MODULATION-MODE ASSIGNMENT IN SVD-ASSISTED

MULTIUSER MIMO-OFDM SYSTEMS

Sebastian Aust

, Andreas Ahrens

and C´esar Benavente-Peces

Hochschule Wismar, University of Technology, Business and Design, Philipp-M¨uller-Straße 14, 23966 Wismar, Germany

Universidad Polit´ecnica de Madrid, Ctra. Valencia. km. 7, 28031 Madrid, Spain

Keywords:

Multiple-Input Multiple-Output System, Orthogonal Frequency Division Multiplexing, Singular-Value

Decomposition, Bit Allocation, Power Allocation, Wireless Transmission.

Abstract:

In order to comply with the demand on increasing available data rates in particular in wireless technologies,

systems with multiple transmit and receive antennas, also called MIMO (multiple-input multiple-output) sys-

tems, have become indispensable for future generations of wireless systems. Due to the strongly increasing

demand in high-data rate transmission systems, frequency non-selective MIMO links have reached a state of

maturity and frequency selective MIMO links are in the focus of interest. In this ﬁeld, the combination of

MIMO transmission and OFDM (orthogonal frequency division multiplexing) can be considered as an es-

sential part of fulﬁlling the requirements of future generations of wireless systems. However, single-user

scenarios have reached a state of maturity. By contrast multiple users’ scenarios require substantial further

research, where in comparison to ZF (zero-forcing) multiuser transmission techniques, the individual user’s

channel characteristics are taken into consideration in this contribution. The performed joint optimization of

the number of activated MIMO layers and the number of transmitted bits per subcarrier along with the appro-

priate allocation of the transmit power shows that not necessarily all user-speciﬁc MIMO layers per subcarrier

have to be activated in order to minimize the overall BER under the constraint of a given ﬁxed data throughput.

1 INTRODUCTION

The requirements for transmission capacity for

speech, data and multimedia information will proba-

bly increase continuously in the future. With the lim-

itation of available resources such as transmit power

or bandwidth, the demand to increase the spectral ef-

ﬁciency of future transmission systems is clearly rec-

ognizable.

Multicarrier transmission such as OFDM (orthog-

onal frequency division multiplexing) represents a

suitable method for the digital signal transmission

over linear distorting channels (Bingham, 2000), (van

Nee and Prasad, 2000), (Hwang et al., 2003). The

available transmission bandwidth is decomposed into

a number of narrowband channels in which data

streams are transmitted with reduced speed. Further-

more, it offers a great spectral efﬁciency which is a re-

quirement in current communication systems to trans-

mit at high data rates over band limited channels, spe-

cially those aimed at transmitting multimedia content.

However, in order to comply with the demand on

increasing available data rates in particular in wire-

less technologies, systems with multiple transmit and

receive antennas, also called MIMO (multiple-input

multiple-output) systems, have become indispensable

and can be considered as an essential part of increas-

ing both the achievable capacity and integrity of fu-

ture generations of wireless systems (Zheng and Tse,

2003), (K¨uhn, 2006).

Since the capacity of MIMO systems increases

linearly with the minimum number of antennas at

both, the transmitter as well as the receiver side,

MIMO schemes have attracted substantial attention

(McKay and Collings, 2005), (Mueller-Weinfurtner,

2002).

With the increasing desire for high-data rate com-

munication, frequency non-selective MIMO links

have reached a state of maturity. By contrast, fre-

quency selective MIMO links require substantial fur-

ther research. Spatial-temporal vector coding (STVC)

introduced by RALEIGH seems to be an appropriate

candidate for broadband transmission channels. Un-

fortunately, such solutions appear to be highly com-

plex (Raleigh and Ciofﬁ, 1998), (Raleigh and Jones,

1999). Therefore, complexity-reduced solutions are

Aust S., Ahrens A. and Benavente-Peces C..

MODULATION-MODE ASSIGNMENT IN SVD-ASSISTED MULTIUSER MIMO-OFDM SYSTEMS.

DOI: 10.5220/0003443900770086

In Proceedings of the International Conference on Wireless Information Networks and Systems (WINSYS-2011), pages 77-86

ISBN: 978-989-8425-73-7

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

of great interest, where multicarrier transmission such

as OFDM combined with multiple transmit and re-

ceive antennas seems to be a promising solution to

reduce the complexity signiﬁcantly.

The combination of MIMO transmission and

OFDM, as investigated in this work, can be consid-

ered as an essential part of fulﬁlling the requirements

of future generations of wireless systems. However

single-user scenarios have reached a state of maturity.

By contrast multiple users’ scenarios in frequency-

selective channel conditions require substantial fur-

ther research (Ahrens and Benavente-Peces, 2010),

(Liu et al., 2008).

