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.

Under the assumption of perfect channel state information at the transmitters (CSIT), it is known that structured codes offer significant advantages for secure communication in an interference network, e.g., structured jamming signals based on lattice codes may allow a receiver to decode the sum of the jamming signal and the signal being jammed, even though they cannot be separately resolved due to secrecy constraints, subtract the aggregate jammed signal, and then proceed to decode desired codewords at lower power levels. To what extent are such benefits of structured codes fundamentally limited by uncertainty in CSIT? To answer this question, we explore what is perhaps the simplest setting where the question presents itself — a$Z$interference channel with secure communication. Using sum-set inequalities based on Aligned Images bounds we prove that the GDoF benefits of structured codes are lost completely under finite precision CSIT. The secure GDoF regions of the$Z$interference channel and the$Z$broadcast channel are obtained as a byproduct of the analysis.

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.

Sum-set inequalities based on Aligned-Images bounds have been recently introduced as essential elements of converse proofs for asymptotic/approximate wireless network capacity characterizations under robust assumptions, i.e., assumptions that limit channel knowledge at the transmitters to finite precision. While these sum-set inequalities have produced robust Generalized Degrees of Freedom (GDoF) results for various wireless networks, their scope and limitations in general are not well understood. To explore these limitations, in this work we study the robust secure GDoF of a symmetric 3-user many-to-one interference channel. We identify regimes where existing sum-set inequalities are sufficient, settling the GDoF for those settings. For the remaining regime we conjecture the form of new sum-set inequalities that may be needed, whose validity remains an open problem for future work.

Under the assumption of perfect channel state information at the transmitters (CSIT), it is known that structured codes offer significant advantages in an interference network, e.g., lattice alignment allows a receiver to directly decode the sum of aligned interfering codewords at higher power levels even though individual codewords are not resolvable, subtract the aggregate interference, and then proceed to decode desired codewords at lower power levels. To what extent are such benefits of structured codes fundamentally limited by uncertainty in CSIT? To answer this question, we explore what is perhaps the simplest setting where the question presents itself - a Z interference channel with secure communication. Using sum-set inequalities based on Aligned Images bounds we prove that the GDoF benefits of structured codes are lost completely under finite precision CSIT. The secure GDoF region of the Z interference channel is obtained as a byproduct of the analysis.

Significant progress has been made recently in Generalized Degrees of Freedom (GDoF) characterizations of wireless interference channels (IC) and broadcast channels (BC) under the assumption of finite precision channel state information at the transmitters (CSIT), especially for smaller or highly symmetric network settings. A critical barrier in extending these results to larger and asymmetric networks is the inherent combinatorial complexity of such networks. Motivated by other fields such as extremal combinatorics and extremal graph theory, we explore the possibility of an extremal network theory, i.e., a study of extremal networks within particular regimes of interest. As our test application, we study the GDoF benefits of transmitter cooperation in a K user IC over the simple scheme of power control and treating interference as Gaussian noise (TIN) for three regimes of interest - a TIN regime identified by Geng et al. where TIN was shown to be GDoF optimal for the K user interference channel, a CTIN regime identified by Vi and Caire where the GDoF region achievable by TIN is convex without time-sharing, and an SLS regime identified by Davoodi and Jafar where a simple layered superposition (SLS) scheme is shown to be optimal in the K user MISO BC, albeit only for K ≤ 3. The SLS regime includes the CTIN regime, and the CTIN regime includes the TIN regime. As our first result, we show that under finite precision CSIT, TIN is GDoF optimal for the K user IC throughout the CTIN regime. Furthermore, under finite precision CSIT, appealing to extremal network theory we obtain the following results. In the TIN regime as well as the CTIN regime, we show that the extremal GDoF gain from transmitter cooperation over TIN is bounded regardless of the number of users. In fact, the gain is exactly a factor of 3/2 in the TIN regime, and 2 - 1/K in the CTIN regime, for arbitrary number of users K > 1. However, in the SLS regime, the gain is ⊖(log2(K)), i.e., it scales logarithmically with the number of users.

We study the GDoF gain of transmitter cooperation (TC) over power control and treating interference as noise (TIN) for 3 regimes - a TIN regime where TIN is GDoF optimal for the K user IC, a CTIN regime where the GDoF region achieved by TIN is convex without time-sharing, and an SLS regime where a simple layered superposition scheme is optimal in the K user MISO BC for K≤3. Under finite precision CSIT, appealing to extremal network theory we obtain the following results. In the TIN regime as well as the CTIN regime, the extremal GDoF gain from TC over TIN is Θ (1). In fact, the gain is at most a factor of 2 in the CTIN regime and exactly 3=2 in the TIN regime for K > 1. In the SLS regime, the extremal GDoF gain is Θ(log(K)).

The channel impulse response (CIR), which characterizes the multipath channel between a transmitter and a receiver, can serve as a received position signature for indoor position fingerprinting (FP). Since it takes large system bandwidth to distinguish individual paths along which the signal waves travel in an indoor environment, a small bandwidth may yield an unsatisfactory performance of FP based on mere CIR. In this paper, we apply the multiple signal classification (MUSIC) algorithm, a super-resolution method, to unveil the path-delay signatures covered by bandwidth-limited CIRs. With the pseudospectrum evaluated with MUSIC, we resolve and identify the arrival times of the individual paths at a sub-sample precision. We further propose a super-resolution-aided fingerprinting (SFP) algorithm to estimate the receiver's position by taking the averaged positions of the reference points (RPs) of similar FP signatures with weights evaluated by the difference in pseudospectrum and received power. Experiments in an indoor environment show that SFP reduces the positioning error compared to the FP based on conventional channel state information (CSI), and that demands fewer infrastructures and less protocol complexity than CIR-based FP does to achieve similar performance.

Position fingerprinting (FP), in which the signature of a position is captured from the radio frequency signal, is one of the most efficient indoor positioning algorithms. Besides the received signal strength (RSS), the channel impulse response (CIR) is regarded as a linear temporal filter, which characterizes the multipath channel of the operating environment. Since the CIR requires a larger system bandwidth to distinguishing individual paths along which the signal waves travel, a smaller bandwidth may limit the performance of CIR- based fingerprinting. In this paper, we utilize a super-resolution method, i.e. the multiple signal classification (MUSIC) algorithm, to obtain the pseudo-spectrum for the enhanced resolution of the arriving paths. We create an offline database by the implementation of an OFDM-based channel sounder and obtain the cumulative pseudo-spectrum based on the alignment of the maximal power path. Based on the online#x002F;offline measurements with enhancing resolutions, we propose a super-resolution-aided fingerprinting (S- FP) to estimate the position by finding the reference points (RPs) with the highest similarity of the cumulative pseudo-spectrum. The experimental results show that S-FP reduces the localization error compared with the conventional CIR FP.

Fine timing estimation in timing synchronization scheme of orthogonal frequency division multiplexing systems gives an estimate of symbol starting time index corresponding to the path with maximal power within an interval suggested by coarse timing stage. The actual starting index fed to the following stages is brought forward by an amount that should be adaptive to the estimated index to optimize system performance. In this paper, a method of detecting the estimated starting time index of path with maximal power in channel impulse response is proposed based on conventional preamble with repetitive structure. To deal with the adverse effect of fractional timing offset on the detection metric, we propose a preamble composed of cyclic-shifted parts and the accompanying fine timing and detection scheme. Simulation with time-varying wireless channel shows the detection methods makes use of the time diversity provided by time-varying paths and has good error performance. The scheme with proposed preamble further reduces probability of error detection with the diversity in fractional timing offset provided inherently in the parts of preamble.