Multiuser multiple-input multiple-output (MIMO) downlink (DL) transmission schemes experience both multiuser interference (MUI) as well as inter-antenna interference. However, instead of treating all the users jointly as in zero-forcing (ZF) multiuser transmission techniques, the investigated singular value decomposition (SVD) and geometric mean decomposition (GMD) assisted DL multiuser MIMO systems take the individual user's channel characteristics into account. The performed joint optimization of the number of activated MIMO layers and the number of bits per symbol along with the appropriate allocation of the transmit power shows that not necessarily all user-specific MIMO layers have to be activated in order to minimize the overall BER under the constraint of a fixed data throughpu

Ahrens, Andreas

Aust, Sebastian

Benavente Peces, César

English

Servicio de Coordinación de Bibliotecas de la Universidad Politécnica de Madrid

Modulation-Mode and Power-Assignment for SVD 
and GMD-assisted Downlink MIMO Systems 
Sebastian Aust, Andreas Ahrens 
Hochschule Wismar, University of Technology, Business and Design 
Department of Electrical Engineering and Computer Science 
Philipp-Miiller-StraBe 14, 23966 Wismar, Germany 
Email: andreas.ahrens@hs-wismar.de 
César Benavente-Peces 
Universidad Politécnica de Madrid 
E.U.I.T de Telecomunicación 
Ctra. Valencia, km. 7, 28031 Madrid, Spain 
Email: cesar.benavente@upm.es 
Abstract—Multiuser multiple-input multiple-output (MIMO) 
downlink (DL) transmission schemes experience both multiuser 
interference (MUI) as well as inter-antenna interference. How-
ever, instead of treating all the users jointly as in zero-forcing 
(ZF) multiuser transmission techniques, the investigated singular 
value decomposition (SVD) and geometric mean decomposition 
(GMD) assisted DL multiuser MIMO systems take the individual 
user's channel characteristics into account. The performed joint 
optimization of the number of activated MIMO layers and the 
number of bits per symbol along with the appropriate allocation 
of the transmit power shows that not necessarily all user-specific 
MIMO layers have to be activated in order to minimize the 
overall BER under the constraint of a fixed data throughput. 
I. I N T R O D U C T I O N 
Adaptive modulation is a promising technique to increase the 
spectral efficiency of wireless transmission systems by adapt-
ing the signal parameters dynamically to changing channel 
conditions. However, in order to comply with the demand 
on increasing available data rates in particular in wireless 
technologies, systems with multiple transmit and receive an-
tennas, also called MIMO systems, have become indispensable 
and can be considered as an essential part of increasing both 
the achievable capacity and integrity of future generations 
of wireless systems [1], [2]. However, single-user MIMO 
transmission schemes for both non-frequency and frequency 
selective MIMO channels have attracted a lot of attention 
and reached a state of maturity [1], [3]. By contrast, MIMO-
aided multiple-user systems require substantial further re-
search where both multiuser as well as multi-antenna inter-
ferences have to be taken into account. In this work, SVD-
and GMD-assisted downlink (DL) multiuser multiple-input 
multiple-output (MIMO) systems are considered, which take 
the individual user's channel characteristics into account [4], 
[5] rather than treating all users channels jointly as in ZF 
multiuser transmission techniques. Whereas SVD transforms a 
MIMO channel into multiple single-input single-output (SISO) 
channels having unequal gains, GMD with further transmit 
preprocessing (e. g. Tomlinson-Harashima Precoding) is able 
to decompose the MIMO channel into multiple SISO channels 
