5.2 Throughput Analysis
5.2.2 Approximation of Decoding Failure Probability
In order to estimateD, we have to estimatePrf(mt). However, it is difficult to find the closed form of Prf(mt). The reason is because the SINR,ςk, is a random variable. To solve this dilemma, as mentioned in Chap. 3, if the HPPP femto BS network is operated at a low outage probability, there exists a dominant interferer [93]. Based on our assumption, the dominant interfer isF1. The observation of F1 in the HPPP inspired us to simplify the Prf(mt) by considering the dominance ofF1. Based on the major is the average interference of all other interfering femto BSs except F1. Therefore, UT should be capable of measuring the combination of interference and signal strengths from FS and F1 respectively. In realistic communication system, this requirement is also defined in the capability about UE [112]. In (5.8), In each sub-packet transmission,
S
ς_ is used to represent the SINR when F1 transmits a sub-packet simultaneously with
FSand ςS is used to represent the SINR when F1 is idle and FS transmits one sub-packet. Based on (5.8), we approximate the bandwidth efficiency,βS, which UT
receives in each sub-packet transmission.
70
which may take mt sub-packet transmissions. We define x to represent how many times that F1transmits sub-packets simultaneously with FS during the mt sub-packet transmissions. Based on the proposed protocol, x should follow binomial distribution.
It is clear that the summation of bandwidth efficiency in (5.2) decreases with the increase of x. Therefore, we define Xminmt as the minimum value of x which the summation of bandwidth efficiency in (5.2) is lower than R.
)}
0 ,
| )
( (
min
min arg{ S t S t t
x
m x m x R m x m
X t ≡
β
+ −β
< ≤ ≤ (5.10)Therefore, Prf(mt) can be approximated with the following equation:
∑
=
− −
⋅
= t
mt
t
m
X x
x m T x
T t f t
x m m
P
min
) Pr 1 ( Pr )
~ (
(5.11)
In the next section, we will verify our proposal through simulations.
5.3 Simulations
In this section, the pathloss model, packet scheduling, deployment of femto BSs are implemented based on the proposed deployment model and transmission protocol.
Simulation parameters are listed in Table 5-1. Based on Table 5-1 and (5.1), the threshold for low outage probability,λU, is estimated (~ 10−3.34 m-3). To simulate the achievable throughput under fully coverage, we assumeλ =10−5 (m-3)in the first simulation. Then, we decide dn and the following SINR by applying HPPP with given
λ. We will compare the throughputDNum andDApp, which the failure probability inside is obtained through simulations and proposed approach respectively.
In Fig. 5-2, we adjust PrT between 0.5, 0.75, and 1 to verify DNum and DApp. In Fig. 5-2, it is clear that our model provides close estimation for the throughput of femto BS networks. Furthermore, we find out that DNumand DApp match exactly when PrT is close to 1.
Table 5-1 Parameters of simulations
Then, we increase the femto BS density to a value much higher than λU , )
m ( 10−2 -3
λ = , to see if our approximation is incorrect. Simulation results are plotted in Fig. 5-3. In Fig. 5-3, it is clear that the achievable throughput decreases to a very low level when λ is every high. Even so, we find that DNum and DApp still match exactly, which means our proposal also provides an efficient way to estimate the throughput even though the femto BS density is much higher than the feasible density boundλU. From Fig. 5-3, we can conclude that the 1st nearest node still dominates Prf(mt) even the femto BS density locates on the area which the outage probability is very high. Another reason that our approach can also be applied when λ >λU is because we still consider the infleucne of other interferers by taking their average interference in our approach.
Notation Value Definition
} ,
{PS Pfn 30 (dBm) Radiation powers of {FS,Fn} }
,
{δS δfn 37 (dB) Path-loss constants of {FS,Fn} }
,
{ηSηfn 3 Path-loss exponents of {FS,Fn}
λ 10-5,10-2 (m-3) Femto BS density
ε 1 Minimum distance of {dS,dn}
Nf 10 Number of interfering femto BSs in the simulation N0 -100 (dBm) Noise power
dS 3 (m) Distance between the UT and FS
dn HPPP Distance between the UT and Fn. The values are provided through HPPP.
