Using ideas from Generalized Degrees of Freedom (GDoF) analyses and extremal network theory, this work studies the extremal gain of optimal power control over binary (on/off) power control, especially in large interference networks, in search of new theoretical insights. Whereas numerical studies have already established that in most practical settings binary power control is close to optimal, the extremal analysis shows not only that there exist settings where the gain from optimal power control can be quite significant, but also bounds the extremal values of such gains from a GDoF perspective. As its main contribution, this work explicitly characterizes the extremal GDoF gain of optimal over binary power control as$\Theta (\sqrt {K})$for all$K$. In particular, the extremal gain is bounded between$\lfloor \sqrt {K}\rfloor $and$2.5\sqrt {K}$for every$K$. For$K=2,3,4,5,6$users, the precise extremal gain is found to be 1, 3/2, 2, 9/4 and 41/16, respectively. Networks shown to achieve the extremal gain may be interpreted as multi-tier heterogeneous networks. It is worthwhile to note that because of their focus on asymptotic analysis, the sharp characterizations of extremal gains are valuable primarily from a theoretical perspective, and not as contradictions to the conventional wisdom that binary power control is generally close to optimal in practical, non-asymptotic settings.

In order to discover larger networks and parameter regimes where sharp Generalized Degrees of Freedom (GDoF) characterizations may be found based on the optimality of robust schemes for interference and broadcast networks with channel state information at the transmitters (CSIT) limited to finite precision, we explore the impact of secrecy constraints. In the absence of secrecy constraints, the largest such parameter regime for$K$user interference networks is the CTIN regime (so named for theConvexity of the GDoF region achieved by Treating Interference as Noise (TIN)) originally discovered by Yi and Caire, whose optimality was established by Chanet al.For the corresponding broadcast networks the largest regime is the SLS (Simple Layered Superposition) regime discovered by Davoodi and Jafar, but only for small networks with$K\leq 3$users. By including secrecy constraints, we identify much larger regimes, the STIN regime and the SLS regime, where GDoF are fully characterized for arbitrary number of users under finite precision CSIT, for interference networks and broadcast networks, respectively. The optimal achievable scheme in both cases is based on TIN along with power control and jamming. Proofs of optimality rely on a combination of secrecy constraints and Aligned Images sum-set inequalities.

In this paper, we study probabilistic time-of-arrival (ToA) and angle-of-arrival (AoA) joint localization in real indoor environments. To mitigate the effects of multipath propagation, the joint localization algorithm incorporates into the likelihood function Gaussian mixture models (GMM) and the Von Mises-Fisher distribution to model time bias errors and angular uncertainty, respectively. We evaluate the algorithm performance using a proprietary prototype deployed in an indoor factory environment with infrastructure receivers in each of the four corners at the ceiling of a 10 meter by 20 meter section. The field test results show that our joint probabilistic localization algorithm significantly outperforms baselines using only ToA or AoA measurements and achieves 2-D sub-meter accuracy at the 90%-ile. We also numerically demonstrate that the joint localization algorithm is more robust to synchronization errors than the baseline using ToA measurements only.

The robust principles of treating interference as noise (TIN) when it is sufficiently weak, and avoiding it when it is not, form the background of this work. Combining TIN with the topological interference management (TIM) framework that identifies optimal interference avoidance schemes, we formulate a TIM-TIN problem for multilevel topological interference management, wherein only a coarse knowledge of channel strengths and no knowledge of channel phases is available to transmitters. To address the TIM-TIN problem, we first propose an analytical baseline approach, which decomposes a network into TIN and TIM components, allocates the signal power levels to each user in the TIN component, allocates signal vector space dimensions to each user in the TIM component, and guarantees that the product of the two is an achievable number of signal dimensions available to each user in the original network. Next, a distributed numerical algorithm called ZEST is developed. The convergence of the algorithm is demonstrated, leading to the duality of the TIM-TIN problem in terms of generalized degrees-of-freedom (GDoF). Numerical results are also provided to demonstrate the superior sum-rate performance and fast convergence of ZEST.

We study a symmetric Gaussian wiretap channel with a helper, where a confidential message is sent from a transmitter to a legitimate receiver, in the presence of a helper and an eavesdropper, under a weak notion of secrecy constraint. For this setting, we characterize the optimal secure generalized degrees-of-freedom (GDoF). The result reveals that, adding a helper can significantly increase the secure GDoF of the wiretap channel. The result is supported by a new converse and a new scheme. In the proposed scheme, the helper sends a cooperative jamming signal at a specific power level and direction. In this way, it minimizes the penalty in GDoF incurred by the secrecy constraint. In the secure rate analysis, the techniques of noise removal and signal separation are used.