Considering the entirety of the antennas of all mo-

bile terminals at one end and the antennas of the base

station at the other end of the communication link,

state of the art interference cancellation is based on

a central signal processing unit, e. g. a central unit

at the base station, where joint detection can be ap-

plied in the uplink (UL) and joint transmission in the

downlink (DL), respectively (Meurer et al., 2000),

(Choi and Murch, 2004), (Joham et al., 2005). Widely

used linear preprocessing techniques such as Mini-

mum Mean Square Error or Zero Forcing (ZF) have

attracted a lot of research and have reached a state of

maturity, too (Choi and Murch, 2003).

Multiple users’ scenarios in frequency-selective

MIMO channels using STVC were investigated in

(Ahrens and Benavente-Peces, 2010), where, based

on the proposed signal processing, multiuser as well

as multi-antenna interferences are perfectly elimi-

nated. Therein, it was shown that not necessarily all

user-speciﬁc MIMO layers have to be activated in or-

der to minimize the overall BER. Furthermore, power

allocation was found to be beneﬁcial for minimizing

the overall BER.

Against this background, in this paper a SVD-

assisted multiuser MIMO-ODFM scheme is investi-

gated, where multiuser interferences as well as multi-

antenna interferences are perfectly eliminated on each

subcarrier. Instead of treating all users’ channels

jointly as in ZF (zero-forcing) multiuser transmission

techniques, the investigated solutions take the indi-

vidual users’ channel characteristics into account (Liu

et al., 2008). The novel contribution of this paper is

that we demonstrate the beneﬁts of amalgamating a

suitable choice of activated MIMO layers and num-

ber of bits per subcarrier 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 2 introduces the subcarrier-speciﬁc

MIMO-OFDM system model, while the proposed so-

lutions of bit and power allocation are discussed in

section 3. The associated performance results are pre-

sented and interpreted in section 4. Finally, section 5

provides some concluding remarks.

2 MIMO-OFDM SYSTEM MODEL

In this section a subcarrier-speciﬁc MIMO-OFDM

system model for both single-user and multi-user

scenarios is developed where the arising subcarrier-

speciﬁc interferences are perfectly eliminated. The

system model considered in this work consists of a

single base station (BS) supporting K mobile stations

(MSs). The BS is equipped with n

transmit antennas,

while the kth (with k = 1,..., K) MS has n

receive

antennas, i. e. the total number of receive antennas

including all K MSs is given by n

∑

k=1

In order to combat the effects of the frequency se-

lective MIMO channel, OFDM is used as transmis-

sion technique (Bahai and Saltzberg, 1999), (Bing-

ham, 2000). Together with a sufﬁcient guard in-

terval length, interferences between the subcarriers

can be avoided and only symbols that are transmit-

ted over the different antennas at same subcarrier can

interfere each other. Thus, the arising multi-antenna

and multiuser interferences between the different data

streams, transmitted over the same subcarrier, re-

quire appropriate subcarrier-speciﬁc signal process-

ing strategies.

2.1 Single-user System

Considering a single-user MIMO link (K = 1) com-

posed of n

transmit and n

receive antennas, the

obtained (n

)-MIMO-OFDM system transmits an

N-point IFFT (N subchannels) modulated data signal

over every transmit antenna. The subcarrier-speciﬁc

system is modelled by

(κ)

= H

(κ)

·c

(κ)

+ n

(κ)

. (1)

In (1), the (n

×1) vector c

(κ)

contains the complex

input symbols transmitted over the κth subcarrier on

each input. Applying OFDM with a sufﬁcient guard

interval length, the (n

×n

) matrix H

(κ)

in (1) results

(κ)







(κ)

··· h

(κ)

··· h

(κ)







, (2)

with the elements h

(κ)

νµ

describing the couplings of

the data symbols on the subchannel κ. The elements

can be ascertained calculating the FFT of the chan-

nel impulse response from transmitter µ to receiver

WINSYS 2011 - International Conference on Wireless Information Networks and Systems

Figure 1: Resulting single-user SVD-based MIMO-OFDM

system model with guard interval (GI).

ν. Finally, u

(κ)

describes the (n

×1) received vector

and n

(κ)

is the (n

×1) vector of the Additive, White

Gaussian Noise (AWGN) having a variance of U

for

both the real and imaginary parts.

The subcarrier-speciﬁc interference, introduced

by the non-diagonal matrix H

(κ)

, requires appropri-

ate signal processing strategies. A popular technique

is based on the singular-value decomposition (SVD)

of the matrix H

(κ)

, which can be written as

(κ)

= U

(κ)

·V

(κ)

·D

(κ)H

, (3)

where U

(κ)

and D

(κ)

are unitary matrices and V

(κ)

a real-valued diagonal matrix of the positive square

roots of the eigenvalues of the matrix H

(κ)

sorted in descending order. The transpose and con-

jugate transpose (Hermitian) of D

(κ)

are denoted by

(κ)T

and D

(κ)

, respectively. Using D

(κ)

as prepro-

cessing matrix at the transmitter side and U

(κ)H

postprocessing matrix at the receiver side, the over-

all transmission relationship results in

(κ)

= U

(κ)H



(κ)

·D

(κ)

·c

(κ)

+ n

(κ)



= V

(κ)

·c

(κ)

+ w

(κ)

. (4)

Thereby, as D

(κ)

and U

(κ)H

are unitary matrices,

neither the transmit power nor the noise power is

enhanced. The resulting single-user SVD-based

MIMO-OFDM system model is represented in Fig. 1.