Pr O 0.05 Upper threshold of outage probability Tς 0 (dB) SINR bound of outage event
W F 1 (Hz) Bandwidth
T S 1 (s) Duration of one time slot
MB 10 (slots) Transmission limit because of buffer size ND 50 (slots) Transmission limit because of delay limit
72
Fig. 5-2 Comparisons of DNum and DApp curve whenλ =10−5(m-3). It can be found both of the curves are closer when PrT increases.
Fig. 5-3 Comparisons of DNum and DApp curve whenλ =10−2(m-3). It can be found both of the curves are still close to each other.
0 1 2 3 4 5 6 7 8 9 10
0 2 4 6 8
Throughput (bits/s/Hz) (a) PrT =0.5
0 1 2 3 4 5 6 7 8 9 10
0 2 4 6 8
Throughput (bits/s/Hz) (b) PrT =0.75
0 1 2 3 4 5 6 7 8 9 10
0 5 10
R (bits/s/Hz) Throughput (bits/s/Hz) (c) PrT =1
DNum DApp
DNum DApp
DNum DApp
0 1 2 3 4 5 6 7 8 9 10
0 0.2 0.4
Throughput (bits/s/Hz) (a) Pr
T=0.5
0 1 2 3 4 5 6 7 8 9 10
0 0.2 0.4
Throughput (bits/s/Hz) (b) PrT=0.75
0 1 2 3 4 5 6 7 8 9 10
0 0.2 0.4
R (bits/s/Hz) Throughput (bits/s/Hz) (c) PrT=1
DNum DApp
DNum DApp
DNum DApp
Fig. 5-4 Comparisons of DNum and DApp by adjusting the value of λ
Fig. 5-5 Plot of CV(RMSE) by adjusting the value of λ
10-5 10-4 10-3 10-2
0 0.5 1 1.5 2 2.5 3
λ (m-3)
Throughput (bits/s/Hz)
PrT=0.5, DNum PrT=0.5, DApp PrT=0.7, DNum PrT=0.7, DApp PrT=1, DNum PrT=1, DApp
10-5 10-4 10-3 10-2
0 0.02 0.04 0.06 0.08 0.1 0.12
λ (m-3)
CV(RMSE)
PrT =0.5 PrT =0.7 PrT =1
74
In Fig. 5-4, we compare the DNum and DApp by giving different values of λ. It is clear that DNum and DApp are still close to each other when we adjust λ in a wide range of values. So, we observed that adjusting the value of λ does not affect the accuracy of the proposed estimation approach.
In Fig. 5-5, we clarify the estimation error by plotting the coefficient of variation of the root mean square error, CV(RMSE), which is the ratio of RMSE to the average numerical throughout,
) . Mean(
] ) -CV(RMSE) E[(
2
Num Num App
D D
≡ D (5.12)
Given the value of λ and PrT , forty iterations are generated to estimate the estimation error between the numerical throughout and estimated throughout. In each iteration, the values of dn are decided based on HPPP. During the analysis, we find the maximum value of CV(RMSE) is about 0.11. Furthermore, most of the CV(RMSE) values are lower than 0.07, which means we provide an useful and effective approach to estimate the system throughput in a femto BS network.
5.4 Applications
Based on HPPP, we can apply our study to the femto BS networks of different topologies because femto BS provides the OSG/CSG/Hybrid user priority to different users. With different user priority, the interference caused by femto BSs will be different.
Through our proposed model, we can compare the influence of femto BSs to different type of users.
Furthermore, the proposed model can be extended to analyze the throughput of macro BS when interference is from femto BS network. Here, it is assumed that UT is served by a macro BS with distance, dm. All the femto BSs follow HPPP. Then, we can estimate the achievable throughput by applying different λ and dm to verify the influence from the interfering femto BS networks. Moreover, our analysis model can be extended to random networks which the interference sources follow HPPP.
5.5 Conclusion
In this chapter, with the assumptions of uniformly distributed femto BS deployment and low outage probability operation, we simplified the decoding failure probability by considering one dominant interfering femto BS and other interfering femto BSs. Our analytical model estimates the throughout of femto BS netowrks quickly when femto BSs are not cooperated for their data transmission.
