9 problems

Let $N$ be the number of signaling dimensions, let $\mathbf{U}\in\mathbb{U}(N)$ denote the unitary signaling basis, and let $\mathbf{F}_N$ be the normalized $N$-point discrete Four…

Let $\mathbf{B}_L$ and $\mathbf{B}_H$ be the low- and high-frequency basis matrices, respectively, used to model the temporal variation of a channel. In particular, $\mathbf{B}_L$…

Linear-eigenvalue-growth conjecture. There exists an upper bound on the largest eigenvalue of $\mathbf{T}$ that grows linearly with $N$:

Turbo-GAMP is an iterative receiver for OFDM channel estimation, and its design restricts the path delays to a sample-spaced grid. At high signal-to-noise ratio, let the observed e…

Maximum-efficiency conjecture. The maximum efficiency is $d_{max}=1.4998$, achieved when there are $K=3$ users using $N=2{,}001$ subcarriers.

When the input distribution is non-Gaussian, let $x$ be a random variable distributed as one of the input symbols to the intersymbol-interference channel, and define the Shamai–Lar…

Let a frequency-selective channel be used for transmission with a uniform power spectrum and compare an OFDM scheme with a single-carrier (SC) scheme having an optimal receiver. Fr…

Near-optimal uniform power allocation conjecture. With this separation into two groups, both the uniform and waterfilling power allocation schemes would have close to optimal perfo…

Midpoint pairing conjecture. This pairing could have mutual information very close to optimal, because it attempts to maximize the minimum condition number among all pairs.