As a consequence of the processing in (4), the

subcarrier-speciﬁc channel matrix H

(κ)

is trans-

formed into independent, non-interfering layers hav-

ing unequal gains. The resulting subcarrier-speciﬁc

layer-based MIMO-OFDM system model is high-

lighted in Fig. 2.

(κ)

1,ℓ

(κ)

1,ℓ

(κ)

1,ℓ

(κ)

1,ℓ

Figure 2: Resulting subcarrier-speciﬁc layer-based single-

user MIMO-OFDM system model.

The data symbol c

(κ)

1,ℓ

to be transmitted over the

layer ℓ (with ℓ = 1, 2, ... ,min(n

)) at the subcar-

rier κ (with κ = 1,2,.. .,N) is weighted by the layer-

speciﬁc factor

(κ)

1,ℓ

, corresponding to the positive

square root of the eigenvalue in V

(κ)

, and together

with the additivenoise term w

(κ)

1,ℓ

the receiveddata y

(κ)

1,ℓ

results in

(κ)

1,ℓ

(κ)

1,ℓ

·c

(κ)

1,ℓ

+ w

(κ)

1,ℓ

. (5)

Therein, the number of easily separable layers per

subcarrier L is limited by the minimum numbers of

antennas at both sides, the transmitter as well as the

receiver side, i. e.,

L ≤min(n

) . (6)

However, it is worth noting that with the aid of

powerful non-linear near Maximum Likelihood (ML)

sphere decoders it is possible to separate n

> n

number of layers (Hanzo and Keller, 2006).

2.2 Multi-user System

Now, the subcarrier-speciﬁc single-user MIMO-

OFDM system model (K = 1) is extended by consid-

ering a single base station (BS) supporting K mobile

stations (MSs). The (n

×1) user speciﬁc symbol

vector c

(κ)

to be transmitted by the BS over the sub-

carrier κ is given by

(κ)



(κ)

k,1

(κ)

k,2

,. .. ,c

(κ)

k,n



. (7)

The vector c

(κ)

is preprocessed before its transmis-

sion by multiplying it with the (n

×n

) subcarrier-

speciﬁc DL preprocessing matrix R

(κ)

and results in

the (n

×1) user-speciﬁc transmit vector

(κ)

= R

(κ)

. (8)

After subcarrier-speciﬁc DL transmitter preprocess-

ing, the n

-component signal s

(κ)

transmitted by the

BS speciﬁc antennas over the subcarrier κ to the K

MSs results in

(κ)

∑

k=1

(κ)

= R

(κ)

, (9)

with the (n

×n

) preprocessing matrix

(κ)



(κ)

,. .. ,R

(κ)



. (10)

In (9), the overall (n

×1) transmitted DL data vector

(κ)

combines all K DL transmit vectors c

(κ)

(with k =

1,2,. .., K) and is given by

(κ)



(κ)T

.. ., c

(κ)T



. (11)

MODULATION-MODE ASSIGNMENT IN SVD-ASSISTED MULTIUSER MIMO-OFDM SYSTEMS

At the receiver side, the (n

×1) vector u

(κ)

of the

kth MS is given by

(κ)

= H

(κ)

+ n

(κ)

= H

(κ)

+ n

(κ)

. (12)

and can be expressed by

(κ)

= H

(κ)

∑

i=1,i6=k

(κ)

+ n

(κ)

(13)

where the MSs received signals at the subcarrier κ

(with κ = 1,2,. .., N) experience both multi-user and

multi-antenna interferences. In (12), the (n

×n

)

subcarrier-speciﬁc channel matrix H

(κ)

connects the

BS speciﬁc transmit antennas with the n

receive

antennas of the kth MS.

The subcarrier-speciﬁc interference, which is in-

troduced by the off-diagonal elements of the channel

matrix H

(κ)

, requires appropriate signal processing

strategies. A popular technique is based on the SVD

of the system matrix H

(κ)

. Upon carrying out the

SVD of H

(κ)

with n

≥n

and assuming that the rank

of the matrix H

(κ)

equals n

, i.e., rank(H

(κ)

) = n

we get

(κ)

= U

(κ)

·V

(κ)

·D

(κ)H

, (14)

with the (n

× n

) unitary matrix U

(κ)

and the

× n

) unitary matrix D

(κ)H

, respectively. The

×n

) diagonal matrix V

(κ)

can be decomposed

into a (n

×n

) matrix V

(κ)

containing the non-

zero square roots of the eigenvalues of H

(κ)H

(κ)

i. e.,

(κ)







