García Soriano, Lidia 1
Fase 6. Difusión y explotación de los resultados
Spatial modulation (SM) transmitters and receivers aim at reducing the number
of RF chains by activating a subset of antennas M < N depending on the input bit
stream [19, 157, 158]. The essential idea behind SM is to, apart from using conventional
modulation methods to transmit information, encoding additional information onto the
antenna indexes. This generates a 3-dimensional constellation: the first two signal
dimensions corresponding to the conventional Q-QAM symbols and an additional spatial
dimension given by the antenna indexes employed to convey the selected modulation
symbol. The operation principle of conventional SM is illustrated in Fig. 2.9 for a
system with N = 4 and Q = 4 and can be described as follows:
− The antennas serve as a source of information and the number of antennas de-
00 10 Input Bits
...
...
0001 10 11 Antenna selection Symbol Selection 00 10 11 01Figure 2.9: Illustration of the transmission process in spatial modulation.
instance, the scheme of Fig. 2.9 conveys log2(N ) = log2(4) = 2 bits through the
antenna index.
− The remaining bits are subsequently employed to select the modulation symbol.
Therefore, the number of bits that can be simultaneously transmitted in bits per
channel use (bpcu) depends on both the modulation order and the number of
transmit antennas via log2(N )+log2(Q). Specifically, the transmit signal of single-
RF SM transmitter adopts the form
x =0 · · · sql · · · 0T
, (2.28)
where sq is the q-th symbol of the transmit constellation Q and l ∈ {1, . . . , N }
denotes the index of the active antenna. Note that a large number of entries in
the transmitted vector of (2.28) are zero-valued.
− The channel is used as a modulator, i.e., its output (the signal at the receiver) will
be different depending on the antenna employed for transmission. For this to hold,
SM ideally assumes that the antennas are sufficiently well separated so that there
is no spatial correlation between them, and a scenario with sufficient scattering.
− Ideal SM transmission assumes that the receiver has instantaneous CSI knowledge.
This channel knowledge is exploited to estimate both the transmitted signal and
the active antennas. For instance, the optimal maximum likelihood (ML) detection
is given by [159] b l,bsq= arg min l,q (y − hlsq) , (2.29)
Baseband Processing Conventional MIMO RF chain RF chain RF chain RF chain Baseband Processing Spatial Modulation RF chain Fast Switch
(a)
(b)
Figure 2.10: Comparison between the architectures of (a) a conventional MIMO transmitter and (b) a spatial modulation transmitter.
the l-th column of the downlink channel matrix, and bl ∈ {1, . . . , N } and bsq ∈ Q
denote the estimated active antenna index and the estimated constellation symbol,
respectively.
Overall, the above operation allows decreasing the number of RF chains employed
in conventional MIMO transmission, since only one antenna is simultaneously active
[19, 157, 158]. This is explicitly shown in Fig. 2.10, where the block diagrams of both
conventional MIMO and SM transmitters are represented. Fig. 2.10 explicitly shows
that spatial modulation transmitters require a fast switch that varies at the symbol
rate, which constitutes one of the main bottlenecks of these systems [19, 157, 158]. Also
note that the RF hardware benefits come at the cost of a reduced attainable spectral
efficiency Se when compared with MIMO transmitters, where Se increases linearly with
the number of transmit antennas as N log2(Q). In spite of this, the energy efficiency
trade-off can still be favourable for spatial modulation systems, depending on the relative
power consumption of the RF chains w.r.t. the transmission power [62, 160–162].
There exists a conglomerate of uncoded SM systems that have different denomina-
tions according to their modulation order or their number of active antennas as depicted
in Fig. 2.114. This figure highlights in color the schemes where this Thesis has made
contributions on: space shift keying (SSK) and spatial modulation (SM). Specifically,
4
The concept of SM can also be extended to incorporate both space and time dimensions via disper- sion matrices that occupy a number of transmission blocks [163, 164]. For reasons of brevity, this Thesis concentrates on conventional SM, where only the spatial dimension as a means of conveying information is considered.
Spatial modulation (SM)
Modulation: Arbitrary
Number of active antennas: One
Generalized space shift keying (GSSK)
Modulation: No
Number of active antennas: Arbitrary but fixed
Hamming space shift keying (HSSK)
Modulation: No
Number of active antennas: Arbitrary
.
Generalized spatial modulation (GSM)
Modulation: Arbitrary
Number of active antennas: Arbitrary
Figure 2.11: Nomenclature and characteristics of different SM-based systems.
SSK constitutes a low-complexity version of SM where the information is only conveyed
via the spatial-constellation diagram, i.e. sq= 1, ∀ q in (2.28) [18]. The theoretical char-
acterization of the error rates of both SSK and SM has been performed in [18, 165, 166].
