The Basic Port Modulation System Model
Noh, Kim, Lee, J. and Lee, C. (2015) show the codebook design of a point-to-point PM system. Noh et al. consider a Nt×Nr MIMO system showed in Figure 1, which is referred as the basic PM and the proposed PM method is referred as the improved PM in this paper.
The received signal y in Figure 1 can be descripted as
(1) where
Heff =
HF is the effective channel matrix,
is the channel matrix,
is the PM precoding matrix,
P is the number of the ports, and
is the additive white Gaussian noise (AWGN) vector with independent identically distributed (i.i.d) entries according to the zero mean complex Gaussian distribution with variance
N0, i.e.
. The transmit symbol
sk is defined by
(2) where
ρ is the transmit power and
sk is a
P×1 column vector. It is clear that the information bits are conveyed only on the ports in the basic PM system, which means that the basic PM can be regarded as the combination of space-shift keying and precoding. So the spectral efficiency
R of the basic PM system showed in (3) is decided only by the number of the ports.
(3)
Noh, Kim, Lee, J. and Lee, C. (2015) also show that the destination of the PM precoding in FDD Massive MIMO systems is adjusting the precoding matrix F to make PM robust to the spatial correlation and the per antenna power constraint. In other words, the basic PM accomplishes the mapping from the logical antennas to the antenna ports by the precoding process.