The maximal-subset-property conjecture for blind MIMO optimization

Let $n$ be the signal dimension and $k$ the number of samples. Let $\mathbf{X}$ be selected uniformly from the set of all $n\times k$ matrices having the maximal \subset property, and let $\mathbf{A}$ denote the channel gain matrix. Let an ATM be a matrix $\mathbf{T}$ from the class of transformations identified in the paper, and consider the optimization problem defined by equations --.

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

$$\mathbf{U}=\mathbf{T}\mathbf{A}^{-1}$$

for all ATMs $\mathbf{T}$.

This conjecture predicts that sufficiently many uniformly sampled symbols eliminate all spurious optima, leaving exactly the channel-equivalent solutions. The supplied text presents it as a general-$n$ conjecture motivated by the preceding theory and empirical results; no proof or disproof is given.