Channel Estimation in Broadband Millimeter Wave MIMO Systems with Few-Bit ADCs (1610.02735v4)

Abstract: We develop a broadband channel estimation algorithm for millimeter wave (mmWave) multiple input multiple output (MIMO) systems with few-bit analog-to-digital converters (ADCs). Our methodology exploits the joint sparsity of the mmWave MIMO channel in the angle and delay domains. We formulate the estimation problem as a noisy quantized compressed-sensing problem and solve it using efficient approximate message passing (AMP) algorithms. In particular, we model the angle-delay coefficients using a Bernoulli-Gaussian-mixture distribution with unknown parameters and use the expectation-maximization (EM) forms of the generalized AMP (GAMP) and vector AMP (VAMP) algorithms to simultaneously learn the distributional parameters and compute approximately minimum mean-squared error (MSE) estimates of the channel coefficients. We design a training sequence that allows fast, FFT-based implementation of these algorithms while minimizing peak-to-average power ratio at the transmitter, making our methods scale efficiently to large numbers of antenna elements and delays. We present the results of a detailed simulation study that compares our algorithms to several benchmarks. Our study investigates the effect of SNR, training length, training type, ADC resolution, and runtime on channel estimation MSE, mutual information, and achievable rate. It shows that our methods allow one-bit ADCs to perform comparably to infinite-bit ADCs at low SNR, and 4-bit ADCs to perform comparably to infinite-bit ADCs at medium SNR.

• The paper presents EM-enhanced AMP methods to solve the channel estimation problem in mmWave MIMO systems using noisy quantized compressed sensing.
• Simulation results reveal that 1-bit and 4-bit ADCs achieve near-optimal MSE and rates at low and medium SNRs, respectively.
• The study demonstrates a scalable, power-efficient approach that can reduce system costs and facilitate practical mmWave communication deployments.

Overview of Channel Estimation in Broadband Millimeter Wave MIMO Systems with Few-Bit ADCs

The paper under review addresses the challenge of channel estimation in broadband millimeter wave (mmWave) multiple input multiple output (MIMO) systems employing low-resolution, few-bit analog-to-digital converters (ADCs). This work is premised on the observation that mmWave communications hold great potential for future cellular systems due to their high bandwidth capabilities, yet they place significant demands on receiver components and particularly on ADCs.

Problem Formulation and Technical Approach

The central contribution of the work is the formulation of the channel estimation problem in such systems as a noisy quantized compressed-sensing problem. This is motivated by the sparsity present in mmWave channels concerning the angle and delay domains, which the authors exploit. Specifically, they leverage Approximate Message Passing (AMP) algorithms, and their variants, Generalized AMP (GAMP) and Vector AMP (VAMP), enhanced with Expectation-Maximization (EM) to estimate the MIMO channel. These algorithms facilitate the computation of approximately minimum mean-squared error (MMSE) estimates while simultaneously learning the distributional parameters necessary for the estimation process.

Key Findings and Models

The paper is grounded in detailed simulations comparing the performance of the proposed methods across various ADC resolutions, training sequences, and channel conditions. Notably, the results demonstrate that 1-bit ADCs can perform comparably to infinite-bit ADCs in terms of MSE and achievable rates at low SNRs, whereas 4-bit ADCs achieve similar performance at medium SNRs. These findings highlight the efficiency of the proposed methods in compensating for the limited resolution typical of low-powered ADC implementations, which are becoming increasingly relevant in portable devices.

The algorithms introduced, namely EM-GAMP and EM-VAMP, are distinctly beneficial due to their ability to operate without a requirement for a detailed prior on channel distributions and their scalability to large antenna array configurations typical of mmWave systems.

Implication and Future Directions

The theoretical underpinnings and empirical evaluations laid out in this paper have several important implications for the design and deployment of future mmWave communication systems. Practically, the adoption of few-bit ADCs could lead to significant reductions in power and cost, making these systems feasible for wide-scale deployment. Theoretically, the paper reinforces the utility of probabilistic frameworks, such as AMP, to handle the complexity and dimensionality of real-world communication systems efficiently.

Future research could explore the impact of channel correlation, as the proposed models assume IID components. Addressing such correlation could further enhance channel estimation accuracy. Additionally, investigation into the combination of spatial correlation with the temporal and spectral sparsity merits attention, which could yield robust estimation strategies in varied and dynamic environments.

Conclusion

Overall, this paper offers a meaningful contribution to mmWave MIMO system development, particularly in its novel approach to channel estimation with few-bit ADCs. It not only advances the state-of-the-art in computational techniques for channel estimation but also provides a pragmatic pathway for improving system efficiency in real-world deployments. This aligns with the broader trajectory of research and development in expansive wireless communication paradigms.