2230 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 4, JULY 2008
Fig. 1. SM–OFDM system model.
and four transmit antennas are considered as an example here.
In general, any number of transmit antennas and any digital
modulation scheme can be used. The constellation diagram and
the number of transmit antennas determine the total number
of bits to be transmitted on each subchannel at each instant.
The combination of BPSK and four transmit antennas in this
illustration results in a total of three information bits to be trans-
mitted on each subchannel. Instead, four quadrature-amplitude
modulation (QAM) and two transmit antennas can be used to
transmit the same number of information bits, as shown in
Table I. The number of bits that can be transmitted on each
OFDM subchannel for a system that uses a QAM constellation
diagram of size M (m = log
2
(M)) and N
t
transmit antennas
is [22]
˜m = log
2
(N
t
)+m. (1)
This shows that the constellation diagram and the number of
transmit antennas can be traded off for any number of trans-
mitted information bits. In addition, SM increases the spectral
efficiency by the base-two logarithm of the total number of
transmit antennas. This can be viewed as a disadvantage for
a large number of transmit antennas as compared to, for exam-
ple, V-BLAST. Note that, in V-BLAST, the spectral efficiency
linearly increases with the number of transmit antennas. For
example, consider a MIMO system with eight transmit and
receive antennas. If V-BLAST is used with 16 QAM, a spectral
efficiency of 32 b/s/Hz can be achieved. However, if SM is
used with the same configuration and modulation order, the
spectral efficiency is only 7 b/s/Hz. In order for SM to achieve
the spectral efficiency of V-BLAST with 16 QAM, it requires
2
28
transmit antennas, which is not feasible. This means that
SM cannot compete with V-BLAST when a large number of
antennas and high modulation orders are involved. However, it
is generally accepted that a large number of transmit antennas
is impractical with current technology, particularly when con-
sidering the cost that comes from adding antennas for an end-
TABLE I
SM M
APPING TABLE:3b/SYMBOL/SUBCHANNEL
user system. For instance, two competing approaches have been
proposed for the MIMO-oriented version of the IEEE 802.11n
standard: 1) one with a 2 × 2 MIMO matrix and 2) another
with a 4 × 4 matrix. The current 802.11n draft provides for up
to four transmit antennas, even though compliant hardware is
not required to support that many antennas [27].
With SM mapping, the matrix X(k) has one nonzero element
in each column at the position of the mapped transmit antenna
number. All other elements in that column are set to zero. For
instance, in Fig. 1, an input bit sequence of [011]
T
[highlighted
column vector in Q(k)] is mapped to the BPSK symbol +1 and
the second transmit antenna by using the SM mapping table.
This means that only the second antenna transmits this symbol
on the first OFDM subchannel, whereas all other antennas
transmit zero power. As a result, the first column vector in X(k)
is [0 + 1 0 0]
T
. The second bit sequence is [111]
T
and is
mapped to [000+1]
T
, and so on. The resulting symbols in
each row vector x
κ
(k) are the data that will be transmitted on all
subchannels and from antenna κ. Then, each row vector x
κ
(k)
is modulated using an OFDM modulator.