Symbol-Level and Multicast Precoding for Multiuser Multiantenna Downlink: A State-of-the-Art, Classification, and Challenges

Abstract

Precoding has been conventionally considered as an effective means of mitigating the interference and efficiently exploiting the available in the multiantenna downlink channel, where multiple users are simultaneously served with independent information over the same channel resources. The early works in this area were focused on transmitting an individual information stream to each user by constructing weighted linear combinations of symbol blocks (codewords). However, more recent works have moved beyond this traditional view by: i) transmitting distinct data streams to groups of users and ii) applying precoding on a symbol-per-symbol basis. In this context, the current survey presents a unified view and classification of precoding techniques with respect to two main axes: i) the switching rate of the precoding weights, leading to the classes of block-and symbol-level precoding, ii) the number of users that each stream is addressed to, hence unicast-/multicast-/broadcast-precoding. Furthermore, the classified techniques are compared through representative numerical results to demonstrate their relative performance and uncover fundamental insights. Finally, a list of open theoretical problems and practical challenges are presented to inspire further research in this area. 1

A Framework for One-Bit and Constant-Envelope Precoding Over Multiuser Massive MISO Channels

“…Our numerical experience also indicates that good results are generally yielded if we choose a small initial λ and increase λ gradually (which means a not too large c). The intuition for such a parameter selection is that we may tackle the problem better if we gradually increase the hardness of the problem; note that our problem in (22) is convex when λ = 0, and concave (and undesirable) for sufficiently large λ. Furthermore, the smoothing parameter σ should not be too small.…”

“…Constellation-Dependent Designs: The previously described distortion-minimization methods use second-order metrics to measure distortion, which do not consider symbol constellations. It has been recently known that, even for free-space precoding, distortion or interference can be beneficially aligned to improve symbol-error probability (SEP) performance when symbol constellation structures are taken into design consideration [21,22]. Such notion is known as constructive interference or symbol-level precoding.…”

RLS Precoding for Massive MIMO Systems with Nonlinear Front-End

“…To this end, one can include the RF chains in the channel model, and design the precoder for the end-to-end channel. An example of this approach was studied in [4] where the authors developed a symbol-level precoding scheme [5] for MIMO settings with nonlinear PAs. Another example is [6] in which the end-to-end precoding was studied in sample domain considering waveform optimization and pulse shaping.…”

Power Minimizer Symbol-Level Precoding: A Closed-Form Sub-Optimal Solution

“…Despite the performance advantages of SLP schemes, one of the main factors that limits their applicability in practice is the increased complexity at the transmitter side [5]. Broadly speaking, the SLP module needs to compute the output once per symbol slot, or alternatively, one may design the precoder's output beforehand for every possible combination of users' symbols [4].…”