(κ)

k,1

0 ··· 0

(κ)

k,2

0 0 ···

(κ)

k,n







, (15)

and a (n

×(n

−n

)) zero-matrix V

(κ)

according

(κ)



(κ)





(κ)



. (16)

Additionally, the (n

×n

) unitary matrix D

(κ)

can be

decomposed into a (n

×n

) matrix D

(κ)

constituted

by the eigenvectors corresponding to the non-zero

eigenvalues of H

(κ)H

(κ)

and a (n

×(n

−n

)) ma-

trix D

(κ)

constituted by the eigenvectors correspond-

ing to the zero eigenvalues of H

(κ)H

(κ)

. The decom-

position of the matrix D

(κ)H

results in

(κ)H

. (17)

Finally, the subcarrier-speciﬁc downlink received sig-

nal u

(κ)

of the kth MS may be expressed as

(κ)

= U

(κ)

(κ)H

(κ)

+ n

(κ)

, (18)

with the vector n

(κ)

of the Additive, White Gaussian

Noise (AWGN). Taking all MSs received DL signals

(κ)

into account, the (n

×1) receive vector results

(κ)



(κ)T

,. .. ,u

(κ)T



. (19)

The overall DL signal vector u

(κ)

including the re-

ceived signals of all K MSs can be expressed by

(κ)

= U

(κ)

(κ)H

(κ)

+ n

(κ)

, (20)

with the overall (n

×1) noise vector

(κ)



(κ)T

,. .. ,n

(κ)T



, (21)

the (n

×n

) block diagonal matrix U

(κ)







(κ)

0 ··· 0

0 U

(κ)

0 0 ··· U

(κ)







, (22)

the (n

×n

) block diagonal matrix V

(κ)







(κ)

0 ··· 0

0 V

(κ)

0 0 ··· V

(κ)







, (23)

and the (n

×n

) matrix D

(κ)

which is given by

(κ)



(κ)

,. .. ,D

(κ)

K u



. (24)

In order to suppress the DL multiuser interferences

(MUI) at the subcarrier κ perfectly, the DL prepro-

cessing matrix R

(κ)

has to be designed to satisfy the

following condition

(κ)H

(κ)

= P

(κ)

, (25)

with the real-valued (n

×n

) diagonal matrix P

(κ)

taking the transmit-power constraint into account. In

order to satisfy (25), R

(κ)

can be deﬁned as follows

(κ)

= D

(κ)



(κ)H

(κ)



−1

(κ)

. (26)

WINSYS 2011 - International Conference on Wireless Information Networks and Systems

Taking the ZF design criterion for the DL prepro-

cessing matrix into account, the matrix P

(κ)

simpli-

ﬁes to an (n

× n

) diagonal matrix, i. e. P

(κ)

×n

, with the parameter

(κ)

describing

the transmit-power constraint. When taking the DL

preprocessing matrix, deﬁned in (26), into account,

the overall subcarrier-speciﬁc received vector of all K

MSs, deﬁned in (20), can be simpliﬁed to

(κ)

= U

(κ)

+ n

(κ)

. (27)

Therein, the (n

×n

) block diagonal matrix P

(κ)

given by

(κ)







(κ)

0 ··· 0

0 P

(κ)

0 0 ··· P

(κ)







. (28)

In (27), the user-speciﬁc (n

×1) vector u

(κ)

can be

expressed as

(κ)

= U

(κ)

+ n

(κ)

, (29)

with the user-speciﬁc (n

×n

) power allocation

matrix

(κ)







(κ)

k,1

0 ··· 0

(κ)

k,2

0 0 ···

(κ)

k,n







(30)

As long as the transmit power is uniformly distributed

over the number of activated MIMO layers per sub-

carrier, the matrix P

(κ)

simpliﬁes to

(κ)

×n

. (31)

After postprocessing of the received signal vectors

(κ)

with the corresponding unitary matrix U

(κ)H

, the

user-speciﬁc decision variables at the subcarrier κ re-

sult with U

(κ)H

(κ)

= w

(κ)

= U

(κ)H

(κ)

= V

(κ)

+ w

(κ)

, (32)

or alternatively for the whole system with

(κ)H

(κ)

= w

(κ)

= U

(κ)H

(κ)

= V

(κ)

+ w

(κ)

, (33)

where subcarrier-speciﬁc interferences between the

different antenna data streams as well as MUI im-

posed by the other users are avoided. The resulting

multiuser SVD-based MIMO-OFDM system model

is represented in Fig. 3, whereas the resulting layer-

speciﬁc system model is depicted in Fig. 4

Figure 3: Resulting multiuser SVD-based MIMO-OFDM

system model with guard interval (GI).