having equal gains, which might be more convenient for 
the design of transmit transmission schemes. Against this 
background, in this paper SVD- and GMD-assisted multiuser 
MIMO schemes are investigated, where both multiuser inter-
ferences as well as multi-antenna interferences are perfectly 
eliminated. The novel contribution of this paper is that we 
demonstrate the benefits of amalgamating a suitable choice of 
activated MIMO layers and number of bits per symbol along 
with the appropriate allocation of the transmit power under the 
constraint of a given fixed data throughput. The remaining part 
of this paper is organized as follows: Section II introduces the 
multiuser system model, while the proposed uncoded solutions 
are discussed in section III. The associated performance results 
are presented and interpreted in section IV. Finally, section V 
provides some concluding remarks. 
II. M U L T I U S E R S Y S T E M M O D E L 
The system model considered in this work consists of a single 
base station (BS) supporting K mobile stations (MSs). The BS 
is equipped with nx transmit antennas, while the th (with 
= 1 , . . . ,iT) MS has n^k receive antennas, i.e. the total 
number of receive antennas including all K MSs is given by 
nR = Xl/c=i nR/c- The (nR& x 1) user specific symbol vector 
Cfc to be transmitted by the BS is given by 
\ T 
Cfc = (c/c , l ,C/c,2, • • • jck,nKk) (1) 
The vector c& is preprocessed before its transmission by 
multiplying it with the (nx XiiR^j DL preprocessing matrix 
R/c and results in the (nx x 1) user-specific transmit vector 
Sfc = RfcCfc. After DL transmitter preprocessing, the % -
component signal s transmitted by the BS to the K MSs results 
in 
K 
s = /_\Sk = r^c 
k=l 
with the (riT x TÍR) preprocessing matrix 
R = ( R i , R 2 , , R K ) 
(2) 
(3) 
In (2), the overall (TÍR X 1) transmitted DL data vector c 
combines all K DL transmit vectors c& (with = 1, 2 , . . . , K) 
and is given by 
(ci T T Co . -K) (4) 
At the receiver side, the (nRfc x 1) received signal vector ufc 
of the th MS results in 
ufc = Hfc s + nfc = Hfc R e + nfc 
and can be expressed by 
ufc — Hfc Rfc Cfc 
K 
/ „ Hfc Rj nfc 
(5) 
(6) 
where the MSs received signals experience both multi-user and 
multi-antenna interferences. In (5), the (nRfc x nT) channel 
matrix Hfc connects the n T BS specific transmit antennas with 
the nRfc receive antennas of the th MS. It is assumed that 
the coefficients of the (nRfc x nT) channel matrix Hfc are 
independent and Rayleigh distributed with equal variance. The 
interference, which is introduced by the channel matrix Hfc, 
requires appropriate signal processing strategies. A popular 
technique is based on the SVD of the system matrix Hfc as 
described in [4]. Therein, after pre- and postprocessing of 
the transmitted and received signal vectors, the user-specific 
decision variables result in 
Yfc = VfcuPfc Cfc Wfc (7) 
where interferences between the different antenna data streams 
as well as MUI imposed by the other users are avoided 
as shown in [4]. In (7), the (nRfc x nRfc) diagonal matrix 
Vfc
 u contains the non-zero square roots of the eigenvalues of 
Hf Hfc and the user-specific (nRfc x nRfc) diagonal power 
allocation matrix Pfc is given by Pfc = Vft~lnKkxnKk with 
the parameter A//? taking the transmit-power constraint into 
account as highlighted in [4]. Finally the additive, white 
Gaussian noise (AWGN) vector is given by wfc. 
III. OPTIMIZATION OF THE UNCODED SYSTEM 
In general, the user-specific quality of data transmission can be 
informally assessed by using the signal-to-noise ratio (SNR) 
at the detector's input defined by the half vertical eye opening 
and the noise power per quadrature component according to 
Q = 
(Half vertical eye opening) (UA 
