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146 4 System Level Aspects for Single Cell Scenarios

4.8 Integration of COFDM Systems with

Multiple Antennas and Design of Adaptive

Medium Access Protocols

D. Martini, B. Wolz, B. Rembold, B. Walke, RWTH Aachen University,

Germany

4.8.1 Abstract

Besides medium access in time and frequency domain, the space and polarization

domain can be exploited using multiple antenna (MIMO) systems for space divi-

sion multiple access. SDMA combined with OFDM are the key technologies for

future wireless and mobile communication systems as speciﬁed in standards such

as IEEE 802.16d, IEEE 802.11n and 3GPP LTE. This work focuses on the devel-

opment and prototype implementation of Medium Access Control (MAC) protocols

of a demonstration system that uses multiple antennas. The goal is to serve all

user terminals (UT) best by taking their instantaneous channel condition into ac-

count. A number of candidate channel-adaptive MAC protocols were designed to

be implemented in a stochastic event driven simulator based on the openWNS tool.

The protocol stack under study operates in between a multi-media load generator

and an interference engine that calculates the current SINR at the receiver depen-

dent on the direction of arrival (DoA). The contribution of a IEEE 802.16 speciﬁc

transceiver chain is fed-in from link-level simulation results providing DoA speciﬁc

bit-error characteristics. The openWNS tool is mainly employed to compare the

performance of the MAC protocols, the usefulness of the interface between MAC

and PHY and the constraints of an SDMA enabled scheduler. Besides simulation

studies to understand the performance critical parameters, an analytical validation

of the used simulator and a complexity analysis of a number of SDMA based service

disciplines was performed. The demonstration system was completely implemented

using a modular FPGA system and two high-performance power PCs that to per-

form MAC in real time. The contribution of MIMO technologies to improve the

system capacity was evaluated by means of the SINR values that results from the

studied antenna conﬁgurations. While the FPGA hardware was taken from a former

project, the bidirectional transceiver chains including multiport antennas were new

designed and implemented, resulting in a realtime 4x4 bidirectional MIMO testbed.

4.8.2 MAC Frame for SDMA Operation and Spatial

Grouping

A multi-cellular scenario served by 120

◦

antennas each serving 15 UTs was chosen

operated with re-use one. Transmit power is 1 W and UTs control their power

between 200 mW and 1 W. The scheduler decides based on data volume in MAC-

and PHY layer, signaling overhead per UT and SINR of an UT, estimated based

on the beamforming algorithm information. Figure 4.16 shows an example two-

dimensinal MAC frame to serve two spatially separated data streams. Above the

4.8 Integration of COFDM Systems 147

MAC frame the transmit situation is shown using abstract antenna diagrams. The

ﬁrst part of the frame is transmitted omnidirectional to implement broadcast mode.

DL-MAP (blue) and UL-MAP (green) and arrows are shown pointing to the time

instants contained in the MAPs, where up to four radio bursts can be transmitted,

spatially separated. Similar applies to the UL-MAP.

UTs cannot be arbitrarily scheduled for concurrent SDMA transmissions since

their spatial separability by the beam-forming antenna array depends on their rel-

ative spatial positions. Spatially separated concurrent transmissions cannot be as-

sumed to be orthogonal. Therefore, a hierarchical scheduling algorithm is introduced

that ﬁrst computes a spatial grouping of UTs that can be well separated by the base

station’s (BS) beamforming antenna. The result of this grouping is a set of groups

of UTs. Users of the same spatial group can be separated and thus be served at

the same time. Users in diﬀerent groups must be separated in the time domain.

Structuring of the scheduling process into two hierarchical steps adds ﬂexibility and

simplicity to the scheduling process. The grouping process is independent from the

TDMA scheduling and vice versa. Thus, spatial grouping and group scheduling pro-

cedures can be freely combined and interchanged according to the speciﬁc needs of

the system. Spatial grouping of UTs has been proposed earlier [2] and hierarchical

grouping and scheduling in an SDMA enhanced IEEE 802.16 systems is proposed

ﬁrst in [4]. Since an optimal grouping is far too complex to be applied, a greedy al-

gorithm to sort spatial groups according to achievable throughput was used resulting

in grouping gain slightly below the optimal grouper’s gain. A tree-based heuristic

algorithm only estimating the most promising spatial groups appear well suited to

reduce run-time complexity to be applicable in real-time condition, with a grouping

gain comparable to that of the greedy algorithm.

Simulation Results

Figure 4.17 shows the aggregate DL cell throughput versus oﬀered traﬃc. Satura-

tion is reached where the throughput deviates to grow linearly with oﬀered traﬃc.

Clearly, with omnidirectional it is lower than with SFIR or SDMA transmission.

Under SDMA with up to 4 parallel transmissions, the throughput curve climbs from

a value of about 22 MBit/s, where the ﬁrst UTs reach saturation, to a ﬁnal maximum

of 30 MBit/s. SDMA transmission with up to 4 beams achieves about 440% gain

compared to omnidirectional transmission. Most of the results on MIMO based

MAC protocols, grouping etc. gained in this project are available from [3]. The

scheduler algorithms developed for multiple antenna systems were implemented on

a real-time hardware platform.

