第三章 利用多重存取改善頻譜效率
4.5 數值結果
0
1 1
1 1
0 1
2 2
V V
e
j U j U
P V U d
j
(37)
圖十：BEP 的 BPSK
4.5 數值結果
這個章節要說明用感知網路干擾模型去觀察主要次級網路之間的共存。舉個 數值的例子。假設沒有其他指定的值，主要和次級訊號都在 dmin = 1 m、dmax = 60 m、b= 1.5，有 Rayleigh fading 的條件下。本研究先觀察在主要使用者的 BEP 下，感知網路干擾的效應。圖九為 BPSK 的 BEP 對 Eb/N0，分別在訊雜比 SIR=Eb/PI
= −16, −12, and −8 dB 作圖，次級網路密度為λ = 0.1 users/m2，並在 single-threshold 協定下，ζ = −40 dBm。由圖九觀察得知，模擬與分析結果 是相符合的，這樣一來就確立了在 Section IV-D 的 BEP 分析，也再次確認 truncated-stable 的干擾模型是有效的。
為了確立次級使用者的空間密度效應，與主要 BEP 下的 activating
threshold，圖十以在 single-threshold 協定下，正規化的 activity threshold ζ 的函數表示 BPSK 的 BEP；Eb/N0 = 10 dB、SIR = −10 dB、λ = 0.1, 0.01,and 0.001 users/m2。如同我們預期，可以觀察到當節點密度 λ 或是 threshold ζ 增加的時候，主要 BEP 會有很嚴重的衰減。只要給定次級密度，此分析架構就可
52
以設計出一個 activity threshold，並確保目標 BEP 在主要使用者端。
為證明在感知網路干擾的 fading 效應，接下來考慮主要與次級信號的 Nakagami-m fading，即√Yi∼Nakagam (m, 1)、|Hi|∼Nakagami (m, 1)。圖十 一顯示，當 Nakagami fading 參數 m=1、3、5，離主要使用者最大距離 dmax 的 函數表示感知網路干擾 Ist的變異數(平均功率)。次級網路的使用者密度λ = 0.01users/m2，並根據 single-threshold 協定，ζ = −30 dBm ，每個使用者傳 輸功率 PI = 0 dBm。這個例子可以看出，threshold ζ 固定，fading 參數 m 增 加(fading 較不顯著)，因為次級的 activity 較少，在主要使用者的感知網路干 擾會抵消。可以看出如果 fading 較不顯著(較大的 m 值)，在任何 dmax 值下，感 threshold β 的函數，在 single-threshold 協定，表示感知網路干擾 Ist的變異 數。在這個例子，K=0dBm、密度λ = 0.1 users/m2、次級使用者傳輸功率為 PI = 0 dBm。主要使用者散佈在距離基地台 dminp = 1 m 到 dmaxp = 1000 m 的環形區 域間；同時，通訊連結在 Rayleigh fading 的影響下，即|Hp| ∼ Rayleigh (1/2)。
根據 primary power control policy，設定四個功率值-5、-15、-25、-35dBm，
最小所需功率為 P*=-95dBm。由圖片可以看出，若主要網路做了功率控制，感知 網路干擾的變異數也會增加，不論β是多少。這是因為當主要使用者離基地台越 近，他的傳輸功率會減少。結果，次級使用者的 activity 增加，active 次級使 用者的數量會很大。 有 Nakagami-m fading(即√Y∼Nakagami(2,1)、|Hi|∼Nakagami(2,1))；方塊中 的區域有兩個不同的次級空間密度：在紅色區塊，λ = 0.01、黃色區塊，λ = 0(即 沒有次級使用者)。PDFs fIfa (x)根據三個主要使用者位置的情況作圖：i)在大的 方塊中間，ii)在低密度(零密度)區域的中心，iii)在大型方塊的右上角。又可 以由圖十四觀察得知，當主要使用者移動到角落的時候，感知網路干擾會比較不
嚴重。這是因為當主要使用者在角落的時候，主要與次級使用者間的距離增加。
此外，這個架構也可以用來討論，指定區域中，次級使用者的不均勻空間分布問 題。因此，由統計干擾模型，可以找出主要使用者容易受到感知網路影響的位置。
圖十一：感知網路干擾的改變
圖十二：感知網路干擾的變化
54
圖十三：感知網路干擾的變化
圖十四：感知網路干擾的 PDF
4.6 結論
在本章中，針對感知網路干擾的整合提出一個新的統計模型；它可以解釋感 傳程序、空間分布結點、次要空間重用協定，以及像 path loss、shadowing、
通道衰變這類的環境相關條件。此研究考慮次要空間重用協定的兩種型式，也就 是 single-threshold 與 multiple-threshold 協定；針對各個協定都要定義出 對於主要使用者的感知網路的干擾，它的特徵函數和累積量。利用截角穩定分布