Additionally, there are three research areas in SSK and SM particularly related to this
Thesis, namely, signal detection, signal pre-scaling and the application of the SM prin-
ciples to the multiple access channel (MAC):
− Signal detection. The efforts for enhancing the performance attainable by SSK
and SM have been mainly focused on the design of detection algorithms for point-
to-point systems [19,157,167]. The fundamental objective behind this research line
is to reduce the computational complexity of the ML detector in (2.29), while ap-
proximating its attainable performance (see, e.g. [168–171] and references therein).
Particularly related to this Thesis are [172, 173], where the sparsity of the trans-
mitted signals in SSK and GSSK is leveraged for devising single-user detectors
based on compressive sensing (CS). Indeed, Chapter 5 also relies on the principles
behind CS for proposing a SM detector, although for scenarios with a multiplicity
Massive MIMO Base Station User 1 Communication Channel G
..
.
1 nt 2..
.
User 2..
.
..
.
User K..
.
N 1 nt 2 1 nt 2 1 2 3Figure 2.12: Illustration of the uplink of a LSAS with SM. The mobile terminals only activate a subset of antennas for transmission towards the BS.
− Signal pre-scaling. Although conventional SM systems only consider CSI avail-
ability at the receiver for the purpose of detection, a parallel line of research
has demonstrated the benefits of exploiting CSI availability at the transmitter.
For instance, a number of suboptimal constellation shaping algorithms have been
proposed in [163, 174–177]. Similarly, the focus of [178–180] is also placed on de-
veloping pre-scaling algorithms, but their application is limited to systems with
a single receive antenna. Instead, the schemes developed in [181–184] facilitate
the application of symbol pre-scaling to multiple antenna systems. However, these
schemes only adapt the transmission power [181, 182], do not devise the candidate
pre-scaling factors according to the channel conditions [183], or have a substantial
complexity due to the need of solving multiple convex optimization problems be-
fore reaching convergence [184]. In order to address the above-mentioned issues,
Chapter 4 proposes a pre-scaling strategy for SSK multiple antenna systems based
on semidefinite programming.
− Application of SM to the multiple access channel (MAC). The works de-
tailed above solely concentrate on point-to-point systems. Instead, contemporary
works consider the application of SM to the MAC, where a multiplicity of SM
terminals convey information towards a BS, generally considered to incorporate a
large number of antennas as shown in Fig. 2.12 [159, 185, 186]. Indeed, the the-
oretical analyses carried out in [159, 185, 186] demonstrate that SM systems can
provide performance improvements over conventional MIMO systems with identi-
Baseband signal processing FBB RF chain M RF chain 1 RF chain 2 1 2 N > M K data streams Digital Analog RF signal processing FRF N-1
Figure 2.13: Simplified block diagram of a hybrid analog-digital precoding sys- tem.
also considered in [187–191] for enhancing the performance of conventional point-
to-point detection algorithms. Essentially, these detection schemes take advantage
of the knowledge that only a given subset of antennas will be active per user. In
other words, the transmitted signals have a specific structure. Still, the above algo-
rithms, which have developed contemporarily to this Thesis, do not fully optimize
the detection procedure, where additional complexity savings can be achieved. In
this line, Chapter 5 designs a detection algorithm for SM with the purpose of
providing further complexity and performance benefits in the MAC of LSAS.
2.3.3 Hybrid Analog-Digital Precoding and Detection for LSAS
Hybrid analog-digital precoding and detection schemes aim at reducing the number
of RF chains by translating part of the signal processing operations to the RF domain
[20, 192–195]. Indeed, this approach is crucial in mmWave systems due to the reduced
number of degrees of freedom offered by the communication channel and the need for
providing beamforming gains [156]. The employment of hybrid precoding and detection
at mmWaves is further motivated by the cost of the RF chains at these high frequencies,
which is significantly increased w.r.t. the components working below 3 GHz [16, 193]. In
practical terms, this introduces a limitation in the number of RF chains that mmWave
systems can implement. The composite precoding matrix F of hybrid analog-digital
precoding systems can be decomposed as [193]
where FBB ∈ CM ×K represents the digital baseband precoding matrix and FRF ∈ CN ×M characterizes the analog beamforming network (ABFN). The equivalent hardware block diagram of hybrid analog-digital precoding systems is shown in Fig. 2.13. Since
FRFadmits multiple hardware implementations, additional constraints must be enforced
in its definition. Overall, hybrid precoding systems allow reducing both the analog
hardware and signal processing complexities at the expense of a reduced flexibility when
compared with fully-digital designs [147, 195–197]. The operation of hybrid analog-
digital systems in realistic systems is explored in Chapter 8, where the importance of
accounting for the particularities of performing part of the signal processing on the RF