22 problems

Let ${\bf h}^{\textrm{eff}}_i$ denote the effective channel vector for user $i$ in a system with $M$ transmit dimensions and an effective-channel subspace of dimension $N$. Chi-squ…

Let $B=\operatorname{diag}(b_1,\ldots,b_k)$ with $b_i<1$ for all $i$, let $H=\operatorname{diag}(h_1,\ldots,h_n)$, and let $\Gamma\in\mathbb{R}^{n\times k}$ and…

Let $C(\sigma^2)$ denote the mutual information (MI) of a two-hop, double-scattering MIMO channel, and let $\overline{C}(\sigma^2)$ and $V(\sigma^2)$ be the asymptotic mean and var…

Consider a Gaussian MIMO channel with memory under a total (average) power constraint. Its operational capacity is the maximum reliably achievable transmission rate, while its info…

Gap-removal conjecture. This gap can be completely removed with tighter bounds for the variational distance between the discrete and continuous Gaussians.

Consider a MIMO channel using one-bit transceivers, and let SLM subsets denote the signal-level-modulation subsets used by the transmission method. Uniform-subset conjecture. The c…

Outage Probability Conjecture for TIMO. The pairs $(q_1,q_2)$ minimizing $f(q_1,q_2)$ over $\mathcal{D}$ belong to

Outage Probability Conjecture. Every covariance matrix attaining the infimum has the stated form: power is allocated equally among some $k$ transmit dimensions and is zero on the r…

For the discrete-time stationary and ergodic $n_{\mathrm{r}}\times n_{\mathrm{t}}$ MIMO phase noise channel in model B1, the upper and lower multiplexing-gain bounds do not match w…

Full relay-cooperation looseness conjecture. The main reason for this mismatch is that the upper bound is too loose in this range of $M/N$.

Full relay-cooperation looseness conjecture. The upper bound obtained by assuming full cooperation among the relays is loose in general.

For each $i\in\{1,\dots,t\}$, consider an $n i$-complex-dimensional translated lattice shaped by a unit-volume complex hypercube, used over the $t\times r$ MIMO channel with a latt…

BDUT optimality conjecture. The value $\delta^*$ defined above is the Poltyrev capacity without any transmission constraint. Although the BDUT capacity need not a priori equal the…

Let $\{R_n\}_{n=1}^\infty$ be a real sequence, and let $\ell_n$ be the remainder sequence in the finite-dimensional approximation of Feinstein's upper bound, with…

Let $P$ denote the transmit power, $K$ the number of users, and let $\mathcal{R}_{[K]}$ be the achievable rate of the proposed opportunistic interference alignment schemes with $K$…

Let $\mathbf{D}$ be the transmit covariance matrix under uniform power allocation, with $\mathbf{D}=\frac{p}{n_t}\mathbf{I}_{n_t}$, where $p$ is the allocated power and…

Let $\Gamma(\mathbf{Q},R)$ denote the goodput-to-power ratio, let $P_{\mathrm{out}}(\mathbf{Q},R)$ denote the outage probability, and let $\overline{P}$ be the available transmit-p…

For a $K$-user MIMO interference channel with $N_t$ transmit antennas and $N_r$ receive antennas, let $d(K,N_t,N_r)$ denote the degrees of freedom achieved by the interference-alig…

The paper considers the two-user compound MIMO broadcast channel with confidential messages and its secure degrees-of-freedom (s.d.o.f.) region. An achievable s.d.o.f. region is es…

Let $K$ users communicate over constant $N_{\rm R}\times N_{\rm T}$ MIMO interference channels, with each user achieving one degree of freedom, so that $d_1=\ldots=d_K=1$. Achievab…

Concavity conjecture. The function $f(\boldsymbol\lambda)$ is concave on $\mathcal{D}^{N}$.

Variance-smoothing conjecture. For a large class of channels in the medium- to high-$\mathrm{SNR}$ regime,