（truncated-stable distributions），可以得到感知網路感擾的統計模型。更 進一步的去延伸這個模型，使其具有功率控制和 shadowing 的效應，並在感知網 路干擾存在的條件下定義出 BEP。數據結果指出，此研究的模型在各種不同的情 境條件下，對於感知網路干擾統計行為的擷取是有效的。本章發展出的架構，讓 讀者可以定義感知網路干擾，在未來可以成功的佈署感知網路。此外，這個架構 也可以被應用在 macrocell users 在多層網路的隨機分布封閉路徑 femtocell，
所造成的跨層干擾效應研究上。
4.7 參考資料
[1] FCC, ―Policy task force report (et docket-135),‖ 2002.
[2] M. A. McHenry, ―NSF Spectrum Occupancy Measurements Project Summary,‖
Shared Spectrum Company, 2005.
[3] FCC, ―Notice of proposed rule making, in the matter of facilitating opportunities for flexible, efficient and reliable spectrum use employing cognitive radio
technologies (et docket no. 03-108) and authorization and use of software defined radios (et docket no. 00-47), FCC 03-322,‖ Dec. 2003.
[4] S. Haykin, ―Cognitive radio: Brain-empowered wireless communications,‖ IEEE J. Sel. Areas Commun., vol. 23, no. 2, pp. 201–220, Feb. 2005.
[5] I. F. Akyildiz, W. Lee, M. C. Vuran, and S. Mohanty, ―Next generation/dynamic spectrum access/cognitive radio wireless networks: A survey,‖ Computer
Networks, vol. 50, no. 13, pp. 2127–2159, Sep. 2006.
[6] Q. Zhao and B. M. Sadler, ―A survey of dynamic spectrum access,‖ IEEE Signal Process. Mag., vol. 24, no. 3, pp. 79–89, May 2007.
[7] A. Goldsmith, S. A. Jafar, I. Maric, and S. Srinivasa, ―Breaking spectrum gridlock with cognitive radios: An information theoretic perspective,‖ Proc.
IEEE, vol. 97, no. 5, pp. 894–914, May 2009.
[8] A. Ghasemi, , and E. S. Sousa, ―Spectrum sensing in cognitive radio networks:
56
Requirements, challenges and design trade-offs,‖ IEEE Commun. Mag., vol. 46, no. 4, pp. 32–39, Apr. 2008.
[9] D. Cabric, S. M. Mishra, and R. W. Brodersen, ―Implementation issues in
spectrum sensing for cognitive radios,‖ in Proc. IEEE Asilomar Conf. on Signals, Systems, and Computers, Pacific Grove, CA, Nov. 2004, pp.772–776.
[10] A. Sonnenschein and P. M. Fishman, ―Radiometric detection of spread- spectrum signals in noise,‖ IEEE Trans. Aerosp. Electron. Syst., vol. 28,no. 3, pp. 654–660, Jul. 1992.
[11] R. Tandra and A. Sahai, ―SNR walls for signal detection,‖ IEEE J. Sel Topics Signal Process., vol. 2, no. 1, pp. 4–17, Feb. 2008.