Noise Power (Us 
(8) 
which is often used as a quality parameter [3]. When applying 
the proposed system structure for the th user, the applied 
signal processing leads to different eye openings per activated 
MIMO layer £ (with £= 1,2,..., L and L < nR k describing 
the number of activated user-specific MDVIO layers) and per 
transmitted symbol block m according to 
U Afc vt:i yg (m) TJ{£) ' usk (9) 
TW where Uñ\¿ denotes the half-level transmit amplitude assuming 
£-ary QAM, JQ^I represents the corresponding positive 
square roots of the eigenvalues of the matrix H^ Hfc and 
TABLE I 
Investigated user-specific QAM transmission modes 
throughput 
8 bit/s/Hz 
8 bit/s/Hz 
8 bit/s/Hz 
8 bit/s/Hz 
8 bit/s/Hz 
layer 1 
256 
64 
16 
16 
4 
layer 2 
0 
4 
16 
4 
4 
layer 3 
0 
0 
0 
4 
4 
layer 4 
0 
0 
0 
0 
4 
p^l' represents the corresponding power allocation weight-
ing parameters. Together with the noise power per quadrature 
component, introduced by the additive, white Gaussian noise 
(AWGN) vector wfc in (7), the th user-specific SNR per 
MIMO layer i at the time m becomes 
U.m) 
6k 
U Afc 
Ul 
(10) 
Using the parallel transmission over L MIMO layers, the 
overall mean transmit power becomes Psk = X^=i^Vfc-
Considering QAM constellations, the average user-specific 
transmit power P sy per MDVIO layer I may be expressed as 
[6] 
m _ p s k u. ) ' < k£ (11) 
Assuming that the transmit power is uniformly distributed over 
the number of activated MIMO layers, i. e., P sy = P s k/L, the 
layer-specific signal-to-noise ratio at the time m results with 
the ratio of symbol energy to noise power spectral density 
EB/N0 = Psfc/(2[/2) and (10), (11) and (9) in 
U.m) 
Qk 
(m) Jm) 
' JJk,£ Sfc,£ 
Ea 
L( kl I) No 
(12) 
In order to transmit at a fixed data rate while maintaining 
the best possible integrity, i. e., bit-error rate, an appropriate 
number of user-specific MDVIO layers has to be used, which 
depends on the specific transmission mode, as detailed in 
Table I for the exemplarily investigated two-user multiuser-
system (nRfc = 4 (with = 1,2), if = 2,nR = n T = 8). 
However, the user-specific BER of the uncoded MIMO system 
is dominated by the specific layers having the lowest SNR's. 
As a remedy, a MIMO-layer transmit power allocation (PA) 
scheme is required for minimizing the overall BER under 
the constraint of a limited total MIMO transmit power. The 
proposed PA scheme scales the th user half-level transmit 
amplitude U^ of the ¿th MIMO layer by the factor \Ji^. 
This results in a MIMO layer-specific transmit amplitude of 
£/s fc Jpk£ for the QAM symbol of the transmit data vector 
transmitted at the time m over the MIMO layer i. Together 
with the DL preprocessing design, the layer-specific power 
allocation parameter at the time m results in: 
V^? = v / ^v^? (13) 
A natural choice is to opt for a PA scheme, which results in 
an identical signal-to-noise ratio 
(£,m) _ 
£pAfc — 
U, PAfc 
ul 
~(m) 3 ^ 7 / ?
( m )
 Es 
L( k£ I) N0 (14) 
(e,m) for all activated MIMO layers at the time m, i. e., in gyp^ k' = 
constant for I = 1,2, • • •, L. The power to be allocated to 
each activated MIMO layer at the time m can be shown to be 
calculated as follows [3]: 
~(m) 
PkJ ( k£ 
I) L 
Jm) 
?fc,£ 
L 
E 
(15) 
(Mkw-1) 
Am) 
Another decomposition that has attracted a lot of interest 
within the last years is called geometric mean decomposition 
(GMD) [7], [8] and avoids the unequal weighting of the user-
specific MDVIO layers introduced by the SVD at the cost of 
remaining interferences between the different antenna data 
streams. The GMD of the system matrix Hfc results in: Hfc = 
U G k • V G k • D Q k, where UG k and D§ k have orthonormal 
columns and V G k is a real-valued upper triangular matrix. 
