Precoding: Difference between revisions

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==Precoding for Multi-user MIMO Systems==

In [[multi-user MIMO]], a multi-antenna transmitter communicates simultaneously with multiple receivers (each having one or multiple antennas). This is known as [[space-division multiple access]] (SDMA). From an implementation perspective, precoding algorithms for SDMA systems can be sub-divided into linear and nonlinear precoding types. The capacity achieving algorithms are nonlinear,<ref name=weingarten>H. Weingarten, Y. Steinberg, and S. Shamai, [http://www.stanford.edu/class/ee360/suppRead/read1/WeingartenSteinbergShamai2006.pdf The capacity region of the Gaussian multiple-input multiple-output broadcast channel] {{webarchive|url=https://web.archive.org/web/20121023102937/http://www.stanford.edu/class/ee360/suppRead/read1/WeingartenSteinbergShamai2006.pdf |date=2012-10-23 }}, IEEE Transactions on Information Theory, vol. 52, no. 9, pp. 3936–3964, 2006.</ref> but linear precoding approaches usually achieve reasonable performance with much lower complexity. Linear precoding strategies include maximum ratio transmission (MRT),<ref name=lo>T. Lo, [https://dx.doi.org/10.1109/26.795811 Maximum ratio transmission], IEEE Transactions on Communications, vol. 47, no. 10, pp. 1458–1461, 1999.</ref> [[Zero-forcing precoding|zero-forcing]] (ZF) precoding,<ref name=joham>M. Joham, W. Utschick, and J. Nossek, [https://dx.doi.org/10.1109/TSP.2005.850331 Linear transmit processing in MIMO communications systems], IEEE Transactions on Signal Processing, vol. 53, no. 8, pp. 2700–2712, 2005.</ref> and transmit Wiener precoding.<ref name=joham/> There are also precoding strategies tailored for low-rate [[feedback]] of [[channel state information]], for example random beamforming.<ref name=sharif>M. Sharif and B. Hassibi, [http://iss.bu.edu/sharif/mimobc-final.pdf On the Capacity of MIMO Broadcast Channels With Partial Side Information], IEEE Transactions on Information Theory, vol. 51, no. 2, pp. 506-522, 2005.</ref> Nonlinear precoding is designed based on the concept of [[dirty paper coding]] (DPC), which shows that any known interference at the transmitter can be subtracted without the penalty of radio resources if the optimal precoding scheme can be applied on the transmit signal.<ref name=weingarten/>

While performance maximization has a clear interpretation in point-to-point MIMO, a multi-user system cannot simultaneously maximize the performance for all users. This can be viewed as a [[multi-objective optimization]] problem where each objective corresponds to maximization of the capacity of one of the users.<ref name=fnt2013/> The usual way to simplify this problem is to select a system utility function; for example, the weighted sum capacity where the weights correspond to the system's subjective user priorities. Furthermore, there might be more users than data streams, requiring a [[scheduling algorithm]] to decide which users to serve at a given time instant.