波束成形是第五代無線通訊網路的重要功能之一。在波束成形系統中，基站和用戶設備遵循波束掃描程序來對齊它們的波束。在波束掃描期間，每個用戶設備必須按照基於波束的隨機存取協定指示其選擇的波束。根據隨機存取通道的配置選項可以定義各種波束映射模式。波束映射模式的不適當設置可能會導致隨機存取通道中的負載不平衡問題。因此，波束映射模式與基於波束的隨機存取協定的效能之間的明確數學關係對於協定優化至關重要。本文提出了一個分析模型來估計基於波束的隨機存取協定的效能，並推導出TR 37.868中考慮的存取成功機率、平均存取延遲、傳輸次數的累積分佈函數和存取延遲的累積分佈函數的效能指標。此外，提出了一種波束映射方案，來為給定的隨機存取通道配置設置最佳波束映射模式。通過大量的電腦模擬驗證了分析模型和波束映射方案的有效性。

Beamforming is one of the important features for 5G New Radio (NR) networks. In a beamforming system, the base station (gNB) and user equipment (UE) follow a beam-sweeping procedure to align their beams. During beam-sweeping, each UE has to indicate its selected beam following a beam-based random-access protocol. Various beam mapping patterns can be defined based on the configuration options of random-access channels (RACHs). An explicit mathematical relationship between the performance of beam-based RA protocol and the beam mapping patterns is crucial to the protocol optimization since the improper setting of the beam mapping pattern may render a load unbalance issue in the RACHs. This paper presented an analytical model to estimate the performance of beam-based RA protocol. The performance metrics of access success probability, average access delay, cumulative distribution function (CDF) of the number of transmissions, and CDF of access delay considered in TR 37.868 [1] were derived. A beam mapping scheme was then proposed to set the best beam mapping pattern for a given RACH configuration. The effectiveness of the analytical model and the beam mapping scheme was verified by extensive simulations.

[1] Study on RAN improvements for machine-type communications, V11.0.0, 3GPP TR 37.868, Sep. 2011.
[2] R. Guo, E. Lin, R. Zen and R. Kuo, “On beam-based access technology for 5G,” IEEE Wireless Commun., vol. 23, no. 5, pp. 2-3, Oct. 2016.
[3] Study on new radio access technology: Physical layer aspects, V14.2.0, 3GPP TR 38.802, Sep. 2017.
[4] Study on New Radio (NR) access technology, V16.0.0, 3GPP TR 38.912, Jul. 2020.
[5] Physical layer procedures for control, V16.2.0, 3GPP TS 38.213, Jun. 2020.
[6] L. G. Roberts, “ALOHA packet system with and without slots and capture,” in ACM SIGCOMM Comput. Commun. Rev., Apr. 1975, pp. 28-42.
[7] N. Abramson, “The ALOHA system: Another alternative for computer communications,” in AFIPS Conf. Proc., Nov. 1970, pp. 281-285.
[8] H. Okada, Y. Igarashi, and Y. Nakanishi, “Analysis and application of framed ALOHA channel in satellite packet switching networks -- FADRA method,” Electron. Commun. in Japan, vol. 60, pp. 60-72, Aug. 1977.
[9] H. H. Tan and H. Wang, “Performance of multiple parallel slotted ALOHA channels,” in Proc. IEEE INFOCOM, Mar. 1987, pp. 931-940.
[10] Y. Kuo, S. Lien, D. Deng and Y. J. Wang, “Latency-optimal beam sweeping for millimeter-wave communications,” presented at the 2018 IEEE Globecom Workshops, Abu Dhabi, United Arab Emirates, Dec. 9-13, 2018.
[11] W. Wu, N. Cheng, N. Zhang, P. Yang, K. Aldubaikhy and X. Shen, “Performance analysis and enhancement of beamforming training in 802.11ad,” IEEE Trans. Vehicular Technology, vol. 69, no. 5, pp. 5293-5306, May 2020.
[12] P. Zhou, X. Fang, Y. Fang, Y. Long, R. He and X. Han, “Enhanced random access and beam training for millimeter wave wireless local networks with high user density,” IEEE Trans. Wireless Commun., vol. 16, no. 12, pp. 7760- 7773, Dec. 2017.
[13] IEEE standard for information technology-- Telecommunications and information exchange between systems-- Local and metropolitan area networks-- Specific requirements-- Part 11: Wireless LAN medium access control (MAC) and physical layer (PHY) specifications-- Amendment 3: Enhancements for very high throughput in the 60 GHz band, IEEE 802.11ad, Dec. 2012.
[14] IEEE P802.11ay/D4.0 standard for information technology-- Telecommunications and information exchange between systems-- Local and metropolitan area networks-- Specific requirements-- Part 11: Wireless LAN medium access control (MAC) and physical layer (PHY) specifications-- Amendment3: Enhanced throughput for operation in license-exempt bands above 45 GHz, IEEE P802.11ay/D4.0, Jun. 2019.
[15] C. Wei, R. Cheng and S. Tsao, “Performance analysis of group paging for machine-type communications in LTE networks,” IEEE Trans. Vehicular Technology, vol. 62, no. 7, pp. 3371-3382, Sep. 2013.
[16] C. Wei, G. Bianchi, and R. Cheng, “Modeling and analysis of random access channels with bursty arrivals in OFDMA wireless networks,” IEEE Trans. Wireless Commun., vol. 14, no. 4, pp. 1940-1953, Apr. 2015.
[17] R. Harwahyu, R. G. Cheng, C. H. Wei and R. F. Sari, “Optimization of random access channel in NB-IoT,” IEEE Internet of Things Journal, vol. 5, no. 1, pp. 391-402, Feb. 2018.
[18] R. Cheng, C. Wei and S. Tsao, “Iterative contending-user estimation method for OFDMA wireless networks with bursty arrivals,” in 2013 IEEE Symp. Comput. and Commun., Jul. 2013, pp. 240-245.
[19] Medium Access Control (MAC) protocol specification, V16.4.0, 3GPP TS 38.321, Mar. 2021.
[20] J. W. Won, K. M. Kim and T. J. Lee, “Enhanced random access with beamforming techniques in 5G networks,” in Proc. 15th Int. Conf. Ubiquitous Inf. Manag. Commun. (IMCOM), 2021, pp. 1-4, doi: 10.1109/IMCOM51814.2021.9377362.
[21] Radio Resource Control (RRC) protocol specification, V16.4.1, 3GPP TS 38.331, Mar. 2021.
[22] “PRACH resource selection for SSB and CSI-RS,” 3GPP TSG-RAN WG2 Meeting 103, Gothenburg, Sweden, R2-1811918, Aug. 2018.
[23] Physical channels and modulation, V16.2.0, 3GPP TS 38.211, Jun. 2020.
[24] C. Wei, R. Cheng and S. Tsao, “Modeling and estimation of one-shot random access for finite-user multichannel slotted ALOHA systems,” IEEE Commun. Letters, vol. 16, no. 8, pp. 1196-1199, Aug. 2012.