The (nRfc x nT) matrix VGfc can be decomposed into a 
(nRfc x nRfc) real-valued upper triangular matrix V G f c u and 
a («Rfc x (nT - nRfc)) zero-matrix V G f c n according to 
VGfc = (V G f c u V G f c n ) = (VGfcuO) (16) 
Therein, the diagonal elements of the real-valued upper trian-
gular matrix V G k u are equal to the geometric mean of the 
positive square roots of the eigenvalues of the matrix Hf Hfc. 
For a given time m, the diagonal elements V£¿ of the matrix 
V G k u can be obtained by 
/nRk \ V " R f c 
V£,£= Í I I V ^ M ) £=l,2,---,nRk . (17) 
If the GMD is constrained to the best L < nRk layers, the 
diagonal elements of the matrix V G k u result in 
V=i / 
and the corresponding real-valued upper triangular matrix 
V G k u changes to 
Vee = e = i,2,---,L (18) 
'Gfcu — 
/ 
V 
«1,1 
0 
0 
0 
«1,2 
«2,2 
0 
0 
0 
0 
«1,L 
V2,L 
VL,L 
0 
\ 
(19) 
The remaining interferences between the different antenna data 
streams can be removed by combining GMD with conventional 
zero-forcing VBLAST (Vertical Bell Laboratories Layered 
Space-Time Architecture [9]), where sequential nulling and 
cancellation is applied. However, in order to avoid the error-
propagation at the receiver side, dirty paper precoding could be 
implemented at the transmitter side, if channel state informa-
tion is available. The proposed iterative transmitter preprocess-
Ck 
T> 
-J 
modulo 
•-k 
Vckur 
z - 1 
<*u 
O 
Fig. 1. Iterative user-specific DL interference cancellation scheme 
ing structure is depicted in Fig. 1. The modulo operation has 
to be performed according to the chosen modulation alphabet 
[10] and the matrix V G fcur results in 
V G f c u r = ( V G f c u - d i a g ( V G f c u ) ) . (20) 
«1,1 
The preprocessed transmit data vector ck(p) can be obtained 
iteratively with p > Í and cfc(0) = 0. 
IV. RESULTS 
In this contribution fixed transmission modes are used regard-
less of the channel quality. Assuming predefined transmission 
modes, a fixed data rate can be guaranteed. Considering a 
non-frequency selective SDM (spatial division multiplexing) 
single-user MDVIO link (K = 1) composed of nx = 4 transmit 
and nR = 4 receive antennas, the obtained BER curves are 
depicted in Fig. 2 for the different QAM constellation sizes 
and MIMO configurations of Table I, when transmitting at 
a bandwidth efficiency of 8 bit/s/Hz. Assuming a uniform 
distribution of the transmit power over the number of activated 
MIMO layers, it turns out that not all MIMO layers have to 
be activated in order to achieve the best BERs. 
PA can be used to balance the bit-error probabilities in 
the different number of activated MIMO layers. As shown 
in Fig. 2, unequal PA is only effective in conjunction with the 
10" 
jo 10" 
o 
CD 
-O 10" 
10" 
Y (256,0,0,0) QAM 
D (64,4,0,0)QAM 
J> (16,4,4,0)QAM 
O (4,4,4,4)QAM 
12 14 16 18 
10-log10(Es/N0) 
20 22 
( ¡ n d B ) ^ 
24 
Fig. 2. BER with PA (dotted line) and without PA (solid line) when using 
the transmission modes introduced in Table I and transmitting 8 bit/s/Hz over 
non-frequency selective channels 
$ (16,4,4,0) QAM, SVD 
12 14 16 18 20 22 24 
10-logio(Es/N0) ( i n d B ) ^ 
Fig. 3. BER with PA (dotted line) and without PA (solid line) when using 
the transmission modes introduced in Table I and transmitting 8 bit/s/Hz over 
non-frequency selective channels 
optimum number of MIMO layers and at high SNR. Using 
all MIMO layers, our PA scheme would assign much of the 
total transmit power to the specific symbol positions per data 
block having the smallest singular values and hence the overall 
performance would deteriorate. 
Next to the investigated SVD approach, GMD concen-
trates the channel energy on the number of activated MIMO 
layers at the cost of remaining interferences. However, the 