Simulation results have been provided to validate our approach. Furthermore, the simulation results showed that the proposed model can also be applied when the outage probability is high. In addition to femto BS networks, the model can be generally applied to different system deployments which follow the assumptions of HPPP random networks.
76
C HAPTER 6
C ONCLUSION
In our dissertation, we have studied the features of femto BS networks and the influence of femto BS towards the cellular network.
In Chap. 2, we broadly introduced the features of femto BSs. The femto BS is different from traditional base stations and other indoor wireless access techonlogies in the following aspects:
1) Flexibility of deployment 2) Huge number of femto BSs 3) User priority
4) Self-Organization Network (SON) 5) Operation Modes.
However, femto BSs also bring new technical problems , which include:
i) Deployment issue ii) Interference mitigation iii) Load balancing iv) CSG/OSG Conflict
In Chap. 2, we have summarized the preliminary studies addressing these technical
problems.
In Chap. 3, we estimated the range of feasible femto BS density to provide ubiquitous coverage for cellular network through the deployments of femto BSs. In the analysis, we proposed a novel 3-D HPPP model to analyze the random locations of femto BS networks. Because of different user priority that femto BS provides and the influence of macro BS, four scenarios were proposed during our analysis:
Scenario a): macro BS is the serving BS;
Scenario b): F1 is the serving BS;
Scenario c): CSG femto BS is the dominant interference source to a non-CSG user;
Scenario d): OSG femto BS network.
To limit the outage probability observed by the target user under a pre-defined threshold, we have verified the range of feasible femto BS density based on the four scenarios.
Numerical results showed that the our conclusion from the assumption of dominating interfering source is actually a good representation of user performance in above four different scenarios, which can be used to provide a quick evaluation of the limit in femto BS density under the low outage probability criterion.
In Chap. 4, we extended our observations about the closed form of E[ln(Rn)] in the 3-D space to the m-dimensional HPPP. E[ln(Rn|m)] represents the nth nearest node in the m-dimensional space. Moreover, we further extended our conclusion to the condition which n is a half-integer. To extend our works, we proposed a lookup table construction and linear interpolation approach to estimate the fading figure of Nakagami fading channel. Our proposed approach is simple in implementation. The verification results also showed that our proposed estimators outperforms in a wide range when the number of samples is limited. Because Nakagami distribution fits very well in the urban and indoor environment, our proposed approach about fading figure estimation can also be embedded in the femto BS networks for the channel estimation.
In Chap. 5, we proposed a simple approach to estimate the throughput of femto BS networks. Considering the effects of randomly distributed interference sources, low outage probability, non-cooperated packet transmission, and HARQ packet transmission, we have identified a fast estimation approach of downlink throughput in a femto BS network. Simulations were also provided to verify the results. Our proposed approach
78
can be applied to not only the femto BS networks but also the random networks which the interference sources follow HPPP.
In conclusion, we have created a 3-D HPPP model to estimate the influence and beinfits that femto BS networks bring. Furthermore, we extended our research to the m-dimensional HPPP. Our research results can be generally applied to different wireless networks. Moreover, our study about E[ln(Rn|m)] can also be widely applied in the wireless communications.
R EFERENCE
[1] 3rd Generation Partnership Project; Technical Specification Group Services and System Aspects; Vocabulary for 3GPP Specifications, 3GPP TR 21.905 V11.1.0, Jun.
2012.
[2] D. J. Goodman, Wireless Personal Communications Systems. Boston, MA:
Addison-Wesley, 1997.
[3] J. G. Andrews, H. Claussen, M. Dohler, S. Rangan, and M. C. Reed, “Femtocells:
Past, Present, and Future,” IEEE J. Selected Areas Commun., vol.30, no. 3, pp.497-508, Apr. 2012.
[4] V. Chandrasekhar, J. G. Andrews, and A. Gatherer, “Femtocell Networks: A Survey,”
IEEE Commun. Mag., vol. 46, no. 9, pp. 59-67, Sep. 2008.
