We study the generalized degrees of freedom (gDoF) of the block-fadingnoncoherent2-user interference channel (IC) with a coherence time of$T$symbol durations and symmetric fading statistics. We demonstrate that a standard training-based scheme for the noncoherent IC is suboptimal in several regimes. We study and analyze several alternate schemes: the first is a new noncoherent scheme using rate-splitting. We also consider a scheme that treats interference-as-noise (TIN) and a time division multiplexing (TDM) scheme. We show that a standard training-based scheme for the noncoherent IC is outperformed by one of these schemes in several regimes: our results demonstrate that in the very weak interference regime, the TIN scheme is the best; in the strong interference regime, the TDM scheme and the noncoherent rate-splitting scheme give better performance; in other cases either of the TIN, TDM or noncoherent rate-splitting scheme could be preferred. We also study the noncoherent IC with feedback and propose another noncoherent rate-splitting scheme. Again for the feedback case, our results demonstrate that a standard training-based scheme can be outperformed by other schemes.

We study the generalized degrees of freedom (gDoF) of block-fading noncoherent multiple input multiple output (MIMO) channels with asymmetric distributions of link strengths and a coherence time of T symbol durations. We derive the optimal signaling structure for communication for the asymmetric MIMO channel, which is distinct from that for the MIMO channel with independent and identically distributed (i.i.d.) links. We extend the existing results for the single input multiple output (SIMO) channel with i.i.d. links to the asymmetric case, proving that selecting the statistically best antenna is gDoFoptimal. Using the gDoF result for the SIMO channel, we prove that for T = 1, the gDoF is zero for MIMO channels with arbitrary link strengths. We show that selecting the statistically best antenna is gDoF-optimal for the multiple input single output (MISO) channel. We also derive the gDoF for the 2 x 2 MIMO channel with different exponents in the direct and cross links. In this setting, we show that it is always necessary to use both the antennas to achieve the gDoF, in contrast to the results for the 2 x 2 MIMO channel with i.i.d. links. We show that having weaker crosslinks, gives gDoF gain compared to the case with i.i.d. links. For the noncoherent MIMO channel with i.i.d. links, the traditional method of training each transmit antenna independently is degrees of freedom (DoF) optimal, whereas we observe that for the asymmetric 2 x 2 MIMO channel, the traditional training is not gDoF-optimal. We extend this observation to a larger MxM MIMO channel by demonstrating a strategy that can achieve larger gDoF than a traditional trainingbased method.

We study the generalized degrees of freedom (gDoF) of the noncoherent diamond (parallel relay) wireless network with asymmetric distributions of link strengths. We use the noncoherent block-fading model introduced by Marzetta and Hochwald, where no channel state information is available at the transmitters or at the receivers and the channels remain constant for a coherence time of T symbol durations. We first derive an upper bound for the capacity of this channel and then derive the optimal structure for the solution of the upper bound optimization problem. Using the optimal structure, we solve the upper bound optimization problem in terms of its gDoF. Using insights from our upper bound signaling solution, we devise an achievability strategy based on a novel scheme that we call train-scale quantize-map-forward (TS-QMF). This scheme uses training in the links from the source to the relays, scaling and quantizing at the relays combined with nontraining-based schemes. We show the optimality of this scheme by comparing it to the upper bound in terms of the gDoF. In noncoherent point-to-point multiple-input-multiple-output (MIMO) channels, where the fading realization is unknown to the transmitter and the receiver, an important tradeoff between communication and channel learning was revealed by Zheng and Tse, by demonstrating that not all the available antennas might be used, as it is suboptimal to learn all their channel parameters. Our results in this paper for the diamond network demonstrate that in certain regimes of relative channel strengths, the gDoF-optimal scheme uses a subnetwork, demonstrating a similar tradeoff between channel learning and communication. In some regimes, it is gDoF-optimal to do relay selection, i.e., use a part of the network. In the other regimes, even when it is essential to use the entire network, it is suboptimal to learn the channel states for all the links in the network, i.e., traditional training-based schemes are suboptimal in these regimes.

We develop a characterization of fading models, which assigns a number called logarithmic Jensen's gap to a given fading model. We show that as a consequence of a finite logarithmic Jensen's gap, an approximate capacity region can be obtained for fast fading interference channels (FF-ICs) for several scenarios. We illustrate three instances where a constant capacity gap can be obtained as a function of the logarithmic Jensen's gap. First, for an FF-IC with neither feedback nor instantaneous channel state information at transmitter (CSIT), if the fading distribution has finite logarithmic Jensen's gap, we show that a rate-splitting scheme based on the average interference-to-noise ratio can achieve its approximate capacity. Second, we show that a similar scheme can achieve the approximate capacity of FF-IC with feedback and delayed CSIT, if the fading distribution has finite logarithmic Jensen's gap. Third, when this condition holds, we show that point-to-point codes can achieve approximate capacity for a class of FF-ICs with feedback. We prove that the logarithmic Jensen's gap is finite for common fading models, including Rayleigh and Nakagami fading, thereby obtaining the approximate capacity region of FF-IC with these fading models.

We study the generalized degrees of freedom (gDoF) of the block-fading noncoherent MIMO channel with asymmetric distributions of link strengths, and a coherence time of T symbol durations. We first derive the optimal signaling structure for communication over this channel, which is distinct from that for the i.i.d MIMO setting. We prove that for T = 1, the gDoF is zero for MIMO channels with arbitrary link strength distributions, extending the result for MIMO with i.i.d links. We then show that selecting the statistically best antenna is gDoF-optimal for both Multiple Input Single Output (MISO) and Single Input Multiple Output (SIMO) channels. We also derive the gDoF for the 2×2 MIMO channel with different exponents in the direct and cross links. In this setting, we show that it is always necessary to use both antennas to achieve the optimal gDoF, in contrast to the results for 2 × 2 MIMO with identical link distributions. We also show that having weaker crosslinks gives gDoF gain compared to the case with identically distributed links.

Superposition codes with rate-splitting have been used for all approximately optimal strategies for the interference channel, with and without feedback. As rate-splitting requires fore-knowledge of channel parameters or statistics, in this paper we explore schemes for the interference channel (with feedback) that do not use superposition or rate-splitting. We demonstrate that point-to-point codes designed for inter-symbol-interference channels, along with time-sharing can approximately achieve the entire rate region of the interference channel with feedback. We show that such a scheme also approximately achieves the rate-region for the interference channel with fading, for a large class of fading distributions.

Multiple relay selection enables a cooperative system to obtain better performance than single relay selection and yet avoid challenging problems such as synchronization that are associated with having all the relays transmit. While its benefits have been well characterized, the problem of developing distributed, scalable schemes that discover the best subset of relays remains to be fully investigated. The problem is challenging because the relays are spatially separated from each other and have only local channel knowledge. We investigate the popular, low feedback, and distributed timer scheme and derive a novel, optimal timer mapping that maximizes the probability of selecting the best two relays. This has applications in several cooperative schemes proposed in the literature. We derive several novel structural properties about the optimal mapping, which reduce the complexity of finding it from the large space of all functions to a one-dimensional search that can be solved using a computationally efficient, iterative algorithm. Our extensive benchmarking shows that the optimal mapping outperforms several relay discovery schemes proposed in the literature. The approach can be generalized to selecting the best l relays, as well.