Per-antenna Constant Envelope Precoding for Large Multi-User MIMO Systems (1201.1634v2)

Abstract: We consider the multi-user MIMO broadcast channel with $M$ single-antenna users and $N$ transmit antennas under the constraint that each antenna emits signals having constant envelope (CE). The motivation for this is that CE signals facilitate the use of power-efficient RF power amplifiers. Analytical and numerical results show that, under certain mild conditions on the channel gains, for a fixed $M$, array gain is achievable even under the stringent per-antenna CE constraint (essentially, for a fixed $M$, at sufficiently large $N$ the total transmitted power can be reduced with increasing $N$ while maintaining a fixed information rate to each user). Simulations for the i.i.d. Rayleigh fading channel show that the total transmit power can be reduced linearly with increasing $N$ (i.e., an O(N) array gain). We also propose a precoding scheme which finds near-optimal CE signals to be transmitted, and has O(MN) complexity. Also, in terms of the total transmit power required to achieve a fixed desired information sum-rate, despite the stringent per-antenna CE constraint, the proposed CE precoding scheme performs close to the sum-capacity achieving scheme for an average-only total transmit power constrained channel.

• The paper proposes a low-complexity per-antenna CE precoding scheme that achieves an O(N) array power gain while effectively controlling multi-user interference.
• It employs a non-linear least squares formulation to compute phase angles that minimize interference, operating with an O(MN) complexity.
• Numerical results under i.i.d. Rayleigh fading show that the technique significantly reduces transmit power, approximating the sum-capacity performance within about 2.0 dB.

Overview of Per-antenna Constant Envelope Precoding in Large Multi-User MIMO Systems

The paper presents a detailed investigation into per-antenna constant envelope (CE) precoding for large multi-user MIMO systems operating over Gaussian Broadcast Channels (GBC). The authors explore the challenges and opportunities presented by implementing constant envelope transmission constraints at each antenna, primarily motivated by the need to integrate power-efficient and non-linear RF power amplifiers in large antenna systems.

Precoding Strategy and Theoretical Insights

The paper derives theoretical insights to show that multi-user interference (MUI) can be controlled, and array gain achieved, despite the stringent constant envelope constraint per antenna. Such findings are established under certain mild assumptions on the channel conditions, particularly in scenarios where the base station (BS) has a large number $N$ of antennas compared to the number $M$ of single-antenna users. This leads to an analytical demonstration that, with increasing $N$, the total transmit power can be reduced while maintaining a fixed information rate per user, signifying an achievable $O(N)$ array power gain.

Proposed CE Precoding Scheme

The authors propose a low-complexity CE precoding scheme that aims to minimize MUI energy while maintaining the constant envelope constraint. The scheme is capable of finding near-optimal CE signals within an operational complexity of $O(MN)$. The approach uses a non-linear least squares (NLS) problem formulation to compute the phase angles that minimize interference, enabling transmission of signals with constant amplitude from each antenna.

Numerical Results and Practical Implications

Simulations demonstrate that for an i.i.d. Rayleigh fading channel, the transmit power required is reduced linearly with increasing antenna number while maintaining a fixed desired information sum-rate. This indicates the significant array gain achievable under the considered channel scenarios. Furthermore, the paper reveals that for large $N$, the gap in required total transmit power compared to the sum-capacity achieving scheme with average-only power constraint is small (approximately 2.0 dB), underlining the practical efficiency of the proposed precoding scheme.

Future Directions and Implications

The research suggests potential power savings in practical deployments of large antenna arrays, making it an attractive option for future wireless communication systems. These insights broaden the scope for deploying non-linear and power-efficient RF components in future networks without compromising on signal quality or system performance. Future work includes perfecting the generation of continuous-time constant-envelope signals and addressing scenarios involving larger alphabets or more complex modulation schemes.

Conclusion

This paper contributes valuable theoretical and practical innovations to the design of energy-efficient multi-user MIMO systems. By rigorously analyzing the conditions under which per-antenna CE constraints remain effective, it sets the groundwork for further exploration into energy conservation techniques in large-scale MIMO networks, ultimately promoting greener and more efficient wireless communication practices.