Abstract
The "replica method" of statistical physics is employed for the large-system analysis of vector precoding for the Gaussian multiple-input multiple-output broadcast channel. The transmitter comprises a linear front-end combined with nonlinear precoding, minimizing transmit energy by means of input alphabet relaxation. For the common discrete lattice-based relaxation, the problem violates replica symmetry and a replica symmetry breaking (RSB) ansatz is taken. The limiting empirical distribution of the precoder's output and the limiting transmit energy are derived for one-step RSB. Particularizing to a "zero-forcing" (ZF) linear front-end, a decoupling result is derived. For discrete lattice-based relaxations, the impact of RSB is demonstrated for the transmit energy. The spectral efficiencies of the aforementioned precoding methods are compared to linear ZF and Tomlinson-Harashima precoding (THP). Focusing on quaternary phase shift-keying (QPSK), significant performance gains of both lattice and convex relaxations are revealed for medium to high signal-to-noise ratios (SNRs) when compared to linear ZF precoding. THP is shown to be outperformed as well. Comparing certain lattice-based relaxations for QPSK against a convex counterpart, the latter is found to be superior for low and high SNRs but slightly inferior for medium SNRs in terms of spectral efficiency.
| Original language | English |
|---|---|
| Article number | 6157078 |
| Pages (from-to) | 1413-1440 |
| Number of pages | 28 |
| Journal | IEEE Transactions on Information Theory |
| Volume | 58 |
| Issue number | 3 |
| DOIs | |
| State | Published - Mar 2012 |
| Externally published | Yes |
Bibliographical note
Funding Information:Manuscript received January 21, 2010; revised October 12, 2011; accepted October 13, 2011.Date of current version February 29, 2012. This work was supported in part by the Research Council of Norway under Grant 171133/V30, and in part by the European Commission under Grant “Newcom++” EU-IST-NoE-FP6-2007-216715. The material in this paper was presented in part at the 46th Annual Allerton Conference on Communication, Control and Computing, Mon-ticello, IL, September 2008, and in part at the 10th International Symposium on Spread Spectrum Techniques and Applications (ISSSTA), Bologna, Italy, August 2008.
Funding
Manuscript received January 21, 2010; revised October 12, 2011; accepted October 13, 2011.Date of current version February 29, 2012. This work was supported in part by the Research Council of Norway under Grant 171133/V30, and in part by the European Commission under Grant “Newcom++” EU-IST-NoE-FP6-2007-216715. The material in this paper was presented in part at the 46th Annual Allerton Conference on Communication, Control and Computing, Mon-ticello, IL, September 2008, and in part at the 10th International Symposium on Spread Spectrum Techniques and Applications (ISSSTA), Bologna, Italy, August 2008.
| Funders | Funder number |
|---|---|
| Seventh Framework Programme | 216715 |
| European Commission | EU-IST-NoE-FP6-2007-216715 |
| Norges Forskningsråd | 171133/V30 |
Keywords
- Antenna arrays
- R-transform
- broadcast channel
- decoupling principle
- lattice
- multiple-input multiple-output
- precoding
- replica method
- zero-forcing (ZF)