficient cognitive small cell with imperfect hybrid spectrum sensing. IEEE Trans Wirel Commun 16(2):730–743CrossRefGoogle Scholar
20.
Liang Y, Zeng Y, Peh ECY, Hoang A (2008) Sensing-throughput tradeoff for cognitive radio networks. IEEE Trans Wirel Commun 7(4):1326–1337CrossRefGoogle Scholar
21.
Ng DWK, Lo ES, Schober R (2012) Energy-efficient resource allocation in multi-cell OFDMA systems with limited backhaul capacity. IEEE Trans Wirel Commun 11(10):3618–3631CrossRefGoogle Scholar
22.
Xiong C, Li GY, Liu Y, Chen Y, Xu S (2013) Energy-efficient design for downlink OFDMA with delay-sensitive traffic. IEEE Trans Wirel Commun 12(6):3085–3095CrossRefGoogle Scholar
23.
Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, CambridgeCrossRefMATHGoogle Scholar
24.
Chen Y, Zhao Q, Swami A (2008) Joint design and separation principle for opportunistic spectrum access in the presence of sensing errors. IEEE Trans Inf Theory 54(5):2053–2071MathSciNetCrossRefMATHGoogle Scholar
25.
Jiang C, Chen Y, Gao Y, Liu KJR (2013) Joint spectrum sensing and access evolutionary game in cognitive radio networks. IEEE Trans Wirel Commun 12(5):2470–2483CrossRefGoogle Scholar
26.
Xie R, Yu FR, Ji H (2012) Dynamic resource allocation for heterogeneous services in cognitive radio networks with imperfect channel sensing. IEEE Trans Veh Technol 61(2):770–780CrossRefGoogle Scholar
27.
Almalfouh SM, Stuber GL (2011) Interference-aware radio resource allocation in OFDMA-based cognitive radio networks. IEEE Trans Veh Technol 60(4):1699–1713CrossRefGoogle Scholar
28.
Wong CY, Cheng R, Lataief K, Murch R (1999) Multiuser OFDM with adaptive subcarrier, bit, and power allocation. IEEE J Sel Areas Commun 17(10):1747–1758CrossRefGoogle Scholar
29.
Kang X, Zhang R, Motani M (2012) Price-based resource allocation for spectrum-sharing femtocell networks: a stackelberg game approach. IEEE J Sel Areas Commun 30(3):538–549CrossRefGoogle Scholar
30.
Son K, Lee S, Yi Y, Chong S (2011) Refim: a practical interference management in heterogeneous wireless access networks. IEEE J Sel Areas Commun 29(6):1260–1272CrossRefGoogle Scholar
31.
Shen Z, Andrews JG, Evans BL (2005) Adaptive resource allocation in multiuser OFDM systems with proportional rate constraints. IEEE Trans Wirel Commun 4(6):2726–2737CrossRefGoogle Scholar
32.
Further advancements for E-UTRA, physical layer aspects, 3GPP Std. TR 36.814 v9.0.0, 2010Google Scholar
33.
Tao M, Liang Y-C, Zhang F (2008) Resource allocation for delay differentiated traffic in multiuser OFDM systems. IEEE Trans Wirel Commun 7(6):2190–2201CrossRefGoogle Scholar

Copyright information

Authors and Affiliations

Haijun Zhang
- 1
Email author
Theodoros A. Tsiftsis
- 2
Julian Cheng
- 3
Victor C. M. Leung
- 4

1.Beijing Engineering and Technology Research Center for Convergence Networks and Ubiquitous ServicesUniversity of Science and Technology BeijingBeijingChina
2.School of EngineeringNazarbayev UniversityAstanaKazakhstan
3.School of EngineeringThe University of British ColumbiaKelownaCanada
4.Department of Electrical and Computer EngineeringThe University of British ColumbiaVancouverCanada

Resource Allocation in Spectrum-Sharing Cognitive Heterogeneous Networks

Abstract

Keywords

References

Further Reading

Copyright information

Authors and Affiliations

Personalised recommendations

Cite entry