  Spatial covariance matrix (SCM) is essential in many applications of
multi-antenna systems such as massive multiple-input multiple-output (MIMO).
For massive MIMO operating at millimeter-wave bands, hybrid analog-digital
structure has been adopted to reduce the cost of radio frequency (RF) chains.
In this situation, signals received at the antennas are unavailable to the
digital receiver, and as a consequence, traditional sample average approach
cannot be used for SCM reconstruction in hybrid massive MIMO. To address this
issue, beam sweeping algorithm (BSA), which can reconstruct SCM effectively in
hybrid massive MIMO, has been proposed in our previous work. In this paper, a
truncated BSA is further proposed for SCM reconstruction by taking into account
the patterns of antenna elements in the array. Due to the directive antenna
pattern, sweeping results corresponding to predetermined direction-of-angles
(DOA) far from the normal direction are small and thus can be replaced by
predetermined constants. At the cost of negligible performance reduction, SCM
can be reconstructed efficiently by sweeping only the predetermined DOAs that
are close to the normal direction. In this way, BSA can be conducted much
faster than its traditional counterpart. Insightful analysis will be also
included to show the impact of truncation on the performance.