4.8.3 Hardware Implementation of COFDM Systems with

Multiple Antennas

A realtime testbed was developed and used to validate the scheduler algorithms in

“real world” scenario. The demonstrator architecture had to be adapted resulting in

redesign of the analog frontend as well as the digital transceiver. The testbed is based

on OFDM transmission with 256 subcarriers for each UT. A WLAN transceiver chip

148 4 System Level Aspects for Single Cell Scenarios

Figure 4.16: A MAC frame supporting

SDMA operation

Figure 4.17: DL throughput vs. to-

tal oﬀered DL traﬃc for

omnidirectional, SFIR,

and SDMA transmis-

sion modes

is used for the analog frontend operating at a radio frequency of 5.6 GHz with an RF

bandwidth of 25 MHz. The modulation of the radio link is adaptive and is BPSK,

QPSK, 16- or 64-QAM, and can be deﬁned independently for each user. In total the

system can serve four BS antennas and four UTs resulting in a 4x4 MIMO system.

Each antenna combination between 1x1 (SISO) and 4x4 (MIMO) with or without

diversity can be operated. Up- and downlink are separated in time division duplex

(TDD). Digital signal processing performs the linear equalization algorithms ZF and

MMSE in real time [1]. Furthermore, pre-equalization at the transmitter is possible

using channel information from uplink transmission.

−2

−4

−6

−8

−10

−12

−14

−16

−18

−5

diversity gain in SIMO configuration − LOS uplink scenario

attenuation of the transmit power in dB

SNR of user at the receiver in dB

1 X 1 − 16 QAM

1 X 2 − 16 QAM

1 X 3 − 16 QAM

1 X 4 − 16 QAM

Figure 4.18: Diversity gain under SIMO

with diﬀerent number of

antennas

−2

−4

−6

−8

−10

−12

−14

−16

−18

diversity gain in SIMO configuration − LOS uplink scenario − 16 QAM

attenuation of the transmit power in dB

SNR of user at the receiver in dB

user 1 −− 4X2 MIMO

user 2 −− 4X2 MIMO

user 1 −− 4X4 MIMO

user 2 −− 4X4 MIMO

user 3 −− 4X4 MIMO

user 4 −− 4X4 MIMO

Figure 4.19: SNR per user with 4x2 and

4x4 MIMO

As an example Fig. 4.18 presents the measured diversity gain that is obtained

using more than one antenna. Regarding MIMO scenarios diversity also plays an

important role as shown in Fig. 4.19. All user can be served with smaller SNR.

Regarding two users the SNR and therefore the data rate is much higher. The

measurements were taken at the entrance hall of the IHF building. The BS was

equipped with a compact four-port-inverted-F antenna and the UT was ﬁt with

4.8 Integration of COFDM Systems 149

another compact four-port antenna using four orthogonal radiation modes [5].

Bibliography

[1] L. Bruehl, Parallele Prozessorarchitektur fuer die Raum-Zeit-Entzerrung in bre-

itbandigen Funksystemen mit adaptiven Gruppenantennen,PhDthesis,RWTH

Aachen, 2005, Shaker ISBN 3-8322-4523-5.

[2] M. Fuchs, G. Del Galdo, and M. Haardt, “A Novel Tree-based Scheduling Al-

gorithm for the Downlink of Multi-user MIMO Systems with ZF Beamforming,”

in Proc. IEEE Internat. Conf. on Acoustics, Speech, and Signal Proc.(ICASSP,

2005.

[3] C. Hoymann, IEEE 802.16 Metropolitan Area Network with SDMA Enhance-

ment, PhD thesis, RWTH Aachen University, Department of Communication

Networks, Faculty 6, July 2008, http://www.comnets.rwth-aachen.de.

[4] C. Hoymann, H. Meng, and J. Ellenbeck, “Inﬂuence of SDMA-Speciﬁc

MAC Scheduling on the Performance of IEEE 802.16 Networks,” in Proceed-

ings of 12th European Wireless Conference 2006, Athens, Greece, April 2006,

http://www.comnets.rwth-aachen.de.

[5] C. Oikonomopoulos-Zachos and B. Rembold, “A 4-Port Antenna for MIMO

Channels,” in IEEE Conf. of Antennas and Propagartion (EUCAP), pages 1–4,

2007.