[12] R. Tandra, S. M. Mishra, and A. Sahai, ―What is a spectrum hole and what does it take to recognize one: Extended version,‖ Proc. IEEE, vol. 97, no. 5, pp.
824–848, May 2009.
[13] M. Z. Win, ―A mathematical model for network interference,‖ IEEE Commun.
Theory Workshop, Sedona, AZ, May 2007.
[14] M. Z. Win, P. C. Pinto, and L. A. Shepp, ―A mathematical theory of network interference and its applications,‖ Proc. IEEE, vol. 97, no. 2, pp. 205–230, Feb.
2009.
[15] M. Z. Win and R. A. Scholtz, ―Impulse radio: How it works,‖ IEEE Commun.
Lett., vol. 2, no. 2, pp. 36–38, Feb. 1998.
[16] ——, ―Ultra-wide bandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications,‖ IEEE Trans. Commun., vol. 48, no. 4, pp. 679–691, Apr. 2000.
[17] M. Z. Win, ―A unified spectral analysis of generalized time-hopping
spread-spectrum signals in the presence of timing jitter,‖ IEEE J. Sel.Areas Commun., vol. 20, no. 9, pp. 1664–1676, Dec. 2002.
[18] R. A. Scholtz, ―Private conversation,‖ University of Southern California, Sep.
1997, Los Angeles, CA.
[19] J. H. Winters, ―Private conversation,‖ AT&T Labs-Research, Mar. 2001, Middletown, NJ.
[20] L. A. Shepp, ―Private conversation,‖ AT&T Labs-Research, Mar. 2001, Middletown, NJ.
[21] P. C. Pinto and M. Z. Win, ―Communication in a Poisson field of interferers – Part I: Interference distribution and error probability,‖ IEEE Trans. Wireless Commun., vol. 9, no. 7, pp. 2176–2186, Jul. 2010.
[22] ——, ―Communication in a Poisson field of interferers – Part II: Channel capacity and interference spectrum,‖ IEEE Trans. Wireless Commun.,vol. 9, no.
7, pp. 2187–2195, Jul. 2010.
[23] A. Rabbachin, T. Q. S. Quek, P. C. Pinto, I. Oppermann, and M. Z. Win,
―Non-coherent UWB communication in the presence of multiple narrowband interferers,‖ IEEE Trans. Wireless Commun., vol. 9, no. 11, pp. 3365-3379, Nov.
2010.
[24] P. C. Pinto, A. Giorgetti, M. Z. Win, and M. Chiani, ―A stochastic geometry approach to coexistence in heterogeneous wireless networks,‖ IEEE J. Sel. Areas Commun., vol. 27, no. 7, pp. 1268–1282, Sep. 2009.
[25] P. C. Pinto and M. Z. Win, ―Spectral characterization of wireless networks,‖
IEEE Wireless Commun. Mag., vol. 14, no. 6, pp. 27–31, Dec. 2007.
[26] J. F. Kingman, Poisson Processes. Oxford University Press, 1993.
[27] S. Chandrasekhar, ―Stochastic problems in physics and astronomy,‖ Rev. Modern Phys., vol. 15, no. 1, pp. 1–89, Jan. 1943.
[28] S. E. Heath, ―Applications of the Poisson Model to Wireless Telephony and to Cosmology,‖ Ph.D. dissertation, Department of Statistics, Rutgers University, Piscataway, NJ, Mar. 2004, thesis advisor: ProfessorLawrence A. Shepp.
[29] M. Y. Vardi, L. Shepp, and L. Kaufman, ―A statistical model for positron emission tomography,‖ Journal of the American Statistical Association, vol. 80, no. 389, pp. 8–20, Mar. 1985.
[30] M. Beil, F. Fleischer, S. Paschke, and V. Schmidt, ―Statistical analysis of 3D centromeric heterochromatin structure in interphase nuclei,‖ Journal of Microscopy, vol. 217, pp. 60–68, 2005.