3 OPTIMIZATION OBJECTIVES

In general, the user-speciﬁc quality of data transmis-

sion 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

ρ =

(Half vertical eye opening)

Noise Power

)

, (34)

which is often used as a quality parameter (Ahrens

and Lange, 2008). The relationship between the

signal-to-noise ratio ρ = U

and the bit-error

probability evaluated for AWGN channels and M-ary

Quadrature Amplitude Modulation (QAM) is given

by (Proakis, 2000)

BER

log

(M)



1−

√



erfc





. (35)

When applying the proposed system structure for the

kth user, depicted in Fig. 4, the applied signal pro-

cessing leads to different eye openings per activated

MIMO layer ℓ (with ℓ = 1, 2,.. .,L and L ≤ n

de-

scribing the number of activated user-speciﬁc MIMO

(κ)

k,ℓ

(κ)

k,ℓ

(κ)

k,ℓ

(κ)

k,ℓ

(κ)

k,ℓ

Figure 4: Resulting kth user system model per MIMO

layer ℓ (with ℓ = 1,2,. . . ,n

) on subcarrier κ (with κ =

1,2,.. ., N).

MODULATION-MODE ASSIGNMENT IN SVD-ASSISTED MULTIUSER MIMO-OFDM SYSTEMS

layers) and per subcarrier κ (with κ = 1,2,.. .,N) ac-

cording to

(κ)

Akℓ

(κ)

k,ℓ

(κ)

k,ℓ

·U

(κ)

skℓ

, (36)

where U

(κ)

skℓ

denotes the kth user and κth subcar-

rier speciﬁc half-level transmit amplitude assuming

ℓ

-ary QAM,

(κ)

k,ℓ

represents the corresponding

subcarrier-speciﬁc positive square roots of the eigen-

values of the matrix H

(κ)H

(κ)

and

(κ)

k,ℓ

represents

the corresponding power allocation weighting param-

eters (Fig. 4). Together with the noise power per

quadrature component, introduced by the additive,

white Gaussian noise (AWGN) vector w

(κ)

in (32),

the kth user-speciﬁc SNR per MIMO layer ℓ and sub-

carrier κ becomes

(κ)

kℓ



(κ)

Akℓ



. (37)

Realizing a parallel transmission over L MIMO layers

and taking all N subcarriers into account, the overall

mean user-speciﬁc transmit power becomes

∑

κ=1

∑

ℓ=1

(κ)

skℓ

. (38)

Considering QAM constellations, the average user-

speciﬁc transmit power P

(κ)

skℓ

per MIMO layer ℓ and

subcarrier κ may be expressed as (Proakis, 2000)

(κ)

skℓ



(κ)

skℓ



(κ)

kℓ

−1) . (39)

Combining (37) and (39) together with (36), the layer-

speciﬁc SNR at the subcarrier κ results in

(κ)

kℓ

= p

(κ)

k,ℓ

(κ)

k,ℓ

2(M

(κ)

kℓ

−1)

(κ)

skℓ

. (40)

Assuming that the user-speciﬁc transmit power is

uniformly distributed over the number of activated

MIMO layers and subcarriers, the quality on each

subcarrier is affected by both, the choice of the QAM-

constellation sizes per layer and the layer-speciﬁc

weighting factors. 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

MIMO layers has to be used, which depends on the

speciﬁc transmission mode, as detailed in Table 1 for

the exemplarily investigated two-user MIMO-OFDM

system (n

= 4 (with k = 1,2),K = 2,n

= n

= 8).

An optimized adaptive scheme would now use

the particular transmission modes on each subcarrier,

Table 1: Investigated user-speciﬁc transmission modes per

subcarrier.

throughput layer 1 layer 2 layer 3 layer 4

8 bit/s/Hz 256 0 0 0

8 bit/s/Hz 64 4 0 0

8 bit/s/Hz 16 16 0 0

8 bit/s/Hz 16 4 4 0

8 bit/s/Hz 4 4 4 4

e.g., by using bit auction procedures (Wong et al.,

1999), that results in the lowest BER for each MIMO-

OFDM data vector. However, this would lead to a

high signaling overhead. Therefore, in order to avoid

any signalling overhead, ﬁxed transmission modes are

used in this contribution regardless of the channel

quality.

However, it is worth mentioning that in systems

where channel state information is available at the

transmitter side, the knowledge about how the sym-

bols are attenuated by the channelcan be used to adapt

the transmit parameters. In this context, power allo-

cation (PA) can be used to balance the bit-error prob-

abilities in the number of activated MIMO layers.

Applying PA, the information about how the sym-

bols are attenuated by the channel, i. e., the singular-

values, has to be sent via a feedback channel to the

transmitter side and leads to a signalling overhead that

is contradictory to the ﬁx transmission modes that re-

quire no signalling overhead. However, as shown in

(Ahrens and Lange, 2009) a vector quantizer (VQ)

can be used to keep the signalling overhead moderate.

