Constant-Envelope Precoding with Time-Variation Constraint on the Transmitted Phase Angles

We consider downlink precoding in a frequency-selective multi-user massive MIMO system with highly efficient but non-linear power amplifiers at the base station (BS). A low-complexity precoding algorithm is proposed, which generates constant-envelope (CE) transmit signals for each BS antenna. To avoid large variations in the phase angle transmitted from each antenna, the difference of the phase angles transmitted in consecutive channel uses is limited to $[-\alpha \pi ,\alpha \pi ]$ for a fixed $0<\alpha \le 1$. To achieve a desired per-user information rate, the extra total transmit power required under the time variation constraint when compared to the special case of no time variation constraint (i.e., $\alpha =1$), is small for many practical values of $\alpha$. In a i.i.d. Rayleigh fading channel with $80$ BS antennas, $5$ single-antenna users and a desired per-user information rate of $1$ bit-per-channel-use, the extra total transmit power required is less than $2.0$ dB when $\alpha =1\mathrm{/}2$.