[31] D. L. Snyder, ―Filtering and detection for doubly stochastic Poisson processes,‖
IEEE Trans. Inf. Theory, vol. 18, no. 1, pp. 91–102, Jan. 1972.
[32] J. R. Pierce, ―Optical channels: practical limits with photon-counting,‖ IEEE Trans. Inf. Theory, vol. 26, no. 12, pp. 1819–1821, Dec. 1978.
[33] J. R. Pierce, E. C. Posner, and E. R. Rodemich, ―The capacity of the photon counting channel,‖ IEEE Trans. Inf. Theory,vol.27,no.1,pp. 61–77, Jan. 1981.
[34] J. L. Massey, ―Capacity cutoff rate, and coding for direct detection optical channel,‖ IEEE Trans. Commun., vol. 29, no. 11, pp. 1615–1621, Nov. 1981.
[35] E. S. Sousa, ―Performance of a spread spectrum packet radio network link in a Poisson field of interferers,‖ IEEE Trans. Inf. Theory,vol.38, no. 6, pp.
1743–1754, Dec. 1992.
[36] J. Ilow, D. Hatzinakos, and A. N. Venetsanopoulos, ―Performance of FH SS radio networks with interference modeled as a mixture of Gaussian and alpha-stable noise,‖ IEEE Trans. Commun., vol. 46, no. 4, pp. 509–520, Apr. 1998.
[37] C. C. Chan and S. V. Hanly, ―Calculating the outage probability in a CDMA network with spatial Poisson traffic,‖ IEEE Trans. Veh. Technol., vol. 50, no. 1, pp. 183–204, Jan. 2001.
58
[38] F. Baccelli, B. Błaszczyszyn, and F. Tournois, ―Spatial averages of coverage characteristics in large CDMA networks,‖ Wireless Networks, vol. 8, no. 6, pp.
569–586, Nov. 2002.
[39] X. Yang and A. P. Petropulu, ―Co-channel interference modeling and analysis in a Poisson field of interferers in wireless communications,‖ IEEE Trans. Signal Process., vol. 51, no. 1, pp. 64–76, 2003.
[40] J. Orriss and S. K. Barton, ―Probability distributions for the number of radio transceivers which can communicate with one another,‖ IEEE Trans. Commun., vol. 51, no. 4, pp. 676–681, Apr. 2003.
[41] S. P. Weber, X. Yang, J. G. Andrews, and G. de Veciana, ―Transmission capacity of wireless ad hoc networks with outage constraints,‖ IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4091–4102, Dec. 2005.
[42] O. Dousse, F. Baccelli, and P. Thiran, ―Impact of interferences on connectivity in ad hoc networks,‖ IEEE/ACM Trans. Netw., vol. 13, no. 2, pp. 425–436, Apr.
2005.
[43] O. Dousse, M. Franceschetti, and P. Thiran, ―On the throughput scaling of
wireless relay networks,‖ IEEE Trans. Inf. Theory, vol. 52, no. 6, pp. 2756–2761, Jun. 2006.
[44] L. Song and D. Hatzinakos, ―Cooperative transmission in Poisson distributed wireless sensor networks: Protocol and outage probability,‖ IEEE Trans. Wireless Commun., vol. 5, no. 10, pp. 2834–2843, Oct. 2006.
[45] A. Ghasemi and E. S. Sousa, ―Interference aggregation in spectrum- sensing cognitive wireless networks,‖ IEEE J. Sel. Topics Signal Process., vol. 2, no. 1, pp. 41–56, Feb. 2008.
[46] R. Menon, R. M. Buehrer, and J. H. Reed, ―On the impact of dynamic spectrum sharing techniques on legacy radio systems,‖ IEEE Trans. Wireless Commun., vol. 7, no. 11, pp. 4198–4207, Nov. 2008.
[47] W. Ren, Q. Zhao, and A. Swami, ―Power control in spectrum overlay networks:
How to cross a multi-lane highway,‖ IEEE J. Sel. Areas Commun., vol. 27, no. 7, pp. 1283–1296, Sep. 2009.