Here, a VQ for the power allocation parameters in-

stead of the singular values guarantees a better adap-

tion at a given codebook size, since the power level

vectors has less or equal dimensions than the singular-

value vectors (Ahrens and Lange, 2009). Moreover,

its elements are much smaller digits ranged from 0

to 1, rather than from 0 to +∞ in the singular-value

vector case. Hence, the entropy of the power level

vectors is smaller, which beneﬁts the quantization ac-

curacy and the feedback overhead.

Therefore, besides the choice of the transmission

modes, PA can be used to adjust the bit-error proba-

bilities in the activated user-speciﬁc MIMO layers and

has been widely investigated in the literature (Kron-

gold et al., 2000), (Ahrens and Lange, 2008), (Jang

and Lee, 2003).

Analysing the considered MIMO-OFDM system,

the user-speciﬁc BER of the MIMO-OFDM system

is dominated by the speciﬁc layers having the low-

est SNR’s. As a remedy, a MIMO-layer transmit PA

scheme is required for minimizing the overall BER

WINSYS 2011 - International Conference on Wireless Information Networks and Systems

under the constraint of a limited total MIMO transmit

power.

The proposed PA scheme scales the kth user half-

level transmit amplitude U

(κ)

skℓ

of the ℓth MIMO layer

on the subcarrier κ by the factor

˜p

(κ)

k,ℓ

. This re-

sults in a MIMO layer-speciﬁc transmit amplitude of

(κ)

skℓ

˜p

(κ)

k,ℓ

for the QAM symbol of the transmit data

vector transmitted at the subcarrier κ over the MIMO

layer ℓ. Together with the DL preprocessing design,

the layer-speciﬁc power allocation parameter at the

subcarrier κ results in:

(κ)

k,ℓ

(κ)

˜p

(κ)

k,ℓ

. (41)

PA has been widely investigated in the literature,

where optimum solutions tends to be highly complex

(Ahrens and Lange, 2007). In this work a subopti-

mum solution is presented which focusses on the user-

speciﬁc subcarriers.

A natural choice is to opt for a PA scheme, which

results in an identical signal-to-noise ratio

(κ)

PAkℓ



(κ)

PAkℓ



= ˜p

(κ)

k,ℓ

3ξ

(κ)

k,ℓ

(κ)

LN (M

(κ)

kℓ

−1)

(42)

for all activated user-speciﬁc MIMO layers as shown

in (Ahrens and Lange, 2007), i.e., in

(κ)

PAkℓ

= constant (43)

for ℓ = 1,2,.. .,L and κ = 1,2,. .., N. In this particu-

lar case, nearly the same BER can be achieved on all

activated user-speciﬁc MIMO layers and subcarriers

(Ahrens and Lange, 2007).

The proposed suboptimum PA scheme focusses

on the arguments of the complementary error function

and neglects the transmission mode speciﬁc factors in

front of the complementary error function. However,

their inﬂuence, introduced by the layer-speciﬁc QAM

constellation sizes, is by far too small to generate re-

markable differences in the performance as shown in

(Ahrens and Lange, 2007).

4 RESULTS

In this contribution the efﬁciency of ﬁxed user-

speciﬁc transmission modes on each subcarrier is

studied regardless of the channel quality. Assum-

ing predeﬁned transmission modes, a ﬁxed data rate

can be guaranteed. In order to obtain numerical re-

sults for the analyzed subcarrier-speciﬁc signal pro-

cessing strategies, a two-path channel model is in-

vestigated under time-variant conditions between any

10 15 20 25

−8

−6

−4

−2

10 ·log

) (indB) →

bit-error rate →

(256,0,0,0) QAM

(64,4,0,0) QAM

(16,16,0,0) QAM

(16,4,4,0) QAM

(4,4,4,4) QAM

Figure 5: BER without PA when using the transmission

modes introduced in Tab. 1 and transmitting 8 bit/s/Hz per

subcarrier.

given transmit and receive antenna combination. The

exemplary impulse response between the µth transmit

and νth receive antenna as a function of the multicar-

rier symbol duration T

is given by

(νµ)

(t,τ) = g

k,0

(t) ·δ(τ) + g

k,1

(t) ·δ(τ−3/2T

) ,

(44)

whereby the time-variant behaviour is described by

k,0

(t) and g

k,1

(t), respectively. It is assumed that the

path amplitudes have the same averaged power and

undergo a Rayleigh distribution (P¨atzold, 2002). Fur-

thermore, a block fading channel model is applied,

i. e., the channel is assumed to be time invariant for

the duration of one MIMO-OFDM data vector includ-

ing a guard interval length of T

= T

/2. The number

of subcarrier of the investigated OFDM system was

exemplarily chosen to be N = 4.

4.1 Single-user System

Considering a single-user MIMO-OFDM link (K = 1)

composed of n

= 4 transmit and n

= 4 receive an-

tennas, the corresponding calculated BER curves are

depicted in Fig. 5 for the different subcarrier-speciﬁc

QAM constellation sizes and MIMO conﬁgurations

of Table 1, when transmitting at a ﬁxed bandwidth ef-

ﬁciency of 8 bit/s/Hz per subcarrier.