We study a symmetric Gaussian wiretap channel with a helper, where a confidential message is sent from a transmitter to a legitimate receiver, in the presence of a helper and an eavesdropper. For this setting, we characterize the optimal secure generalized degrees-of-freedom (GDoF). The result reveals that, adding a helper can significantly increase the secure GDoF of the wiretap channel. The result is supported by a new converse and a new scheme. In the proposed scheme, the helper sends a cooperative jamming signal at a specific power level and direction. In this way, it minimizes the penalty in GDoF incurred by the secrecy constraint. In the secure rate analysis, the techniques of noise removal and signal separation are used.

We perform a novel indoor channel measurement campaign to characterize the channel impairments for time-of-arrival (ToA) localization. We use precisely calibrated and time-synchronized RF equipment for transmitting and receiving 10 MHz and 100 MHz bandwidth waveforms over the 5.5 GHz DFS band in line-of-sight (LOS) and non-LOS environments. We collect ToA bias statistics with respect to a direct LOS path, where the bias is caused by multipath and NLOS reflections. Indoor wall reflections create significant ToA bias error of up to a couple hundred nanoseconds, corresponding to a positive ranging error of several tens of meters. We show how the WINNER II channel model, commonly used for communications simulations, is not suitable for ToA localization due to the improperly modeled signal timing and unrealistically low bias. The bias statistics based on our measurements are used for simulations of a ToA localization system using conventional and probabilistic multilateration algorithms. We present numerical results which provide insights for system design and performance-cost tradeoffs with regard to infrastructure density and signal bandwidth.

In this work, we first establish that for the class of interference channels identified by Geng et al. where treating interference as noise (TIN) is optimal from the generalized degrees-of-freedom (GDoF) perspective, if the number of antennas at each node is scaled by a common constant factor, then the GDoF region scales by the same factor almost surely, and the TIN scheme remains optimal for the entire GDoF region. Next, we demonstrate that for K-user MIMO interference channels with different antenna numbers for transmitters and receivers, there exist non-trivial parameter regimes where a simple scheme of zero-forcing strong interference and treating the others as noise achieves the sum GDoF.

In a K-user Gaussian interference channel, it has been shown by Geng et al. that if for each user, the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in decibel scale), then power control and treating interference as noise (TIN) is optimal from the perspective of generalized degrees of freedom (GDoF) and achieves the entire channel capacity region to within a constant gap. In this paper, we generalize the optimality of TIN to compound networks. We show that for a K-user compound Gaussian interference channel, if in every possible state for each receiver, the channel always satisfies the TIN-optimality condition identified by Geng et al., then the GDoF region of the compound channel is the intersection of the GDoF regions of all possible network realizations, which is achievable by power control and TIN. Furthermore, we demonstrate that for a general K-user compound interference channel, regardless of the number of states of each receiver, we can always construct a counterpart K-user regular interference channel that has the same TIN region as the original compound channel. The regular interference channel has only one state for each receiver, which may be different from all of the original states. Solving the GDoF-based power control problem for the compound channel is equivalent to solving the same problem in its regular counterpart. Exploring the power control problem further we develop a centralized power control scheme for K-user compound interference channels, to achieve all the Pareto optimal GDoF tuples. Finally, based on this scheme, we devise an iterative power control algorithm which requires at most K updates to obtain the globally optimal power allocation for any feasible GDoF tuple.

We consider 2-user symmetric interference channels with confidential messages. For the linear deterministic model of this channel, we develop inner and outer bounds for the symmetric secure rate, which are shown to match and characterize the symmetric secure capacity for a wide range of channel parameters. For the achievability, we present a cooperative jamming scheme based on interference alignment principle, which is optimal for all regimes where the symmetric secure capacity is established. For the converse, a tighter outer bound than all previously existing ones is provided for the regime where the symmetric secure capacity is still open.

For the K-user interference channel, Geng et al. identify a general condition under which power control and treating interference as noise (TIN) is optimal from the perspective of generalized degrees of freedom (GDoF). In this work, we show that for a K-user compound interference channel, if in every possible state for each receiver, the channel satisfies the TIN-optimality condition of Geng et al., then power control and TIN achieves the entire GDoF region of the compound channel. For an arbitrary compound interference channel, we find a non-trivial counterpart regular interference channel, such that the two have the same TIN region, and the GDoF-optimal power control problems for the two are equivalent.