[5] S. P. Yeh , S. Talwar, S. C. Lee, and H. C. Kim, “WiMAX Femtocells: A Perspective on Network Architecture, Capacity, and Coverage,” IEEE Commun. Mag., vol. 46, no. 10, pp. 58-65, Oct. 2008.
[6] D. López-Pérez, A. Valcarce, G.de la Roche, and J. Zhang, “OFDMA Femtocells: A Roadmap on Interference Avoidance,” IEEE Commun. Mag., vol. 46, no. 9, pp. 41-48, Sep. 2008.
[7] R. Y. Kim, J. S. Kwak, and K. Etemad, “WiMAX Femtocell: Requirements, Challenges, and Solutions,” IEEE Commun. Mag., vol. 47, no. 9, pp. 84-91, Sep. 2009.
[8] H. Claussen, L. T. W. Ho, and L. G. Samuel, “An Overview of the Femtocell Concept,” Bell Labs Technical Journal, vol. 13, no. 1, pp. 221-245, May, 2008.
[9] S. R. Saunders, S. Carlaw, A. Giustina, R. R. Bhat, V. S. Rao, and R. Siegberg, FEMTOCELLS. Hoboken, NJ: Wiley, 2009.
[10] J. Zhang, and G. de la Roche, FEMTOCELLS: TECHNOLOGIES AND DEPLOYMENT. Hoboken, NJ: Wiley, 2010.
[11] A. Stocker, “Small-cell mobile phone systems,” IEEE Trans. Veh. Technol., vol. 33, no. 4, pp. 269 – 275, Nov. 1984.
[12] J. Sydir, and R. Taori, “An Evolved Cellular System Architecture Incorporating Relay Stations,” IEEE Commun. Mag., vol. 47, no. 6, pp.115-121, Jun. 2009.
[13] X. H. You, D. M. Wang, B. Sheng, X. Q. Gao, X. S. Zhao, and M. Chen,
“Cooperative distributed antenna systems for mobile communications,” IEEE Wireless Commun. Mag., vol. 17, no. 3, pp.35-43, Jun. 2010.
[14] IEEE Xplore Digital Library, [Online]. Available:
http://ieeexplore.ieee.org/Xplore/home.jsp
[15] 3rd Generation Partnership Project; Technical Specification Group Radio Access Networks; 3G Home NodeB Study Item Technical Report, 3GPP TR 25.820 V8.2.0, Sep.
2008.
[16]IEEE Standard for Local and metropolitan area networks— Part 16: Air Interface for Broadband Wireless Access Systems Amendment 3: Advanced Air Interface, IEEE Std 802.16m-2011, Nov. 2010.
[17] M.-S. Alouini, and A. J. Goldsmith, “Area Spectral Efficiency of Cellular Mobile Radio Systems,” IEEE Trans. Veh. Technol., vol. 48, no. 4, pp.1047-1066, Jul. 1999.
[18] “Simulation assumptions and parameters for FDD HeNB RF requirements,”
R4-091422, 3GPP TSG RAN WG4 Meeting #50bis, Seoul, Korea, 23 – 27 Mar. 2009.
[19] K. Han, Y. Choi, D. Kim, M. Na, S. Choi, and K. Han, “Optimization of femtocell network configuration under interference constraints,” in Proc. IEEE 7th Int. Symp.
Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks 2009, Seoul, Korea, 23-27 Jun. 2009, pp. 1-7.
80
[20] J. Xiang, Y. Zhang, T. Skeie, and L. Xie, “Downlink Spectrum Sharing for Cognitive Radio Femtocell Networks,” IEEE Syst. J., vol. 4, no. 4, pp. 524-534, Dec. 2010.
[21] J. Liu, T. Kou, Q. Chen, and H. D. Sherali, “Femtocell Base Station Deployment in Commercial Buildings: A Global Optimization Approach,” IEEE J. Selected Areas Commun., vol. 30, no. 3, pp. 652–663, Apr. 2012.
[22]V. Chandrasekhar, and J. Andrews, “Uplink capacity and interference avoidance for two-tier femtocell networks,” IEEE Trans. Wireless Commun., vol. 8, no. 7, pp.3498–
3509, Jul. 2009.
