8 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…

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…

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…

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,