It is shown that in the K-user interference channel, if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in decibel scale), then the simple scheme of using point-to-point Gaussian codebooks with appropriate power levels at each transmitter and treating interference as noise (TIN) at every receiver (in short, TIN scheme) achieves all points in the capacity region to within a constant gap. The generalized degrees of freedom (GDoF) region under this condition is a polyhedron, which is shown to be fully achieved by the same scheme, without the need for time-sharing. The results are proved by first deriving a polyhedral relaxation of the GDoF region achieved by TIN, and then providing a dual characterization of this polyhedral region via the use of potential functions, and finally proving the optimality of this region in the desired regime.

In a K-user Gaussian interference channel, it has been shown that if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in decibel scale), then treating interference as noise (TIN) is optimal from the perspective of generalized degrees of freedom (GDoF) and achieves the entire channel capacity region to within a constant gap. In this paper, we show that for such TINoptimal interference channels, even if the message set is expanded to include an independent message from each transmitter to each receiver, operating the new channel as the original interference channel and treating interference as noise is still optimal for the sum capacity up to a constant gap. Furthermore, we extend the result to the sum-GDoF optimality of TIN in the general setting of X channels with arbitrary numbers of transmitters and receivers.

In a K-user Gaussian interference channel, it has been shown that if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in dB scale), then treating interference as noise (TIN) is optimal from the perspective of generalized degrees-of-freedom (GDoF) and achieves the entire channel capacity region to within a constant gap. In this work, we show that for such TIN-optimal interference channels, even if the message set is expanded to include an independent message from each transmitter to each receiver, operating the new channel as the original interference channel and treating interference as noise is still optimal for the sum capacity up to a constant gap.

The topological interference management problem refers to the study of the capacity of partially connected linear (wired and wireless) communication networks with no channel state information at the transmitters (no CSIT) beyond the network topology, i.e., a knowledge of which channel coefficients are zero (weaker than the noise floor in the wireless case). While the problem is originally studied with fixed topology, in this work we explore the implications of varying connectivity, through a series of simple and conceptually representative examples. Specifically, we highlight the synergistic benefits of coding across alternating topologies.

The robust principles of treating interference as noise (TIN) when it is sufficiently weak, and avoiding it when it is not, form the background for this work. Combining TIN with the topological interference management (TIM) framework that identifies optimal interference avoidance schemes, a baseline TIM-TIN approach is proposed which decomposes a network into TIN and TIM components, allocates the signal power levels to each user in the TIN component, allocates signal vector space dimensions to each user in the TIM component, and guarantees that the product of the two is an achievable number of signal dimensions available to each user in the original network.

The original ergodic interference alignment scheme proposed by Nazer et al. requires symmetric channel phase distribution. In this paper, we investigate a new ergodic interference alignment scheme which can achieve one half interference-free degree of freedom (DoF) for arbitrary phase distribution. Even for symmetric phase distributions, the new scheme achieves a better high SNR offset than the original ergodic interference alignment scheme, and depending upon the magnitude distributions it is shown that the SNR offset improvement with the new scheme over the original scheme can be arbitrarily large. The SNR offset optimal ergodic alignment scheme is based on results in majorization theory.

We show that an M × N user MIMO X network with A antennas at each node has A (MN/M+N-1) degrees of freedom (DoF), thus settling the spatial scale invariance conjecture (scaling the number of antennas at each node by a constant factor will scale the total DoF by the same factor) for this class of networks. The previously known best general DoF inner bound, inspired by the K user interference channel, was based on the decomposition of every transmitter and receiver into multiple single antenna nodes, transforming the network into an AM × AN user SISO X network. While such a decomposition is DoF optimal for the K user interference channel, a gap remained between the best inner and outer bound for the MIMO X channel. Here we close this gap with the new insight that the MIMO X network is only one-sided decomposable, i.e., either all the transmitters or all the receivers (but not both) can be decomposed by splitting multiple antenna nodes into multiple single antenna nodes without loss of DoF. The result is extended to SIMO and MISO X networks as well and in each case the DoF results satisfy the spatial scale invariance property. In addition, the feasibility of linear interference alignment is investigated based only on spatial beamforming without symbol extensions. Similar to MIMO interference networks, we show that when the problem is improper, it is infeasible.