Perfect Output Feedback in the Two-User Decentralized Interference Channel

In this paper, the $\eta$-Nash equilibrium ($\eta$-NE) region of the two-user Gaussian interference channel (IC) with perfect output feedback is approximated to within $1$ bit/s/Hz and $\eta$ arbitrarily close to $1$ bit/s/Hz. The relevance of the $\eta$-NE region is that it provides the set of rate-pairs that are achievable and stable in the IC when both transmitter-receiver pairs autonomously tune their own transmit-receive configurations seeking an $\eta$-optimal individual transmission rate. Therefore, any rate tuple outside the $\eta$-NE region is not stable as there always exists one link able to increase by at least $\eta$ bits/s/Hz its own transmission rate by updating its own transmit-receive configuration. The main insights that arise from this work are: $(i)$ The $\eta$-NE region achieved with feedback is larger than or equal to the $\eta$-NE region without feedback. More importantly, for each rate pair achievable at an $\eta$-NE without feedback, there exists at least one rate pair achievable at an $\eta$-NE with feedback that is weakly Pareto superior. $(ii)$ There always exists an $\eta$-NE transmit-receive configuration that achieves a rate pair that is at most $1$ bit/s/Hz per user away from the outer bound of the capacity region.Comment: Revised version (Aug. 2015

Symmetric Decentralized Interference Channels with Noisy Feedback

International audienceIn this paper, all the rate-pairs that are achievable at a Nash equilibrium (NE) in the two-user linear deterministic symmetric decentralized interference channel (LD-S-DIC) with noisy feedback are identified. More specifically, the Nash region (NR) of the LD-S-DIC with noisy feedback is fully characterized. The relevance of these rate-pairs is that once they are achieved by using NE transmit-receive configurations, none of the transmitter-receiver pairs can increase their individual rates by unilaterally changing their configurations. More importantly, it is shown that the NR of the LD-S-DIC with noisy feedback is larger than the NR of the LD-S-DIC without feedback only in certain cases. When interference is stronger than the desired signals, a larger NR is observed only if the signal to noise ratios (SNRs) of the feedback links are higher than the SNRs of the direct links. Conversely, when desired signals are stronger than interference, a larger NR is observed only if the SNRs of the feedback links are higher than both the signal to interference ratios (SIRs) and the interference to noise ratios (INRs) of the direct links. Previous results, namely the NE region of the two-user LD-S-DIC without feedback and with perfect output feedback are obtained as special cases of the results presented in this contribution

Noisy Channel-Output Feedback Capacity of the Linear Deterministic Interference Channel

In this paper, the capacity region of the two-user linear deterministic (LD) interference channel with noisy output feedback (IC-NOF) is fully characterized. This result allows the identification of several asymmetric scenarios in which imple- menting channel-output feedback in only one of the transmitter- receiver pairs is as beneficial as implementing it in both links, in terms of achievable individual rate and sum-rate improvements w.r.t. the case without feedback. In other scenarios, the use of channel-output feedback in any of the transmitter-receiver pairs benefits only one of the two pairs in terms of achievable individual rate improvements or simply, it turns out to be useless, i.e., the capacity regions with and without feedback turn out to be identical even in the full absence of noise in the feedback links.Comment: 5 pages, 9 figures, see proofs in V. Quintero, S. M. Perlaza, and J.-M. Gorce, "Noisy channel-output feedback capacity of the linear deterministic interference channel," INRIA, Tech. Rep. 456, Jan. 2015. This was submitted and accepted in IEEE ITW 201

Nash Region of the Linear Deterministic Interference Channel with Noisy Output Feedback

In this paper, the $\eta$-Nash equilibrium ($\eta$-NE) region of the two-user linear deterministic interference channel (IC) with noisy channel-output feedback is characterized for all $\eta > 0$. The $\eta$-NE region, a subset of the capacity region, contains the set of all achievable information rate pairs that are stable in the sense of an $\eta$-NE. More specifically, given an $\eta$-NE coding scheme, there does not exist an alternative coding scheme for either transmitter-receiver pair that increases the individual rate by more than $\eta$ bits per channel use. Existing results such as the $\eta$-NE region of the linear deterministic IC without feedback and with perfect output feedback are obtained as particular cases of the result presented in this paper.Comment: 5 pages, 2 figures, to appear in ISIT 201

Cooperative Feedback for MIMO Interference Channels

Multi-antenna precoding effectively mitigates the interference in wireless networks. However, the precoding efficiency can be significantly degraded by the overhead due to the required feedback of channel state information (CSI). This paper addresses such an issue by proposing a systematic method of designing precoders for the two-user multiple-input-multiple-output (MIMO) interference channels based on finite-rate CSI feedback from receivers to their interferers, called cooperative feedback. Specifically, each precoder is decomposed into inner and outer precoders for nulling interference and improving the data link array gain, respectively. The inner precoders are further designed to suppress residual interference resulting from finite-rate cooperative feedback. To regulate residual interference due to precoder quantization, additional scalar cooperative feedback signals are designed to control transmitters' power using different criteria including applying interference margins, maximizing sum throughput, and minimizing outage probability. Simulation shows that such additional feedback effectively alleviates performance degradation due to quantized precoder feedback.Comment: 5 pages; submitted to IEEE ICC 201

Downlink SDMA with Limited Feedback in Interference-Limited Wireless Networks

The tremendous capacity gains promised by space division multiple access (SDMA) depend critically on the accuracy of the transmit channel state information. In the broadcast channel, even without any network interference, it is known that such gains collapse due to interstream interference if the feedback is delayed or low rate. In this paper, we investigate SDMA in the presence of interference from many other simultaneously active transmitters distributed randomly over the network. In particular we consider zero-forcing beamforming in a decentralized (ad hoc) network where each receiver provides feedback to its respective transmitter. We derive closed-form expressions for the outage probability, network throughput, transmission capacity, and average achievable rate and go on to quantify the degradation in network performance due to residual self-interference as a function of key system parameters. One particular finding is that as in the classical broadcast channel, the per-user feedback rate must increase linearly with the number of transmit antennas and SINR (in dB) for the full multiplexing gains to be preserved with limited feedback. We derive the throughput-maximizing number of streams, establishing that single-stream transmission is optimal in most practically relevant settings. In short, SDMA does not appear to be a prudent design choice for interference-limited wireless networks.Comment: Submitted to IEEE Transactions on Wireless Communication

Cooperative Precoding with Limited Feedback for MIMO Interference Channels

Multi-antenna precoding effectively mitigates the interference in wireless networks. However, the resultant performance gains can be significantly compromised in practice if the precoder design fails to account for the inaccuracy in the channel state information (CSI) feedback. This paper addresses this issue by considering finite-rate CSI feedback from receivers to their interfering transmitters in the two-user multiple-input-multiple-output (MIMO) interference channel, called cooperative feedback, and proposing a systematic method for designing transceivers comprising linear precoders and equalizers. Specifically, each precoder/equalizer is decomposed into inner and outer components for nulling the cross-link interference and achieving array gain, respectively. The inner precoders/equalizers are further optimized to suppress the residual interference resulting from finite-rate cooperative feedback. Further- more, the residual interference is regulated by additional scalar cooperative feedback signals that are designed to control transmission power using different criteria including fixed interference margin and maximum sum throughput. Finally, the required number of cooperative precoder feedback bits is derived for limiting the throughput loss due to precoder quantization.Comment: 23 pages; 5 figures; this work was presented in part at Asilomar 2011 and will appear in IEEE Trans. on Wireless Com