Estimation of Sparse MIMO Channels with Common Support (1107.1339v1)

Abstract: We consider the problem of estimating sparse communication channels in the MIMO context. In small to medium bandwidth communications, as in the current standards for OFDM and CDMA communication systems (with bandwidth up to 20 MHz), such channels are individually sparse and at the same time share a common support set. Since the underlying physical channels are inherently continuous-time, we propose a parametric sparse estimation technique based on finite rate of innovation (FRI) principles. Parametric estimation is especially relevant to MIMO communications as it allows for a robust estimation and concise description of the channels. The core of the algorithm is a generalization of conventional spectral estimation methods to multiple input signals with common support. We show the application of our technique for channel estimation in OFDM (uniformly/contiguous DFT pilots) and CDMA downlink (Walsh-Hadamard coded schemes). In the presence of additive white Gaussian noise, theoretical lower bounds on the estimation of SCS channel parameters in Rayleigh fading conditions are derived. Finally, an analytical spatial channel model is derived, and simulations on this model in the OFDM setting show the symbol error rate (SER) is reduced by a factor 2 (0 dB of SNR) to 5 (high SNR) compared to standard non-parametric methods - e.g. lowpass interpolation.

• The paper introduces the Sparse Common Support FRI (SCS-FRI) algorithm, a parametric estimation technique generalizing spectral methods for multiple inputs with common support, showing significant performance gains in simulations.
• Theoretical analysis uses the Fisher Information Matrix to derive and analyze Cramér-Rao bounds for estimating channel parameters under Rayleigh fading conditions with discrete multiple paths.
• The proposed SCS model and SCS-FRI algorithm are applicable to OFDM and CDMA systems, demonstrating substantial reduction in Symbol Error Rate and allowing estimation with fewer pilots for increased data throughput.

Overview of Estimation of Sparse MIMO Channels with Common Support

This paper introduces a novel method for estimating sparse Multiple Input Multiple Output (MIMO) communication channels that share a common support. In current communication standards such as those governing OFDM and CDMA systems, channels exhibit sparse properties while sharing a support set. The core advancement presented in the paper is the development of a parametric sparse estimation technique which draws on finite rate of innovation (FRI) principles, providing robust estimation and a concise description of channels in MIMO systems.

Main Contributions

1. SCS-FRI Algorithm: The authors propose the Sparse Common Support FRI (SCS-FRI) algorithm, which generalizes spectral estimation methods to handle multiple input signals with common support. This algorithm is computationally efficient and shows substantial performance gains in simulations, particularly when applied to OFDM channel estimation.
2. Theoretical Analysis: The paper explores the theoretical lower bounds concerning the estimation accuracy of SCS channel parameters under Rayleigh fading conditions. The Fisher Information Matrix approach is applied to derive and analyze Cramér-Rao bounds for channels having discrete multiple paths.
3. Model Applications: The SCS model is shown to be applicable in OFDM systems characterized by contiguous DFT pilots and CDMA downlink scenarios with Walsh-Hadamard coded schemes. The findings demonstrate a considerable reduction in Symbol Error Rate (SER), by factors ranging from 2 to 5, compared to standard non-parametric methods like lowpass interpolation.
4. Analytical Spatial Channel Model: An analytical model is proposed and validated through simulations. The model accurately characterizes spatial correlations, providing a useful framework for the paper of channels in multi-output systems.

Numerical Results and Implications

Simulations demonstrate the significant efficiency of the SCS-FRI algorithm. It excels in scenarios with exact sparse common support, showcasing improved resilience to noise and enhanced accuracy in estimating Time of Arrival (ToA) compared to traditional methods. The robustness of the algorithm to non-exact SCS channels (where the common support only approximately holds) is also verified.

For multipoint communication frameworks, the paper elaborates on spatial diversity as a means to gain robustness in channel estimation. Importantly, the proposed model allows the estimation of fewer necessary pilots, enhancing data throughput under favorable conditions.

Future Directions

The findings entail several implications for both practical applications and theoretical research in wireless communications. For practical scenarios, the possibility of increased throughput due to reduced pilot overhead offers significant benefits. On the theoretical side, the paper suggests avenues for further exploration in model order estimation, the inclusion of temporal correlation, and improved computational robustness through advanced subspace methods.

In conclusion, the paper presents a well-grounded approach to sparse channel estimation in MIMO systems which promises to enhance communication efficiency and accuracy. It opens pathways for further investigations into the reduction of pilot requirements and leveraging spatial diversity in complex wireless environments.