12 problems

Let a full-duplex multiuser MISO system use MIMO precoding with an increasing number of access-point transmit and receive antennas, and let the downlink signal-to-interference-plus…

Array-densification gain conjecture. The gain of array densification should reduce to zero when

Let the robust beamforming formulation (RBF) be considered, and let the sufficient condition in Lemma $(b)$ be the condition under which the proposed branch-and-bound procedure sol…

Mainlobe initialization conjecture. A good initial estimate $\hat{x}_0$ should lie within the mainlobe set $\mathcal{B}(x_0)$.

Achievable beamforming-gain optimality conjecture. The achievable beamforming gain is optimal for the setting with the second-moment input constraint.

Second-moment beamforming-gain conjecture. The beamforming gain under the second-moment input constraint is the same as under the fourth-moment input constraint:

Let $\bar{\bar{p}}_C$ denote the quantity whose tight upper bound is $\bar{\bar{p}}_{up,C}$. Let $R$ denote the relevant radius parameter. Monotonicity conjecture. The quantity…

Consider the quality-constrained power-minimization (QCPM) problem and the MMSE-SOCP algorithm, which alternates between updating the receive beamformers with the MMSE receiver at…

The system has $M$ microphone signals and an adaptive wideband beamformer (BF) that performs spatial filtering before an adaptive acoustic echo canceller (AEC), whose length is com…

Let ${\bf\Sigma}_1$ and ${\bf\Sigma}_2$ denote the channel covariance matrices, let $\rho$ be the signal-to-noise ratio, and let $\mathcal R_{\sf weighted}$ be the weighted ergodic…

Let ${\bf\Sigma}_1$ and ${\bf\Sigma}_2$ denote the channel covariance matrices, let $\rho$ be the signal-to-noise ratio, and let $\alpha^{\star}(\rho)$ and $\beta^{\star}(\rho)$ ma…

Let $a_{\rm x}$ and $b_{\rm x}$, for ${\rm x}=\mathrm{MR}$ or ${\rm ZF}$, be nonnegative relay power-allocation parameters in the MRR-MRT and ZFR-ZFT beamforming structures, respec…