We in this section show the simulations which compare the BERs of the relay-based CoMP systems with the proposed precoder in the different topologies shown in Fig.4.1 and Fig.4.2. Fig.4.1 demonstrates the simulation environment for our multi-cell commu-nications, and Fig.4.2 represents the case that the MS1 doesn’t suffers interference from other MSs any more. The D1, D2, and D3 are the distances of BS1-to-RS, BS1-to-MS1, and BS1-to-MS2, respectively. And MS2 isn’t belonging to the cellular 1. In our simula-tions, the average channel power is assumed to be inversely proportional to the cubic of the distance between transmitter and receiver. In Fig.4.3, we set D1 = D2 = D3 = D/2 where D is defined as a standard distance that is a distance from the cellular boundary to its BS. The average SNR caused by the path loss of the distance D is assumed as γ = Px/σn2 where Px denotes the received power when the MS signals from a cell bound-ary has been transmitted to the destination, i.e.,the BS. Following this assumption, the other average SNRs can be given by (D/Di)3γ for i = 1, 2, 3. Both ”ML with Exhaustive Search” and ”CVX” (Chapter 3) methods are used to find a pair (p1, p2) that can min-imize the function (2.22). The curve ”ML with Exhaustive Search” and ”CVX” show almost the same BEP performance. But the ”CVX” is a precise and efficient method to find a solution for the power allocation. Compared with Wang and Giannakis’ CNFC
method, both ”ML with Exhaustive Search” and ”CVX have 3dB gain in BER perfor-mance. The curve Simplification detection with ”p1 = 1 and p2 = 1” shows that the BEPs of the MS1 of the cells without designing the power allocation precoders for the RS. In this situation, the MS can’t exploit full diversity at the corresponding BS. The last curve ”One user bound” represents a performance metric based on the MS1 doesn’t suffer any interference. And our scheme can almost achieve this performance bound.
In Fig.4.4, the network topology is set as 2D1 = D2 = D3 = D. The topology would happen when the MSs in Figure 4.1 are located on the cellular boundary. In this situa-tion, applying our method the MS1 and MS2 can achieve the same performance as they do by Wang and Giannakis’ precoder. As the same result in Fig.4.3, our performance in BER is 3dB better than Wang and Giannakis’ CNFC method. In Fig.4.5, the network topology is set as 2D1 = D2 = 2D3/3 = D. The topology is called as asymmetric topology because the two MSs have different distance to the base station. Besides, the differentiated services are clearly showed on this figure. For example, the MS1 in cellular 1 has better performance than the MS2 in cellular 1. The power allocation precoders at RS1 actually can provide the advantage for the MS1. And compared with Wang and Giannakis’ CNFC method, we have 6dB gain in BER performance. In Fig.4.6, the network topology is 2D1 = D2 = D3/3 = D. The differentiated services are also show up in this figure. The performance of the MS in the corresponding BS is also reliable and closed to the one user bound when the topology becomes more asymmetric than in Fig.4.5. Wang and Giannakis’ CNFC method can’t exploit diversity in this topology and the performance gap between their scheme and our method is about 10dB. In the last simulation Fig.4.7, the performance of the MS1 on the cell boundary almost remains the same even though the location of MS2 has been changed.
Figure 4.1: The simulation topology in two cellular case.
Figure 4.2: The simulation topology in single user environment.
0 2 4 6 8 10 12 14 16 18 20
MS1 − Cellular 1 − Wang’s Result ML with Exhaustive Search One uesr bound
Figure 4.3: The topology setting is 2D1 = 2D2 = 2D3 = D. Numerical, Simulation, CVX, and One-User-Bound comparison
0 2 4 6 8 10 12 14 16 18 20
MS1 − Cellular 1 − Wang’s Result MS2 − Cellular 1 − Wang’s Result One user bound
Figure 4.6: The topology setting is 2D1 = D2 = D3/3 = D (Asymmetric Case). The BEP performance of all users.
0 2 4 6 8 10 12 14 16 18 20 10−4
10−3 10−2 10−1 100
Transmit SNR(dB)
BEP
D1 = 0.5D, D
2 = D
MS1 − Cellular 1 D 3 = D MS2 − Cellular 1 D
3 = D MS1 − Cellular 1 D3 = 1.5D MS2 − Cellular 1 D3 = 1.5D MS1 − Cellular 1 D
3 = 2D MS2 − Cellular 1 D
3 = 2D One user bound
Figure 4.7: The topology setting is 2D1 = D2 = D. And the D3 is changed.
