68 problems

Gupta–Kumar connectivity conjecture. The graph

Lognormal approximation conjecture. The uplink inter-cell interference should be well approximated by a lognormal distribution.

A Gaussian half-duplex diamond network has a source, a destination, no direct source–destination link, and $N$ non-interfering half-duplex relays. A relay scheduling policy is appr…

Equal-SINR conjecture. The Pareto-optimal solution occurs when all users achieve the same SINRs, $\SINR[opt]$.

Rich-scattering lower-bound conjecture. For $M_t,M_r>3$, this lower bound reflects the orderwise behavior of the transmission capacity in a rich-scattering environment.

Symmetrized-matrix convexity conjecture. Convexity of $l_{\boldsymbol{M}}$ is linked to the positive semidefiniteness of ${\boldsymbol{M}}+{\boldsymbol{M}}^t$.

Clustering conjecture. The spatial multiclass wireless network displays the same clustering behavior in the stationary regime.

Intermediate time-scale conjecture. The non-trivial behavior expected at a time scale intermediate between $N$ and $N^2$ should occur in any network topology.

Consider a wireless ad hoc network with a covertness constraint, in which mobile nodes may have trajectories with limited correlation rather than being uniformly and independently…

Let $N_t(\lambda)$ be the number of transmit antennas in a MISO cellular network with a physically feasible path loss model. Suppose coordinated beamforming perfectly cancels the i…

Let $N_t(\lambda)$ and $N_r(\lambda)$ denote the numbers of transmit and receive antennas, respectively, and suppose … Consider eigenbeamforming with a single data stream and a phy…

Let $N_t(\lambda)$ and $N_r(\lambda)$ be the numbers of transmit and receive antennas, respectively, with … Consider eigenbeamforming with a single data stream and a physically fea…

The experiments compare hierarchical federated learning (HFL) and federated learning (FL) on CIFAR-10, including sparse variants, and observe a small degradation in the accuracy of…

Let base stations (BSs) denote the radio-access network stations serving cellular users, and let the radio spectrum in use denote the amount of spectrum deployed for cellular commu…

Consider a wireless ad hoc network in which the number of legitimate nodes is not larger than the number of wardens. Preservation regions are regions around wardens used to protect…

MIMO generalization conjecture. The results of the paper can be generalized to MIMO broadcasting when

Deterministic approximation conjecture. If $h$ has a Nakagami-$m$ distribution with $m \geq 3$, then the fading channel can be well approximated by a deterministic channel gain wit…

Let $m$ be the number of friendly nodes, $n$ the number of channel uses, $N_{\mathrm{w}}$ the number of Willies, and let $\gamma>2$. Under the strategy in which nodes sufficiently…

Let $m$ be the number of friendly nodes, $n$ the number of channel uses, and let $\gamma>2$. Friendly nodes at distance less than $\iota>0$ from Bob are turned off, while every oth…

Poisson approximation conjecture for exponential tails. The same approximation method as for polynomial tails can be applied to exponential SIR tails.

Exponential-tail conjecture. For Rayleigh fading,

Lower heavy-tail conjecture.

Let $\mathbf{C}_{j}^{{\rm F}}$ denote the precoding matrix used by the $j$th small-cell network node for its backhaul signal $\mathbf{u}_{j,\mathrm{b}}[t]$. Unitary precoder conjec…

Let $\phi_0$ be the point process on $\mathbf{S}$ corresponding to the stationary distribution of $\phi_t$, with intensity $\beta$. Let $\psi$ be an independently marked Poisson Po…

Let $\gamma$ be a QoS requirement and let $f_c$ be an operating frequency. For the propagation environments whose parameters are listed in Table 1, define … where…