Spatially Sparse Precoding in Millimeter Wave MIMO Systems (1305.2460v1)

Abstract: Millimeter wave (mmWave) signals experience orders-of-magnitude more pathloss than the microwave signals currently used in most wireless applications. MmWave systems must therefore leverage large antenna arrays, made possible by the decrease in wavelength, to combat pathloss with beamforming gain. Beamforming with multiple data streams, known as precoding, can be used to further improve mmWave spectral efficiency. Both beamforming and precoding are done digitally at baseband in traditional multi-antenna systems. The high cost and power consumption of mixed-signal devices in mmWave systems, however, make analog processing in the RF domain more attractive. This hardware limitation restricts the feasible set of precoders and combiners that can be applied by practical mmWave transceivers. In this paper, we consider transmit precoding and receiver combining in mmWave systems with large antenna arrays. We exploit the spatial structure of mmWave channels to formulate the precoding/combining problem as a sparse reconstruction problem. Using the principle of basis pursuit, we develop algorithms that accurately approximate optimal unconstrained precoders and combiners such that they can be implemented in low-cost RF hardware. We present numerical results on the performance of the proposed algorithms and show that they allow mmWave systems to approach their unconstrained performance limits, even when transceiver hardware constraints are considered.

• The paper introduces a spatially sparse precoding strategy that leverages basis pursuit to approximate optimal precoders and combiners for mmWave MIMO systems.
• It demonstrates through numerical results that the proposed algorithms achieve spectral efficiencies nearly matching unconstrained systems in practical configurations.
• The study bridges signal processing theory and hardware limitations, paving the way for efficient, scalable 5G and future wireless network implementations.

Spatially Sparse Precoding in Millimeter Wave MIMO Systems

Overview

This paper focuses on enhancing the spectral efficiency of Millimeter Wave (mmWave) multiple-input multiple-output (MIMO) systems. Given the substantial path loss experienced by mmWave signals, large antenna arrays are employed to counteract these losses through beamforming gains. Traditional MIMO systems leverage digital baseband processing for beamforming and precoding. However, the high cost and power consumption of mixed-signal devices render digital processing impractical for mmWave systems. This makes analog processing in the RF domain more appealing, albeit with constraints on feasible precoders and combiners.

The authors address the precoding and combining challenges by exploiting the spatial structure of mmWave channels. They propose formulating the precoding/combining problem as a sparse reconstruction problem. Using basis pursuit principles, the authors develop algorithms that approximate optimal unconstrained precoders and combiners, thereby allowing implementation in low-cost RF hardware.

Numerical Results and Claims

The numerical results presented in the paper demonstrate that the proposed sparse precoding algorithms enable mmWave systems to approach the performance limits of unconstrained systems, even when considering practical hardware constraints. For example, the results show that in a $64 \times 16$ system, the proposed precoding strategy achieves spectral efficiencies close to the optimal unconstrained solution when transmitting one or two data streams. This indicates the effectiveness of the sparse precoding framework in harnessing the channel structure for near-optimal performance.

Additionally, the paper illustrates that as the number of RF chains and antennas increases, the spectral efficiency gap between the proposed algorithm and the optimal solution narrows. For instance, in a $256 \times 64$ system with six RF chains, the proposed solution achieves nearly perfect performance for both single and dual-stream transmissions. This highlights the scalability of the proposed method to larger arrays, which are typical in mmWave systems.

Practical and Theoretical Implications

Practical Implications: The proposed spatially sparse precoding framework presents a feasible approach for implementing efficient mmWave transceivers with large antenna arrays. The ability to approach the performance of unconstrained systems while adhering to practical hardware limitations supports the deployment of mmWave communication in future wireless networks, such as 5G and beyond. This methodology not only reduces the cost and power consumption of transceivers but also simplifies the hardware design by limiting the reliance on complex digital processing.

Theoretical Implications: The paper bridges the gap between signal processing theory and practical implementation by extending sparse signal recovery techniques to the domain of mmWave MIMO precoding and combining. It shows that the structured nature of mmWave channels can be exploited to design near-optimal precoders using a limited number of RF chains, thus providing a new direction for research in mmWave communication. Additionally, the use of orthogonal matching pursuit for solving sparse reconstruction problems in this context opens the door for further exploration and refinement of algorithmic solutions tailored to mmWave systems.

Future Developments in AI

Future work may focus on refining these precoding algorithms to handle other practical considerations such as channel estimation errors, dynamic channel conditions, and more complex antenna configurations. Moreover, the integration of machine learning techniques could further enhance the adaptability and performance of the proposed framework. For instance, learning-based approaches could be employed to optimize the selection of basis vectors and improve the robustness of precoding strategies against channel estimation inaccuracies. Additionally, research can explore joint optimization of precoders and combiners to maximize overall system performance, incorporating real-time feedback and adaptation mechanisms.

Conclusion

The paper presents a comprehensive solution to the challenges of precoding in mmWave MIMO systems with hardware constraints. By leveraging the inherent sparse structure of mmWave channels, the authors propose practical algorithms that enable near-optimal performance using low-cost RF hardware. The promising numerical results and theoretical insights set the stage for further advancements in mmWave communication, paving the way for efficient and scalable wireless systems.

Overall, the paper is a significant step towards realizing high-performance mmWave MIMO systems suitable for next-generation wireless networks, emphasizing the importance of sparse signal recovery techniques in modern communication system design.