Chapter 5 Conclusions
We have introduced a power allocation method for the relay node to provide differen-tiated services in multi-cell communications. The differendifferen-tiated services are possible in multi-cell communications and subscriber’s diversity gain at corresponding BS is guar-anteed. Besides, the SP provides an efficiency search for the power allocation method.
However, we only considered the simple scenario that consists of two adjacent cells whcih have two individual subscribers both using the BPSK modulation. In the future, the power allocation method would be extended to high order modulation and more complex topologies.
Bibliography
[1] 3GPP LTE-Advanced, “http://www.3gpp.org/lte-advanced,” .
[2] A. B. Carleial, “Interference channels,” in IEEE Trans. Inform. Theory, Jan. 1978, vol. 24, pp. 60 – 70.
[3] Yingda Chen, S. Kishore, and Jing Li, “Wireless diversity through network cod-ing,” in Wireless Communications and Networking Conference, 2006. WCNC 2006.
IEEE, 2006, vol. 3, pp. 1681 – 1686.
[4] Ming Xiao and M. Skoglund, “M-user cooperative wireless communications based on nonbinary network codes,” in Networking and Information Theory, 2009. ITW 2009. IEEE Information Theory Workshop on, 2009, pp. 316 – 320.
[5] Sachin Katti, Shyamnath Gollakota, and Dina Katabi, “Embracing wireless inter-ference: Analog network coding,” in in ACM SIGCOMM. 2007, pp. 397 – 408, MIT.
[6] Tairan Wang and Georgios B. Giannakis, “Complex field network coding for mul-tiuser cooperative communications,” in IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, 2008, vol. 26.
[7] R. Ahlswede, Ning Cai, S.-Y.R. Li, and R.W. Yeung, “Network information flow,”
Information Theory, IEEE Transactions on, vol. 46, no. 4, pp. 1204 – 1216, July 2000.
[8] R. Koetter and M. Medard, “An algebraic approach to network coding,” Network-ing, IEEE/ACM Transactions on, vol. 11, no. 5, pp. 782 – 795, 2003.
[9] Philip Chou Yunnan, Philip A. Chou, Yunnan Wu, and Kamal Jain, “Practical network coding,” 2003.
[10] S. Khattak P. Marsch and G. Fettweis, “A framework for determining realistic capacity bounds for distributed antenna systems,” in Proceedings of the IEEE Information Theory Workshop, Oct. 2006.
[11] A. Sklavos Y. Liu E. Costa H. Haas T. Weber, I. Maniatis and E. Schulzl, “Joint transmission and detection integrated network (joint), a generic proposal for beyond 3g systems,” in Proc. 9th International Conference on Telecommunications, 2002, pp. 479–483.
[12] A. Zoch C. Jandura, P. Marsch and G. Fettweis, “A testbed for cooperative multi cell algorithms,” in Proceedings of the Tridentcom, 2008.
[13] A. Lozano S. Venkatesan and R. Valenzuela, “Network mimo: Overcoming inter-cell interference in indoor wireless systems,” in Signals, Systems and Computers, Nov. 2007, pp. 83 – 87.
[14] O. Somekh A. Sanderovich and S. Shamai, “Uplink macro diversity with limited backhaul capacity,” in Proc. IEEE ISIT, June 2007, pp. 11 – 15, 24 – 29.
[15] L. Vandenberghe S. Boyd, S.-J. Kim and A. Hassibi, “A tutorial on geometric programming,” 2007.
[16] Mung Chiang, “Geometric programming for communication systems,” 2005, avail-able at http://www.princeton.edu/ chiangm/gp.pdf.
[17] E. L. Peterson R. J. Dun and C. Zene, “Geometric programming: Theory and applications,” Wiley, 1967.
[18] R.DEMBO M.AVRIEL and U.PASSY, “Solution of generalized geometric pro-grams,” in INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1975, vol. 9, pp. 149 – 168.
[19] Michael Grant and Stephen Boyd, “Cvx: Matlab software for disciplined convex programming,” available at http://cvxr.com/cvx/.
[20] Yan Xin, Student Member, Zhengdao Wang, and Georgios B. Giannakis, “Space-time diversity systems based on linear constellation precoding,” IEEE Trans. Wire-less Commun, vol. 2, pp. 294–309, 2003.