[48] E. Salbaroli and A. Zanella, ―Interference analysis in a Poisson field of nodes of finite area,‖ IEEE Trans. Veh. Technol., vol. 58, no. 4, pp.1776–1783, May 2009.
[49] H. Inaltekin, M. Chiang, H. V. Poor, and S. B. Wicker, ―The behavior of
unbounded path-loss models and the effect of singularity on computed network characteristics,‖ IEEE J. Sel. Areas Commun., vol. 27, no. 7, pp. 1078–1092, Sep.
2009.
[50] R. K. Ganti and M. Haenggi, ―Interference and outage in clustered wireless ad hoc networks,‖ IEEE Trans. Inf. Theory, vol. 55, no. 9, pp. 4067–4086, Sep.
2009.
[51] F. Baccelli, B. Błaszczyszyn, and P. M¨uhlethaler, ―Stochastic analysis of spatial and opportunistic Aloha,‖ IEEE J. Sel. Areas Commun., vol. 27, no. 7, pp.
1105–1119, Sep. 2009.
[52] V. Chandrasekhar and J. G. Andrews, ―Uplink capacity and interference
avoidance for two-tier femtocell networks,‖ IEEE Trans. Wireless Commun., vol.
8, no. 7, pp. 3498–3509, Jul. 2009.
[53] Q. Zhao, L. Tong, A. Swami, and Y. Chen, ―Decentralized cognitive MAC for opportunistic spectrum access in ad hoc networks: A POMDP framework,‖ IEEE J. Sel. Areas Commun., vol. 25, no. 3, pp. 589–600, Apr. 2007.
[54] O. Simeone, I. Stanojev, S. Savazzi, Y. Bar-Ness, U. Spagnolini, and R. Pickholtz,
―Spectrum leasing to cooperating secondary ad hoc networks,‖ IEEE J. Sel.
Areas Commun., vol. 26, no. 1, pp. 203–213, Jan. 2008.
[55] L. C. Wang and A. Chen, ―Effects of location awareness on concurrent transmissions for cognitive ad hoc networks overlaying infrastructure-based systems,‖ IEEETrans.Mobile Comput., vol. 8, no. 5, pp. 577–589,May 2009.
[56] ECC, ―Technical requirements for UWBDAA (detect and avoid) devices to ensure the protection of radiolocation services in the bands 3.1 - 3.4 GHz and 8.5 - 9 GHz and BWA terminals in the band 3.4 - 4.2 GHz,‖ 2008.
[57] G. Samoradnitsky and M. Taqqu, Stable Non-Gaussian Random Processes.
Chapman and Hall, 1994.
[58] R. K. Ganti and M. Haenggi, ―Interference in ad hoc networks with general motion-invariant node distributions,‖ in Proc. IEEE Int. Symp. on Inf. Theory, Toronto, CANADA, Jul. 2008, pp. 1–5.
[59] P. Carr, H. Geman, D. B. Madan, and M. Yor, ―The fine structure of asset returns:
An empirical investigation,‖ The Journal of Business, vol. 75,no. 2, pp. 305–332, Apr. 2002.
[60] N. Bambos and S. Kandukuri, ―Power controlled multiple access (PCMA) schemes for next-generation wireless packet networks,‖ IEEE Trans. Wireless Commun., vol. 9, no. 3, pp. 58–64, Mar. 2002.
[61] G. J. Foschini and Z. Miljanic, ―A simple distributed autonomous power control algorithm and its convergence,‖ IEEE Trans. Veh. Technol., vol. 42, no. 4, pp.
641–646, Nov. 1993.
[62] V. Chandrasekhar, J. G. Andrews, and A. Gatherer, ―Femtocell networks:
Asurvey,‖ IEEE Commun. Mag., vol. 46, no. 9, pp. 59–67, Sep. 2008.
[63] J. Gil-Pelaez, ―Note on the inversion theorem,‖ Biometrika, vol. 38, no. 3/4, pp.
481–482, Dec. 1951.
60