[23] D. Das and V. Ramaswamy, “On the reverse link capacity of a CDMA network of femto-cells,” in Proc. IEEE Sarnoff Symp., Prineoton, NJ, U.S.A., 28-30 Apr. 2008, pp.1–5.
[24]V. Chandrasekhar, J. Andrews, Z. Shen, T. Muharemovic, and A. Gatherer, “Power control in two-tier femtocell networks,” IEEE Trans. Wireless Commun., vol. 8, no. 8, pp. 4316–28, Aug. 2009.
[25] H. S. Jo, C. Mun, J. Moon, and J.G. Yook, “Interference mitigation using uplink power control for two-tier femtocell networks,” IEEE Trans. Wireless Commun., vol. 8, no. 10, pp. 4906–4910, Oct. 2009.
[26] M. Yavuz, F. Meshkati, S. Nanda, A. Pokhariyal, N. Johnson, B. Raghothaman, and A. Richardson, “Interference Management and Performance Analysis of UMTS/HSPA+
Femtocells,” IEEE Commun. Mag., vol. 47, no. 9, pp. 102-109, Sep. 2009.
[27] N. Arulselvan, V. Ramachandran, S. Kalyanasundaram, and G. Han, “Distributed Power Control Mechanisms for HSDPA Femtocells,” in Proc. IEEE 69th Veh. Tech.
Conf., Barcelona, Spain, 26-29 Apr. 2009, pp. 1-5.
[28] X. Chu, Y. Wu, L. Benmesbah, and W. K. Ling, “Resource Allocation in Hybrid Macro/Femto Networks,” in Proc. IEEE Wireless Commun. and Networking Conf.
Workshops 2010, Sydney, Australia, 18 Apr. 2010, pp.1-5.
[29] C. Y. Oh, M. Y. Chung, H. Choo, and T. J. Lee, “A Novel Frequency Planning for Femtocells in OFDMA-Based Cellular Networks Using Fractional Frequency Reuse,” in Proc. 2010 Int. conf. Computational Science and Its Applications, vol. iii, Fukuoka, Japan, 23-26 Mar. 2010, pp. 96-106.
[30] R. T. Juang, P. Ting, H. P. Lin, and D. B. Lin, “Interference Management of Femtocell in Macro-cellular Networks,” in Proc. IEEE Wireless Telecomm. Symp., Tampa, FL, U.S.A., 21-23 Apr. 2010, pp. 1-4.
[31] P. Lee, T. Lee, J. Jeong, and J. Shin, ”Interference Management in LTE Femtocell Systems Using Fractional Frequency Reuse,” in Proc. IEEE The 12th Int. Conf.
Advanced Commun. Tech., Phoenix Park, Korea, 7-10 Feb. 2010, pp.1047-1051.
[32]A. Ghosh, N. Mangalvedhe, R. Ratasuk, B. Mondal, M. Cudak, E. Visotsky, T. A.
Thomas, J. G. Andrews, P. Xia, H. S. Jo, H. S. Dhillon, and T. D. Novlan,
“Heterogeneous Cellular Networks: From Theory to Practice,” IEEE Commun. Mag., vol.
50, no. 6, pp.54-64, Jun. 2012.
[33] I. G¨uvenc¸, M. R. Jeong, F. Watanabe, and H. Inamura, “A Hybrid Frequency Assignment for Femtocells and Coverage Area Analysis for Co-Channel Operation,”
IEEE Commun. Lett., vol. 12, no. 12, pp. 880-882, Dec. 2008.
[34] Y. Bai, J. Zhou, and L. Chen, ”Hybrid Spectrum Usage for Overlaying LTE Macrocell and Femtocell,” in Proc. IEEE Global Telecomm. Conf. 2009, Honolulu, HI, U.S.A., 30 Nov. - 4 Dec. 2009, pp.1-6.
[35] X. Li, L. Qian, and D. Kataria, “Downlink power control in co-channel macrocell femtocell overlay,” in Proc. IEEE 43rd Annu. Conf. Inform. Sci. and Syst., Baltimore, MD, U.S.A., 18-20 Mar. 2009, pp. 383-388.
