  Motivated by current interest in understanding statistical properties of
random landscapes in high-dimensional spaces, we consider a model of the
landscape in $\mathbb{R}^N$ obtained by superimposing $M>N$ plane waves of
random wavevectors and amplitudes. For this landscape we show how to compute
the "annealed complexity" controlling the asymptotic growth rate of the mean
number of stationary points as $N\to \infty$ at fixed ratio $\alpha=M/N>1$. The
framework of this computation requires us to study spectral properties of
$N\times N$ matrices $W=KTK^T$, where $T$ is diagonal with $M$ mean zero i.i.d.
real normally distributed entries, and all $MN$ entries of $K$ are also i.i.d.
real normal random variables. We suggest to call the latter Gaussian
Marchenko-Pastur Ensemble, as such matrices appeared in the seminal 1967 paper
by those authors. We compute the associated mean spectral density and evaluate
some moments and correlation functions involving products of characteristic
polynomials for such and related matrices.
