Integer-Forcing Linear Receivers (1003.5966v4)

Abstract: Linear receivers are often used to reduce the implementation complexity of multiple-antenna systems. In a traditional linear receiver architecture, the receive antennas are used to separate out the codewords sent by each transmit antenna, which can then be decoded individually. Although easy to implement, this approach can be highly suboptimal when the channel matrix is near singular. This paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer-valued entries. Rather than attempting to recover transmitted codewords directly, the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix. The codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords. Provided that the effective channel is full rank, these integer combinations can then be digitally solved for the original codewords. This paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter(s), which corresponds either to a multi-user uplink scenario or to single-user V-BLAST encoding. In this setting, the proposed integer-forcing linear receiver significantly outperforms conventional linear architectures such as the zero-forcing and linear MMSE receiver. In the high SNR regime, the proposed receiver attains the optimal diversity-multiplexing tradeoff for the standard MIMO channel with no coding across transmit antennas. It is further shown that in an extended MIMO model with interference, the integer-forcing linear receiver achieves the optimal generalized degrees-of-freedom.

• The paper introduces the integer-forcing linear receiver that decodes integer-valued linear combinations to overcome ZF and MMSE limitations.
• The paper demonstrates superior diversity-multiplexing tradeoff and optimal degrees-of-freedom performance at high SNRs in MIMO channels.
• The paper offers a practical decoding solution that reduces complexity while achieving near-optimal performance without joint ML processing.

Integer-Forcing Linear Receivers

The paper "Integer-Forcing Linear Receivers" presents a novel approach to linear receiver architectures for multiple input, multiple output (MIMO) systems, focusing particularly on the integer-forcing technique. The central objective of the paper is to address the limitations of conventional linear receivers, such as zero-forcing (ZF) and minimum mean square error (MMSE), which can be suboptimal under certain channel conditions, especially when the channel matrix is near-singular.

Overview and Contributions

The proposed integer-forcing receiver architecture utilizes receive antennas to construct an effective channel matrix with integer-valued entries. This is a departure from typical linear architectures, where the system attempts to individually decode codewords from transmitted streams. Instead, the integer-forcing receiver first recovers linear combinations of the codewords, corresponding to the entries of the effective channel matrix. These linear combinations, guaranteed to be codewords themselves, can be solved digitally to retrieve the original data streams, provided that the matrix is full-rank.

This approach is particularly geared towards scenarios involving no coding across transmit antennas and where channel state information (CSI) is only available at the receiver end. Such scenarios include multiuser uplink systems or single-user systems utilizing vertical Bell Labs layered space-time (V-BLAST) encoding.

Numerical Results and Analysis

The paper demonstrates that the integer-forcing receiver yields superior performance compared to conventional linear receivers like ZF and linear MMSE in terms of achieving the optimal diversity-multiplexing tradeoff (DMT) at high signal-to-noise ratios (SNR) for the standard MIMO channel setup. Furthermore, integer-forcing has been shown to achieve optimal generalized degrees-of-freedom in extended MIMO models that include interference.

Practical Implications

From a practical standpoint, the integer-forcing architecture offers significant advantages for implementing MIMO systems where the complexity and performance of joint ML decoders are prohibitive. By optimizing the selection of an integer matrix suitable for the particular channel conditions, the architecture balances the tradeoff between performance and complexity, thus extending the capacity achievable through linear receivers without the need for complex coding strategies.

Theoretical Implications and Future Directions

Theoretically, the paper's findings suggest new avenues for further exploration in the context of receiver architectures for complex MIMO scenarios, including those influenced by high-dimensional interference. It calls into question the conventional approach to linear decoding and provides a foundation for future research aimed at bridging the performance gap between linear receivers and optimal decoding schemes.

The future exploration of integer-forcing might focus on:

• Enhancing algorithmic strategies for faster and more efficient determination of full-rank integer matrices.
• Investigating the integration of this architecture into systems with complex or spatially distributed antennas.
• Exploring the use of this technique in scenarios with imperfect or partial CSI.

In conclusion, this work presents a significant contribution to the development of linear receiver architectures, introducing an approach that promises improved performance metrics in various MIMO configurations while remaining practical for real-world implementation.