remaining interferences can easily be compensated by dirty 
paper precoding such as the investigated iterative Tomlinson-
Harashima precoding, which transfers the whole MIMO link 
into a number of multiple SISO channels having equal gains. 
The obtained BER curves are depicted in Fig. 3 and show 
the potential of GMD based signal processing in conjunction 
with the investigated iterative Tomlinson-Harashima precod-
ing. Having layers with equal gains, power allocation can be 
avoided as long as equal QAM constellation sizes are used on 
all activated MIMO layers. 
Comparing the SVD and GMD-based results it turns out 
that not necessarily all MIMO layers have to be activated in 
order to get the lowest BERs. However, GMD-based signal 
processing offers the advantage of multiple SISO channels per 
SDM MIMO data block with equal gains regardless of the 
channel quality that makes power allocation unnecessary and 
outperforms the SVD-assisted solutions. 
The parameters of the exemplarily studied two-users MIMO 
system are chosen as follows: Psk = 1V2, nRfc = 4 (with 
= 1,2), K = 2, n-R = n-T = 8. In this contribution a 
power with the dimension (voltage) (in V2) is used. At a 
real, constant resistor this value is proportional to the physical 
power (in W). The obtained user-specific BER curves are 
depicted in Fig. 4 for the different QAM constellation sizes 
and MIMO configurations of Table I and confirm the obtained 
results within the single-user system (K = 1). Assuming a 
uniform distribution of the transmit power over the number of 
activated MIMO layers, it still turns out that not all MDVIO 
layers have to be activated in order to achieve the best BERs. 
10 ' ' ' ¡ ' 
10 15 20 25 30 
10-logio(Es/N0) ( i n d B ) ^ 
Fig. 4. SVD-based user-specific BERs without PA when using the trans-
mission modes introduced in Table I and transmitting 8 bit/s/Hz over non-
frequency selective channels 
V. CONCLUSION 
Single- and multiuser MDVIO systems in conjunction with 
SVD and GMD assisted signal processing were investigated in 
this work. It turned out, that the choice of the number of bits 
per symbol as well as the number of activated MIMO layers 
substantially affects the performance of a MDVIO system, 
suggesting that not all MIMO layers have to be activated in 
order to achieve the best BERs. The main goal was to find 
that specific combination of the QAM mode and the number of 
MIMO layers, which gives the best possible BER performance 
at a given fixed bit/s/Hz bandwidth efficiency. The Es/N0 
value required by each scheme at BER 10~2 {K = 2) and a 
BER 10~4 {K = 1) was extracted from computer simulations 
and the best systems are shown in bold in Table I. 
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Modulation-mode and power-assignment for SVD-and GMD-assisted downlink MIMO systems

Archivo Digital UPM

Digital Communications.

Diversity and Multiplexing: A Fundamental Tradeoff in Multiple-Antenna Channels.&quot;

Modulation-Mode and Power Assignment for SVD-assisted Downlink Multiuser MIMO Systems,&quot;

Modulation-Mode and Power Assignment in SVD-equalized MIMO Systems.&quot;

Precoding and Signal Shaping for Digital Transmission.

SVD Assisted Joint Transmitter and Receiver Design for the Downlink of MIMO Systems.&quot;

The Generalized Triangular Decomposition.&quot;

The Geometric Mean Decomposition.&quot; Linear Algebra and Its Applications,

V-BLAST: An Architecture for Realizing Very High Data Rates over the Rich-Scattering Wireless Channel,&quot;

Wireless Communications over MIMO Channels — Applications to CDMA and Multiple Antenna Systems.

http://oa.upm.es/7911/2/INVE_MEM_2010_79642.pdf

Modulation-mode and power-assignment for SVD-and GMD-assisted downlink MIMO systems

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