Assuming a uniform distribution of the transmit

power over the number of activated MIMO layers per

subcarrier, it still turns out that not all subcarrier-

speciﬁc MIMO layers have to be activated in order

to achieve the best system performance.

However, the lowest BERs can only be achieved

by using bit auction procedures leading to a high sig-

nalling overhead (Wong et al., 1999). Analyzing the

probability of choosing subcarrier-speciﬁc transmis-

sion modes by using optimal bitloading, as depicted

MODULATION-MODE ASSIGNMENT IN SVD-ASSISTED MULTIUSER MIMO-OFDM SYSTEMS

in Table 2, it turns out that only an appropriate num-

ber of subcarrier-speciﬁc MIMO layers has to be ac-

tivated to reach the best results, e.g., the (16,4, 4, 0)

QAM conﬁguration. Therefore, the results, obtained

by using bit auction procedures, justify the choice of

ﬁxed subcarrier-speciﬁc transmission modes regard-

less of the channel quality as investigated in this con-

tribution.

Table 2: Probability of choosing subcarrier-speciﬁc trans-

mission modes at a ﬁxed data rate by using optimal bitload-

ing (10·lg(E

) = 10 dB and κ = 3).

mode (16,4,4, 0) (16,16,0,0) (64,4, 0,0) (4,4,4,4)

pdf 0.722 0.261 0.016 0.000

Further improvements can be achieved by taking

PA into account. Adaptive power allocation has been

widely investigated in the literature (Krongold et al.,

2000), (Jang and Lee, 2003), (Park and Lee, 2004),

(Ahrens and Lange, 2008) and can be used to balance

the bit-error probabilities in the different number of

activated user-speciﬁc MIMO layers. Using power al-

location, the resulting subcarrier-speciﬁc layer-based

single-user MIMO-OFDM system model is depicted

in Fig. 6.

(κ)

1,ℓ

(κ)

1,ℓ

(κ)

1,ℓ

(κ)

1,ℓ

(κ)

1,ℓ

Figure 6: Resulting subcarrier-speciﬁc layer-based single-

user MIMO-OFDM system model using Power Allocation.

A common strategy is to use the Lagrange mul-

tiplier method in order to ﬁnd the optimal value of

(κ)

1,ℓ

for each MIMO layer ℓ and subcarrier κ,

which often leads to excessive-complexity optimiza-

tion problems (Ahrens and Lange, 2007). There-

fore, suboptimal power allocation strategies having a

lower complexity are of common interest (Ahrens and

Lange, 2007), (Park and Lee, 2004).

A natural choice is to opt for a PA scheme, which

results in an identical signal-to-noise ratio

(κ)

PA1ℓ



(κ)

PA1ℓ



= ˜p

(κ)

1,ℓ

3ξ

(κ)

1,ℓ

LN (M

(κ)

1ℓ

−1)

(45)

for all activated MIMO layers ℓ and subcarriers κ,

i. e., in

(κ)

PA1ℓ

= constant , (46)

for ℓ = 1,2,. .., L and κ = 1, 2, ... ,N. The power to

be allocated to each activated MIMO layer ℓ and sub-

arrier κ can be shown to be calculated by inverting

10 15 20 25

−8

−6

−4

−2

10 ·log

) (indB) →

bit-error rate →

(256,0,0,0) QAM

(16,16,0,0) QAM

(16,4,4,0) QAM

(4,4,4,4) QAM

Figure 7: BER with PA (dotted line) and without PA (solid

line) when using the transmission modes introduced in

Tab. 1 and transmitting 8 bit/s/Hz per subcarrier.

the layer-speciﬁc part ξ

(κ)

1,ℓ

/(M

(κ)

1ℓ

−1) and taking the

transmit power constraint into account as presented in

(Ahrens and Lange, 2007). In this case for each sym-

bol of the transmitted MIMO-OFDM symbol vector

the same half vertical eye opening can be guaranteed,

i. e.,

(κ)

PA1ℓ

= constant . (47)

for all activated MIMO layers ℓ (with ℓ = 1,2,.. .,L)

and all subcarrier κ (with κ = 1,2,. .., N). When

assuming an identical detector input noise variance

for each channel output symbol, the above-mentioned

equal quality scenario (46) is encountered. The only

difference between an optimum PA and the here con-

sidered equal quality scenario is the consideration of

the factor

1−1/

(κ)

1ℓ

(48)

in front of the complementary error function by the

optimum PA. However as shown by (Ahrens and

Lange, 2007) their inﬂuence is by far too small to gen-

erate remarkable differences in the performance.

