在本篇論文中，我們討論在多細胞多天線網路中利用傳送預先編
碼(precoding)的機會式群播排程(opportunistic multicast
scheduling)技術。在此系統中，基地台傳送訊號給所有指定的群體
用戶，因此傳送速率將被最差的指定用戶所限制住。機會式群播排程
在傳統中被用來在單播(unicast)與廣播(broadcast)之間取得平衡
(tradeoff)，但是在多群播環境下因為可以更進一步選擇部分的用戶
來避免產生較大的干擾，因此能擁有更好的效果。我們假設所有基地
台皆擁有要傳送給每群用戶的資料和連接到所有用戶的通道狀態訊
息(channel state information)。此機會式群播排程和傳送預先編
碼器根據兩種最佳化的準則來做設計: 最差的平均用戶吞吐量(the
worst per-user throughput)和加權和吞吐量(weighted sum
throughput)。當給定選擇用戶時，根據這兩個準則找出最佳的傳送
預先編碼器的問題皆會是非凸面(non-convex)的最佳化問題，因此我
們把問題推導成凸面可行性問題(convex feasibility problem)，並
且利用二分法收尋(bisection search)來解出答案。接著，我們在設
法找出最佳的選擇用戶。然而，此問題本質上是個排列組合問題，當
用戶數目增加的時候，這個問題的複雜度會變得相當棘手。因此，我
們提出了一個迭代選擇用戶演算法(iterative user selection
algorithm)，用來降低收尋的複雜度。最後，我們利用電腦模擬來顯
示我們所提出方法的效能。

The use of opportunistic multicast scheduling (OMS) with transmit precoding is examined in
this work for multicell MIMO systems with multiple multicast groups. In multicast systems,
data transmitted by the base-stations (BSs) must be received by all intended receivers and,
thus, the transmission rate is limited by the the worst intended receiver. OMS traditionally
has been used to optimize the tradeoff between unicast and broadcast, but can have an even
larger impact in systems with multiple multicast groups since users can be further selected in
this case to avoid interference. Here, we assume that the base-stations (BSs) have knowledge
of the data intended for all groups as well as the channel state information (CSI) of all links.
The OMS and transmit precoder are designed based on two optimization criteria: the worst
per-user throughput and the weighted sum throughput. Given the user selection, the problem
of finding the optimal transmit precoder under both criteria are non-convex and, thus, are
alternatively formulated as convex feasibility problems, which are solved by bisection search.
Then, an outer optimization is performed to solve for the optimal user selection. However,
since the problem is combinatorial in nature, the complexity of the problem can be intractable
for systems with large number of users. Hence, iterative user selection (IUS) algorithms are
proposed to reduce the complexity of the search. The effectiveness of the proposed schemes
are demonstrated through computer simulations.

[1] U. C. Kozat, “On the throughput capacity of opportunistic multicasting with erasure
codes,” in The IEEE 27th Conference on Computer Communications INFOCOM, Apr.
2008, pp. 520–528.

[2] T.-P. Low, M.-O. Pun, Y.-W. P. Hong, and C.-C. J. Kuo, “Optimized opportunistic
multicast scheduling (oms) over wireless cellular networks,” IEEE Transactions on
Wireless Communications, vol. 9, no. 2, pp. 791–801, Feb. 2010.

[3] P. K. Gopala and H. E. Gamal, “Opportunistic multicasting,” in Conference Record of
the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, Nov. 2004,
pp. 845–849.

[4] ——, “On the throughput-delay tradeoff in cellular multicast,” in International Confer-
ence on Wireless Networks ,Communications and Mobile Computing,, vol. 2, Jun. 2005,
pp. 1401–1406.

[5] D. J. C. MacKay, “Fountain codes,” IEE Proceedings-Communications, vol. 152, no. 6,
pp. 1062–1068, Dec. 2005.

