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On the Capacity of Noncoherent Wireless Networks


Wireless networks are characterized by variation in the network states. In practice the variations are combated by allocating resources for learning the network states. In networks with high mobility users, the variations are fast enough so that allocating separate resources may significantly deplete the resources and quality of communication. In this thesis we study the optimal schemes for nonchoherent networks, where the network channel states are unknown and are changing within given time periods. We address the question on how to optimally allocate the resources for training and communication.

In the first part of the thesis, we consider single flow noncoherent wireless networks, where there is a single information source and a single destination. A simple nontrivial version of this is the noncoherent multiple input multiple output (MIMO) network. We consider the noncoherent MIMO with asymmetric link strengths, which would arise when the antennas are well separated. Examples of this are in the 5G architecture where the basestations can cooperate through a backhaul and when there is device-to-device cooperation through a sidechannel. The study of noncoherent MIMO is also fundamental in understanding the nature of noncoherent networks in the sense that the cut-sets in noncoherent networks form a MIMO. We prove that for single input multiple output (SIMO) and multiple input single input (MISO) networks, it is optimal to use the statistically best antenna. For 2x2 MIMO with symmetric statistics i.e., the direct links have identical statistics and so do the cross links, we derive the generalized degrees of freedom (gDoF) and prove that training-based schemes are not optimal. For larger MxM MIMO we prove that in general, a training scheme that learns all the channel parameters is not optimal in gDoF measure. We then proceed to study the noncoherent diamond network (2-relay channel). We prove that in certain regimes it is optimal to perform a relay selection and operate the network. In other regimes where we need to operate both the relays, it is not optimal to learn all the channel states through training. We propose a novel scheme that partially trains the network and combine it with scaling at the relays and quantize-map-forward operation and prove that our scheme is gDoF optimal.

In the second part of the thesis, we consider multiple flow noncoherent wireless networks. We specifically consider the noncoherent 2-user interference channel, where both the transmitters and the receivers do not know the channels strengths, but the statistics are known. For studying this, we first consider the fast fading interference channel (FF-IC) where the transmitters do not know the channel, but the receivers do know the channel. We extend the existing rate-splitting schemes when the channels are known at the receivers, to the fast fading case by performing rate-splitting based on the statistics of the channel. We prove that this scheme achieves the capacity approximately for a wide range of fading models. With this result for the FF-IC, we proceed to the noncoherent IC. We propose a noncoherent scheme with rate-splitting based on the statistics of the channel. We prove that this schemes achieves higher gDoF than a training-based scheme. The results extend to the case of noncoherent IC with feedback, where the outputs at the receivers are fed back to the corresponding transmitter.

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