Analyzing (46) for a given MIMO-OFDM data

block, nearly the same BER can be achieved on all ac-

tivated MIMO layers and subcarriers. However, tak-

ing the time-variant nature of the transmission chan-

nel into account, different BERs arise for different

MIMO-OFDM data blocks. Therefore, the BER of

the MIMO-OFDM system is mainly dominated by the

data blocks having the lowest SNRs. In order to over-

come this problem, the number of transmit or receive

antennas has to be increased, or coding overthe differ-

ent data blocks should be used (Ahrens et al., 2008).

As shown in Fig. 7, taking all subcarrier into ac-

count, unequal PA is only effective in conjunction

with the optimum number of MIMO layers and at

high SNR.

WINSYS 2011 - International Conference on Wireless Information Networks and Systems

10 15 20 25

−2

−1

10 ·log

) (indB) →

bit-error rate →

(256,0,0,0) QAM

(64,4,0,0) QAM

(16,16,0,0) QAM

(16,4,4,0) QAM

(4,4,4,4) QAM

Figure 8: SVD-based user-speciﬁc BERs without PA when

using the transmission modes introduced in Table 1 and

transmitting 8 bit/s/Hz per subcarrier.

4.2 Multi-user System

The parameters of the analyzed two-users MIMO sys-

tem are chosen as follows: P

= 1V

, n

= 4 (with

k = 1,2), K = 2,n

= n

= 8. In this contribution a

power with the dimension (voltage)

(in V

) is used.

At a real constant resistor this value is proportional to

the physical power (in W).

The obtained user-speciﬁc BER curves are de-

picted in Fig. 8 for the different subcarrier-speciﬁc

QAM constellation sizes and MIMO conﬁgurations

of Table 1 and conﬁrm the obtained results within the

single-user MIMO-OFDM system (K = 1). Based on

the higher total subcarrier-speciﬁc throughput within

the given bandwidth compared to the single-user

system, the gap between the different transmission

modes becomes smaller.

Assuming a uniform distribution of the transmit

power over the number of activated MIMO layers,

it still turns out that not all MIMO layers per sub-

carrier have to be activated in order to achieve the

best BERs. This can still be conﬁrmed by analyzing

the probability of choosing user-speciﬁc transmission

modes within the multiuser DL MIMO-OFDM sys-

tem by using optimal bitloading (Wong et al., 1999),

as depicted in Table 3.

The partitioning of the transmit power to the sub-

Table 3: Probability of choosing user-speciﬁc transmission

modes (K = 2) per subcarrier at a ﬁxed data rate by using

optimal bitloading (10·log

) = 10 dB and κ = 3).

mode (16,4,4, 0) (16,16,0,0) (64,4, 0,0) (4,4,4,4)

pdf 0.950 0.010 0.000 0.039

10 15 20 25

−2

−1

10 ·log

) (indB) →

bit-error rate →

(256,0,0,0) QAM

(16,4,4,0) QAM

(4,4,4,4) QAM

Figure 9: SVD-based user-speciﬁc BERs with PA (dotted

line) and without PA (solid line) when using the transmis-

sion modes introduced in Table 1 and transmitting 8 bit/s/Hz

per subcarrier.

channels is a degree of freedom in the multiuser sys-

tem too and has to be done in such a manner, that

for the whole system a maximum performance with

respect to a given quality criterion and given bound-

ary conditions can be achieved (e. g. minimum bit-

error rate with limited transmit power). In the pro-

posed multiuser MIMO-OFDM system, user-speciﬁc

PA can be done, i. e., the available transmit power per

user P

= 1V

can be distributed over all activated

user-speciﬁc layers on all subcarrier. The obtained

BER curves are depicted in Fig. 9.

As developed within the single-user MIMO-

OFDM system, unequal PA based on the proposed

equal-quality scenario is only effective in conjunc-

tion with the optimum number of MIMO layers and at

high SNR. At the low SNR, as depicted in Fig. 9, the

proposed equal-quality scenario doesn’t lead to any

improvement. Here our results suggest that a uniform

distribution of the transmit power seems to be a good

choice for minimizing the overall BER.

5 CONCLUSIONS

In this paper, the DL performance of a multiuser

MIMO-OFDM system is investigated theoretically

and by software simulation. Frequency selective

MIMO channels are considered and conditions to

eliminate multiuser and multi-antenna interferences

on each subcarrier are established using the SVD of

the individual user subcarrier-speciﬁc channel matrix.

Furthermore, bit and power allocation in multiuser

MIMO-OFDM systems were investigated for con-

stant data throughput per subcarrier. Here, it turned

out that the choice of the number of bits per symbol

MODULATION-MODE ASSIGNMENT IN SVD-ASSISTED MULTIUSER MIMO-OFDM SYSTEMS

as well as the number of activated MIMO layers per

subcarrier substantially affects the performance of a

MIMO-OFDM system, suggesting that not all user-

speciﬁc MIMO layers per subcarrier have to be acti-

vated in order to achieve the best BERs. Addition-

ally, unequal PA was found to be effective in conjunc-

tion with the optimum number of MIMO layers for

the overall performance at the high SNR.

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