[6] T.-P. Low, P.-C. Fang, Y.-W. P. Hong, and C.-C. J. Kuo, “Multi-antenna multicasting
with opportunistic multicast scheduling and space-time transmission,” in IEEE Global
Telecommunications Conference (GLOBECOM), Dec. 2010, pp. 1–5.

[7] T. M. Cover and J. A. Thomas, Elememts of Information Theory. John Wiley and
Sons, Inc., 1991.

[8] T.-P. Low, Y.-W. P. Hong, and C.-C. J. Kuo, “Opportunistic multicast scheduling with
multiple multicast groups,” in IEEE Global Telecommunications Conference (GLOBE-
COM), Dec. 2011, pp. 1–5.

[9] N. D. Sidiropoulos, T. N. Davidson, and Z.-Q. Luo, “Transmit beamforming for physicallayer
multicasting,” IEEE Transactions on Signal Processing, vol. 54, no. 6, pp. 2239–
2251, Jun. 2006.

[10] E. Karipidis, N. D. Sidiropoulos, and Z.-Q. Luo, “Quality of service and max-min fair
transmit beamforming to multiple cochannel multicast groups,” IEEE Transactions on
Signal Processing, vol. 56, no. 3, pp. 1268–1279, Mar. 2008.

[11] N. Bornhorst and M. Pesavento, “An iterative convex approximation approach for transmit
beamforming in multi-group multicasting,” in IEEE 12th International Workshop
on Signal Processing Advances in Wireless Communications (SPAWC), Jun. 2011, pp.
426–430.

[12] A. Schad and M. Pesavento, “Max-min fair transmit beamforming for multi-group multicasting,”
in International ITG Workshop on Smart Antennas (WSA), Mar. 2012, pp.
115–118.

[13] M. K. Kaliszan, E. Pollakis, and S. S. Stanczak, “Efficient beamforming algorithms for
mimo multicast with application-layer coding,” in IEEE International Symposium on
Information Theory Proceedings (ISIT), Aug. 2011, pp. 928–932.

[14] M. Kaliszan, E. Pollakis, and S. Stanczak, “Multigroup multicast with application-layer
coding: Beamforming for maximum weighted sum rate,” in IEEE Wireless Communi-
cations and Networking Conference (WCNC), Apr. 2012, pp. 2270–2275.

[15] D. Gesbert, S. Hanly, H. Huang, S. S. Shitz, O. Simeone, and W. Yu, “Multi-cell mimo
cooperative networks: A new look at interference,” IEEE Journal on Selected Areas in
Communications, vol. 28, no. 9, pp. 1380–1408, Dec. 2010.

[16] H. Zhang and H. Dai, “Cochannel interference mitigation and cooperative processing
in downlink multicell multiuser mimo networks,” EURASIP J. Wireless Commun. Net-
working, vol. 2004, no. 2, pp. 222–235, Dec. 2004.

[17] E. Bj¨ornson, R. Zakhour, D. Gesbert, and B. Ottersten, “Cooperative multicell precoding:
Rate region characterization and distributed strategies with instantaneous and
statistical csi,” IEEE Transactions on Signal Processing, vol. 58, no. 8, pp. 4298–4310,
Aug. 2010.

[18] H. Dahrouj and W. Yu, “Coordinated beamforming for the multicell multi-antenna
wireless system,” IEEE Transactions on Wireless Communications, vol. 9, no. 5, pp.
1748–1759, May 2010.

[19] Y.-F. Liu, Y.-H. Dai, and Z.-Q. Luo, “Coordinated beamforming for miso interference
channel: Complexity analysis and efficient algorithms,” IEEE Transactions on Signal
Processing, vol. 59, no. 3, pp. 1142–1157, Mar. 2011.

[20] M. Grant and S. Boyd, “CVX: Matlab software for disciplined convex programming,
version 1.21,” ../../cvx, Apr. 2011.

[21] J. Qiu, R. Zhang, Z.-Q. Luo, and S. Cui, “Optimal distributed beamforming for miso
interference channels,” IEEE Transactions on Signal Processing, vol. 59, no. 11, pp.
5638–5643, Nov. 2011.