Interference Alignment Under Limited Feedback for MIMO Interference Channels (0911.5509v1)

Abstract: While interference alignment schemes have been employed to realize the full multiplexing gain of $K$-user interference channels, the analyses performed so far have predominantly focused on the case when global channel knowledge is available at each node of the network. This paper considers the problem where each receiver knows its channels from all the transmitters and feeds back this information using a limited number of bits to all other terminals. In particular, channel quantization over the composite Grassmann manifold is proposed and analyzed. It is shown, for $K$-user multiple-input, multiple-output (MIMO) interference channels, that when the transmitters use an interference alignment strategy as if the quantized channel estimates obtained via this limited feedback are perfect, the full sum degrees of freedom of the interference channel can be achieved as long as the feedback bit rate scales sufficiently fast with the signal-to-noise ratio. Moreover, this is only one extreme point of a continuous tradeoff between achievable degrees of freedom region and user feedback rate scalings which are allowed to be non-identical. It is seen that a slower scaling of feedback rate for any one user leads to commensurately fewer degrees of freedom for that user alone.

• The paper demonstrates that with appropriately scaled feedback, full degrees of freedom are maintained in K-user MIMO interference channels.
• It introduces a novel channel quantization method over the composite Grassmann manifold to mitigate limited CSIT challenges.
• The analysis confirms that a feedback bit rate proportional to signal power is crucial for optimal interference alignment performance.

Interference Alignment Under Limited Feedback for MIMO Interference Channels

This paper explores the application of interference alignment (IA) techniques in the context of $K$-user multiple-input multiple-output (MIMO) interference channels, particularly when channels are constrained by limited feedback. The authors propose a method that involves channel quantization over a composite Grassmann manifold to address the challenges posed by limited channel state information at the transmitter (CSIT). The core premise is that, even with limited feedback, it is possible to achieve the full sum degrees of freedom of an interference channel, provided that feedback rates scale appropriately with the signal-to-noise ratio (SNR).

Key Contributions

The paper's main contributions are twofold:

1. Quantization Over Composite Grassmann Manifold: The paper suggests quantizing channels over the composite Grassmann manifold, a strategy that enables each receiver to feed back quantized channel information using a limited number of bits. This quantized information is then used by transmitters to align interference as if perfect channel knowledge were available.
2. Scalability of Feedback Rates: An analysis is provided showing that full degrees of freedom can be maintained if the feedback bit rate scales with the SNR. Specifically, they show a scaling relationship where the feedback bit rate must be proportional to the product of signal power factors.

Analytical Results

For $K$-user MIMO channels, if the feedback rate scales as $N_f\ =\ {\min \{M_t,M_r \} }^2 K(RL - 1) \log P$, where $M_t$ and $M_r$ are the number of transmit and receive antennas, respectively, and $P$ is the power, the IA strategy can achieve the maximal degrees of freedom originally proposed by Cadambe and Jafar. More generalized results are disclosed for SIMO and MISO systems, with a detailed derivation regarding how feedback quantization impacts the interference alignment performance.

Implications

From a theoretical perspective, this research broadens the understanding of how feedback limitations affect interference management in wireless networks. Practically, this implies that even with limited feedback resources, network throughput close to optimal can be achieved, thus promoting efficient utilization of spectral resources. Experimental confirmation of these results could influence future designs of cellular networks where inter-cell interference is a significant concern.

Future Directions

This research opens avenues for further exploration into optimizing feedback strategies, especially in dynamic environments like those with varying interference patterns or in networks with heterogeneous architectures. The methodology could also be extended and tested within alternative system models, such as time-varying channels, to understand the limitations and capabilities of interference alignment in more realistic settings.

In conclusion, the authors provide substantial insights into the trade-offs between feedback rates and achievable degrees of freedom in MIMO interference channels. This work could spur significant advancements in designing systems with limited channel information, effectively balancing performance with practical limitations inherent to real-world wireless communications.