Out-of-band radiation measure for MIMO arrays with beamformed transmission

Paper in proceeding, 2016

The spatial characteristics of the out-of-band radiation that a multiuser MIMO system emits, due to its power amplifiers (modeled by a polynomial model) being nonlinear, are studied by deriving an analytical expression for the continuous-time cross-correlation of the transmit signals. It is shown that, at any spatial point and on any frequency, the received power averaged over many channel realizations from a MIMO base station is the same as from a SISO base station when the two radiate the same amount of power. For a specific channel realization however, the received power can deviate from this average. We show that the deviations from the average are small in a MIMO system with multiple users and that the deviations can be significant with only one user. Using an ergodicity argument, we conclude that out-of-band radiation is less of a problem in massive MIMO, where precoding and array gain let us reduce the total radiated power compared to SISO systems. The requirements on spectral regrowth can therefore be relaxed in MIMO systems without causing more total out-of-band radiation.