[36] V. Chandrasekhar, J. G. Andrews, T. Muharemovic, Z. Shen, and A. Gatherer,
“Power control in two-tier femtocell networks,” IEEE Trans. Wireless Commun., vol. 8, no. 8, pp. 4316-4328, Oct. 2009.
[37] H. Zeng, C. Zhu, and W. P. Chen, “System Performance of Self-Organizing Network Algorithm in WiMAX Femtocells,” in Proc. 4th Annu. Int. Conf. Wireless Internet, no.25, Maui, HI, U.S.A., 17-19 Nov. 2008.
[38] L. G. U. Garcia, K. I. Pedersen, and P. E. Mogensen, “Autonomous Component Carrier Selection: Interference Management in Local Area Environments for LTE-Advanced,” IEEE Commun. Mag., vol. 47, no. 9, pp.110-116, Sep. 2009.
[39]K. Sundaresan, and S. Rangarajan, “Efficient Resource Management in OFDMA Femto Cells,” in Proc. 10th ACM Int. symp. Mobile ad hoc networking and computing, New Orleans, LA, U.S.A., 18-21 May 2009, pp.33-42.
[40] S.Y. Lien, C. C. Tseng, K. C. Chen, and C. W. Su, “Cognitive Radio Resource Management for QoS Guarantees in Autonomous Femtocell Networks,” in Proc. IEEE Int. Conf. Commun. 2010, Cape Town, South Africa, 23-27 May 2010, pp. 1-6.
[41] G. GÜR, S. BAYHAN, and F. ALAGÖZ, “Cognitive Femtocell Networks: An Overlay Architecture for Localized Dynamic Spectrum Access,” IEEE Wireless Commun.
Mag. vol. 17, no. 4, pp.62-70, Aug. 2010.
[42] J. Jin, and B. Li, “Cooperative Resource Management in Cognitive WiMAX with Femto Cells,” in Proc. IEEE Int. Conf. Comput. Commun. 2010, San Diego, CA, U.S.A., 15 - 19 Mar. 2010, pp.1-9.
[43] S. M. Cheng, W. C. Ao, F. M. Tseng, and K.C. Chen, “Design and Analysis of Downlink Spectrum Sharing in Two-tier Cognitive Femto Networks,” IEEE Trans. Veh.
Technol., vol. 61, no. 5, pp. 2194-2207, Jun. 2012.
[44] H. Claussen, L. T. W. Ho, and L. G. Samuel, “Self-optimization of Coverage for Femtocell Deployments,”in Proc. IEEE Wireless Telecomm. Symp. 2008, Pomona, CA, U.S.A., 24-26 Apr. 2008, pp. 278-285.
[45] D. L´opez-P´erez, ´A. Lad´anyi, A. J¨uttner, and J. Zhang, “OFDMA femtocells: A self-organizing approach for frequency assignment,”in Proc. IEEE 20th Int. Symp.
Personal, Indoor and Mobile Radio Commun., Tokyo, Japan, 13-16 Sep. 2009, pp.
2202-2207.
[46] M. Amirijoo, L. Jorguseski, T. Kürner, R. Litjens, M. Neuland, L. C. Schmelz, and U. Türke, “Cell outage management in LTE networks, ” in Proc. IEEE 6th Int. conf.
Symp. Wireless Commun. Systems, Siena-Tuscany, Italy, 7–10 Sep. 2009, pp. 600-604.
[47] Y. Y. Li, M. Macuha, E. S. Sousa, T. Sato, and M. Nanri, “Cognitive Interference Management in 3G Femtocells,” in Proc. IEEE 20th Int. Symp. Personal, Indoor and Mobile Radio Commun., Tokyo, Japan, 13-16 Sep. 2009, pp. 1118-1122.
[48] 3GPP, “3GPP Report of TSG RAN WG1 Meeting,” #62, v0.1.0, Oct. 2010.
