Compressed Sensing Based Multi-User Millimeter Wave Systems: How Many Measurements Are Needed? (1505.00299v1)

Abstract: Millimeter wave (mmWave) systems will likely employ directional beamforming with large antenna arrays at both the transmitters and receivers. Acquiring channel knowledge to design these beamformers, however, is challenging due to the large antenna arrays and small signal-to-noise ratio before beamforming. In this paper, we propose and evaluate a downlink system operation for multi-user mmWave systems based on compressed sensing channel estimation and conjugate analog beamforming. Adopting the achievable sum-rate as a performance metric, we show how many compressed sensing measurements are needed to approach the perfect channel knowledge performance. The results illustrate that the proposed algorithm requires an order of magnitude less training overhead compared with traditional lower-frequency solutions, while employing mmWave-suitable hardware. They also show that the number of measurements need to be optimized to handle the trade-off between the channel estimate quality and the training overhead.

• The paper introduces a compressed sensing technique for sparse mmWave channel estimation, enabling efficient detection of AoA and AoD.
• It significantly reduces training overhead by requiring only 280-330 measurements, independent of the number of users.
• An analytical lower bound on the achievable rate is derived, highlighting the trade-off between estimation accuracy and measurement complexity.

Compressed Sensing Based Multi-User Millimeter Wave Systems: Measurement Insights

The paper "Compressed Sensing Based Multi-User Millimeter Wave Systems: How Many Measurements Are Needed?" explores the challenges and methodologies associated with channel estimation in millimeter wave (mmWave) systems, focusing on optimizing the number of compressed sensing measurements required to achieve near-perfect channel knowledge. This paper is pertinent given the expected deployment of mmWave communications in future cellular systems, where large antenna arrays and directional beamforming are employed to overcome high path-losses and enhance connectivity over longer distances.

The primary challenge addressed in this paper is the acquisition of accurate channel knowledge in the face of the unique hardware and channel conditions present at mmWave frequencies. Specifically, the channel estimation process is hindered by the small signal-to-noise ratios prior to beamforming, the necessity of maintaining low-complexity in hardware design, and the inherent high dimensionality associated with large antenna arrays.

Key Contributions

1. Compressed Sensing Framework: The authors propose a channel estimation technique based on compressed sensing that leverages the sparse nature of mmWave channels. By formulating the channel estimation problem as a sparse problem, this method allows for efficient estimation of angles of arrival (AoA) and departure (AoD), which are crucial for beamforming.
2. Training Overhead Reduction: The proposed framework demonstrates a significant reduction in the training overhead by requiring an order of magnitude fewer measurements than traditional lower-frequency techniques. By decoupling the training overhead from the number of users, this approach shows substantial gains in multi-user scenarios.
3. Downlink System Operation: The paper details a downlink operation method incorporating compressed sensing channel estimation and conjugate analog beamforming, where optimality in training overhead and performance is achieved through careful design of training and measurement matrices.
4. Achievable Rate Analysis: The authors analytically derive a lower bound on the achievable rate as a function of the compressed sensing measurements, providing insights into the fundamental trade-offs between channel estimation accuracy and required measurement complexity.

Numerical Insights

Simulation results underline the effectiveness of the proposed approach, indicating that around 280-330 compressed sensing measurements suffice to reach the performance levels of systems with perfect channel knowledge. This result reflects a substantial training overhead reduction compared to traditional technologies requiring comprehensive exploration of the channel matrix dimensions.

The paper further elucidates that the number of compressed sensing measurements must be optimized to balance the training overhead and the accuracy of mmWave channel estimates. Such optimization becomes particularly pertinent in fast-fading environments where channel coherence times are short.

Implications and Future Directions

The work presents a pragmatic approach to overcoming mmWave communication challenges by integrating compressed sensing into channel estimation strategies. By showcasing the feasibility of employing hardware-compliant and low-training overhead solutions, the paper paves the way for more efficient deployment of mmWave technologies in real-world multi-user scenarios.

Future research could explore the optimization of measurement matrices and enhance the robustness of the compressed sensing framework to handle more complex channel models featuring multi-path or non-line-of-sight conditions. Additionally, extending the principles of this approach to hybrid analog/digital systems could open the door for further reducing hardware complexity while maximizing spectral efficiency. These advancements would be crucial in facilitating the widespread adoption of mmWave technology in next-generation cellular networks.