Towards characterizing the capacity of the building block of MANETs Non-Coherent Multipath Fading Relay Networks in the Wideband Regime – Fawaz, Medard IMPACT NEXT-PHASE GOALS ACHIEVEMENT DESCRIPTION STATUS QUO NEW INSIGHTS MAIN ACHIEVEMENT: HOW IT WORKS: Source: Low-duty cycle peaky FSK signaling Relay: Decode, Frequency Binning and Forward Destination: decodes relayed signal, then source signal using relayed information ASSUMPTIONS AND LIMITATIONS: Wideband regime Relay decodes fully Achievable rate in non-coherent multipath fading relay channel coincides with generalized block-Markov lower bound of AWGN-FD channel -> LB coincides with cut-set upper-bound for -> Capacity Non-coherent peaky frequency binning scheme Min-cut on hypergraph model Capacity of general relay channel unknown • Bounds on general relay channel • Bounds on AWGN relay channel Wideband regime: not interference-limited, but energy-limited point-to-point: Hypergraph Model: min-cut on hypergraph What technical challenge is being undertaken on behalf of the project This work aims at characterizing the capacity of the multipath fading relay channel in the Low SNR/wideband regime, known to be energy-limited but not interference-limited. 2. Why is it hard and what are the open problems The capacity of the general relay channel is still an open problem, although it is a 3-node network and the smallest building block of a MANET. In the low SNR regime, when the band grows large, the relay capabilities are limited by its finite power: the relay cannot make its observation fully available to the destination. Thus, obtaining virtual MIMO gains in the wideband regime is not an obvious possibility. 3. How has this problem been addressed in the past Wideband regime: the capacity of the point-to-point AWGN channel, and the point-to-point multipath fading channel is known to be equal to the received SNR. The power should not be spread, on the contrary, the capacity is achieved by peaky signaling. Relay channels: Upper and lower bounds were given for the general relay channel, and in particular the AWGN channel. A plethora of cooperative strategies have provided achievable rates for relaying networks in the high SNR regime. However, the capacity of the multipath fading relay channel in the low SNR/wideband regime is unknown, and no comparison was established with the bounds on the capacity of the wideband AWGN, as in the point-to-point case. 4. What new intellectual tools are being brought to bear on the problem A hypergraph model is proposed. Peaky signaling schemes known to be optimal in the wideband point-to-point fading channel are combined with frequency binning, in order to achieve the hypergraph min-cut. 5. What is the main intermediate achievement Providing a lower bound on the capacity of the non-coherent multipath fading channel in the wideband regime, and comparing it with the cut-set upper-bound and known lower bounds for the AWGN channel. 6. How and when does this achievement align with the project roadmap (end-of-phase or end-of-project goal) This work aligns with Phase 3 progress criteria: Revolutionize upper bounding techniques through new and different approaches that go beyond the classical MIN-CUT bounds and Fano's inequality that have dominated capacity bounds for the last several decades. Determine the optimal channel/network "coding" that achieves these capacity upper bounds when possible, and characterize for which classes of networks gaps still exist between achievability and upper bounds, and why. 7. What are the even long-term objectives and consequences? The hypergraph model may help giving bounds on the capacity of larger relaying networks in the wideband regime. The power limitation on the relay capabilities when the band grows large raises the question of whether virtual MIMO gains are actually achievable in the wideband regime of the relay channel. 8. Which thrusts and SOW tasks does this contribution fit under and why? This work is part of thrust 1: New Paradigms for Upper Bounds. Extension to larger networks: multiple relays, layers... Open question: closing the gap to Cut-set UB? Virtual MIMO gain in the wideband regime? Towards characterizing the capacity of the building block of MANETs