44 problems

Maximal diversity conjecture. For the general case with $L \leq \min(N_R,N_T)$ transmitting antennas, the maximal diversity is $(N_T-L+1)(N_R-L+1)$, coinciding with the lower bound…

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.

DDF multi-antenna conjecture. DDF will not be able to sustain its optimality even in the low-multiplexing-gain regime when the terminals have multiple antennas.

Clustered-system DMT conjecture. The theorem stating that, for the clustered system, the DMT formula given for $m=1,2$ holds is true for arbitrary $(m,n,k)$.

Asymptotic decorrelation conjecture. The limiting correlation coefficient is

Multiplexing-gain-one conjecture. The multiplexing gain of the sum capacity is equal to $1$.

Consider an $(M_1,N_1),(M_2,N_2)$ two-user MIMO interference channel, with the antenna arrangement and degrees-of-freedom lower bound … where $(x)^+=\max(0,x)$ and $1(\cdot)$ is th…

Consider a MIMO multicarrier system using the multi-slot cross-domain MAMP (MS-CD-MAMP) receiver, with total transmission rate $R_{\rm{MS-CD-MAMP}}^{\rm{total}}$ and constrained ch…

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…

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

Maximal-subset-property conjecture. If $k$ is slightly larger than $n$, then with high probability the only optima of the optimization problem are

Vertex-optimum conjecture. For general $n$, when $k$ is slightly larger than $n$, all non-singular vertices are global optima and solutions to the channel-estimation problem; conse…

Let the elements of an input signal vector be chosen from a Cartesian product of one-dimensional PAM constellations. The constellation constrained capacity is the maximum informati…

Let $S$ denote the spatial sampling factor, let $\bm{X}$ be the transmitted input, and let $\bm{Y}_Q$ be the received signal after 1-bit quantization. In the considered SNR region,…

Let $\mathbf{H}\in\mathbb{C}^{N_\textrm{rx}\times N_\textrm{tx}}$ be a random channel matrix, let $S$ denote the mean SNR, and define the MIMO channel capacity by … A random variab…

Oggier's conjecture. An optimal transmission for this problem is on the directions where the main channel is stronger than the eavesdropper channel, namely on the positive directio…

For a point-to-point SVD-MIMO downlink system, let $m$ denote the number of transmitted streams, let $\rho$ be the transmit signal-to-noise ratio, and let $\beta$ denote the releva…

Lu's conjecture. The ensemble of multi-block division algebra codes might approach the ergodic Rayleigh fading capacity.

The full outer-bound conjecture. The claim that the per-user information-theoretic degrees of freedom equal $\frac{M_T M_R}{M_T+M_R}$ for arbitrary antenna numbers $M,N$ is correct…

Consider a MIMO interference network and scale the number of antennas at every transmitter and receiver by the same positive factor. Let the information-theoretic degrees of freedo…

Consider a MIMO interference network with generic time variations, and allow linear schemes over arbitrarily long symbol extensions. The information-theoretic degrees of freedom ar…

Let a $K$-user MIMO wireless interference network have $M$ antennas at each transmitter and $N$ antennas at each receiver, with each user seeking $d$ degrees of freedom. A system i…

MIMO pre-log conjecture. If

Let $n_t$ and $n_r$ denote the numbers of transmit and receive antennas, respectively, let $T$ be the block length, and let $Q$ be the number of symbols assigned to gather informat…