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By exploiting the channel spatial sparsity, massive MIMO channel is compressed in the beam-domain under certain selected basis spaces and as a result the channel dimension required to be estimated can be greatly reduced.

The function G u i ) to be estimated can be either linear or nonlinear in its coefficients.

In this way, the channel can be compressed in the BD under certain selected basis spaces and the channel dimension required to be estimated can be reduced greatly.

Due to the spatial sparsity of massive MIMO channel, we can compress the massive MIMO channel in the BD under certain selected basis spaces and the channel dimension required to be estimated can be greatly reduced.

Hence, the parameter vector to be estimated can be expressed as ( boldsymbol{uptheta} ={left[begin{array}{cc}hfill mathrm{vecs}{left(boldsymbol{Sigma} right)}^Thfill & hfill {sigma}^2hfill end{array}right]}^Tin varTheta ).

The channel coefficients that need to be estimated can be divided into two groups: the ones that are directly observed by T1 (these are h0 and h2) and the ones that are not (these are h1 and h 2 ′ ).

Some of the samples on which these models are estimated can be quite small, leaving few, if any, observations with a particular characteristic of interest.

In our example, the equivalent channels that are estimated can be expressed as the convolution of two sample-spaced L-path channels.

The specific multiple regression model that is estimated can be specified as follows: Perform.=alpha +{beta}_i Entrepreneur cht.+{gamma}_i Enterprise cht.+{delta}_i External fact.+{varepsilon}_i.

The MAP estimate of ηi is given by As µ is known, once is estimated, can be easily calculated.

Full details on how this was estimated can be found in Additional file 1, and the results in Additional file 2: Tables S1 and Additional file 3: Table S2.