[49] A. Adhikary, V. Ntranos, and G. Caire, “Cognitive Femtocells: Breaking the Spatial ReuseBarrier of Cellular Systems,” in Proc. IEEE Inform. Theory and Applicat.
Workshop 2011, San Diego, CA, U.S.A., 6-11 Feb. 2011, pp. 1-10.
[50] D. L´opez-P´erez, G. de la Roche, A. Valcarce, A. J¨uttner, and J.
Zhang, ”Interference Avoidance and Dynamic Frequency Planning for WiMAX Femtocells Networks,” in Proc. IEEE 11th Singapore Int. Conf. Commun. Systems, Guangzhou, China, 19-21 Nov. 2008, pp. 1579-1584.
[51] H. C. Lee, D.C. Oh, and Y. H. Lee, “Mitigation of Inter-Femtocell Interference with Adaptive Fractional Frequency Reuse,” in Proc. IEEE Int. Conf. Commun., Cape Town, South Africa, 23-27 May 2010, pp. 1-5.
[52] C. W. Chen, C. Y. Wang, S. L. Chao, and H. Y. Wei, “DANCE: a game-theoretical femtocell channel exchange mechanism,” ACM SIGMOBILE Mobile Computing and Communications Review, vol. 14 , no. 1, pp. 13-15, Jul. 2010.
82
[53] S. Y. Lien, Y. Y. Lin, and K. C. Chen, “Cognitive and Game-Theoretical Radio Resource Management for Autonomous Femtocells with QoS Guarantees,” IEEE Trans.
Wireless Commun., vol.10, no. 7, pp.2196-2206, Jul. 2011.
[54] R. Madan, J. Borran, A. Sampath, N. Bhushan, A. Khandekar, and T. Ji, ”Cell Association and Interference Coordination in Heterogeneous LTE-A Cellular Networks,”
IEEE J. Sel. Areas Commun., vol. 28, no. 9, pp.1479-1489, Dec. 2010.
[55] I. G¨uvenc¸, M. R. Jeong, I. Demirdogen, B. Kecicioglu, and F. Watanabe, “Range Expansion and Inter-Cell Interference Coordination (ICIC) for Picocell Networks,” in Proc. IEEE 72th Veh. Technol. Conf., San Francisco, CA, U.S.A., 5-8 Sep. 2011, pp.1-6.
[56] D L´opez-P´erez, A. Valcarce, G. De La Roche, E. Liu, and J. Zhang, “Access Methods to WiMAX Femtocells: A downlink system-level case study,” in Proc. IEEE 11th Singapore Int. Conf. Commun. Systems, Guangzhou, China, 19-21 Nov. 2008, pp.
1657-1662.
[57] H. S. Jo, P. Xia, and J. G. Andrews, “Open, Closed, and Shared Access Femtocells in the Downlink,” [Online]. Available: http://arxiv.org/abs/1009.3522.
[58] H. S. Jo, P. Xia, and J. G. Andrews, “Downlink Femtocell Networks: Open or Closed?,” in Proc. IEEE Int. Conf. Commun. 2011, Kyoto, Japan, 5-9 Jun. 2011, pp. 1-5.
[59] P. Xia, V. Chandrasekhar, and J. G. Andrews, ”Open vs Closed Access FemtoCells in the uplink,” IEEE Trans. Wireless Commun., vol. 9, no. 12, pp.3798-3809, Dec. 2010.
[60] G. L. Stuber, Principles of Mobile Communication 2nd ed. Norwell, MA: Kluwer, 2001.
[61] B. D. Ripley, Spatial Statistics. Hoboken, NJ: Wiley, Aug. 2004.
[62] G. J. G. Upton and B. Fingleton, Spatial Data Analysis by Example Volume 1: Point Pattern and Quantitative Data. Hoboken, NJ: Wiley, Apr. 1985.
[63] F. Baccelli and B. Blaszczyszyn, Stochastic Geometry and Wireless Networks, Foundations and Trends in Networking. Paris, France: NOW Publishers, 2011.
[63] F. Baccelli and B. Blaszczyszyn, Stochastic Geometry and Wireless Networks, Foundations and Trends in Networking. Paris, France: NOW Publishers, 2011.