150 4 System Level Aspects for Single Cell Scenarios

4.9 Large System Analysis of Nearly Optimum

Low Complex Beamforming in Multicarrier

Multiuser Multiantenna Systems

C. Guthy, W. Utschick, Technische Universität München, Germany

4.9.1 Introduction

In general, analytical expressions for the average sum rate in the Multiple-Input

Multiple-Output (MIMO) Broadcast Channel (BC), resulting from signal process-

ing algorithms requiring perfect channel state information at the transmitter, are

diﬃcult to obtain. That is true for the optimum sum capacity [11] as well as near

optimum algorithms such as the Successive Encoding Successive Allocation Method

(SESAM) [9] and its variant with Minimum Mean Square Error (MMSE) trans-

mit ﬁlters [8, Ch. 4.2]. Thus, performance evaluation of these algorithms is only

possible via simulation results. In the large system limit however, i.e., when at

least two system parameters go to inﬁnity at a ﬁxed and ﬁnite ratio [6, 10], the

performance of many algorithms becomes deterministic, although random variables

are used. That is because the eigenvalues of random matrices often converge to an

asymptotic limit, which can be obtained from the asymptotic eigenvalue distribution

(a.e.d.) and which is independent of the current realization of the random matrix.

The most prominent example is the Marčenko-Pastur distribution [5] for Wishart

matrices. Furthermore the analytical expressions in the large system limit often

serve as a good approximation of the system performance also with ﬁnite system

parameters, which makes large system analysis an interesting tool for the analysis

of signal processing algorithms.

In this chapter we will present analytical approximations of the ergodic sum rates

achievable with SESAM with MMSE transmit ﬁlters [8] and zero-forcing transmit

ﬁlters [9] based on large system results with Gaussian i.i.d. channel matrices and an

inﬁnite number of transmit and receive antennas. It will be shown that the results

also serve as good approximations for the average sum rate in systems with ﬁnite

parameters.

4.9.2 System Model

We consider a multi-user multi-carrier MIMO system with C carriers, one base sta-

tion with N antennas and K non-cooperative users with R antennas. The k-th

user’s channel matrix on carrier c, denoted as H

k,c

∈ C

R×N

, consists of uncorre-

lated Gaussian entries with zero mean and variance 1/R. Perfect knowledge of the

matrices H

k,c

at the transmitter is assumed. The additive noise at each receiver is

assumed to be white Gaussian with zero mean and unit covariance matrix.

4.9 Large System Analysis 151

4.9.3 Description of Algorithms

As the optimum solution, both variants of SESAM rely on the principle of Dirty

Paper Coding (DPC). Furthermore they successively allocate data streams to users,

where in each step ﬁlters and user allocation of previously allocated data streams are

kept ﬁxed and the next data stream is allocated to that user such that the increase

in the objective function becomes maximum. The allocation stops, if no increase in

the objective function is possible with a new allocation. Denoting the number of

totally allocated subchannels on carrier c with M

, the achievable sum rate computes

according to

sum



c=1



i=1

log

(1 + p

i,c

In the following we will shortly describe how the subchannel powers p

i,c

and the

channel gains λ

i,c

compute for the two algorithms. For notational convenience, we

assume that the user allocation is given in the following, where π

(i) denotes the

user to which the data stream encoded at i-thplacehasbeenallocatedtooncarrier

c. Certainly, when the algorithm is run, potential subchannel gains have to be

computed for every user and carrier to select the most suitable user and carrier for

each data stream.

SESAM with MMSE Filters

With MMSE ﬁlters, the problem of maximizing sum rate under a total power con-

straint can be solved almost optimally at drastically reduced computational com-

plexity. In this case a simpliﬁed power allocation is assumed such that p

i,c

where P

denotes the available transmit power. The subchannel gains λ

i,c

then

compute according to

i,c

= ρ

⎛

⎜

⎝

(i),c

⎛

⎝

I +

i−1



j=1

(j),c

j,c

(j),c

⎞

⎠

−1

(i),c

⎞

⎟

⎠

, (4.11)

where ρ

(A) denotes the principal eigenvalue of the matrix A. t

j,c

denotes the

transmit ﬁlter in the dual uplink for the j-th data stream on carrier c and is equal

to the unit-norm eigenvector belonging to the principal eigenvalue of the matrix

(i),c

⎛

⎝

I +

i−1



j=1

(j),c

j,c

(j),c

⎞

⎠

−1

(i),c

(4.12)

For SESAM with MMSE ﬁlter the p

i,c

correspond to the powers in the dual uplink. As the

rates in the broadcast and the dual uplink are the same [8], we consider the uplink rates for

the SESAM MMSE algorithm in this chapter.

152 4 System Level Aspects for Single Cell Scenarios

SESAM with Zero-Forcing Filters

With zero-forcing ﬁlters the subchannel gains λ

i,c

are given by

i,c

= ρ

⎛

⎝

(i),c

⎛

⎝

I −

i−1



j=1

j,c

⎞

⎠

(i)

⎞

⎠

, (4.13)

where here the t

j,c

are the downlink transmit ﬁlters for the j-th data stream on

carrier c and equal to the unit-norm eigenvectors corresponding to the principal

eigenvalues of the matrices

⎛

⎝

I −

j−1



=1

,c

⎞

⎠

(j),c

⎛

⎝

I −

j−1



=1

,c

⎞

⎠

Each matrix I −



j−1

=1

,c

projects into the nullspace of the beamformers of the

previously allocated data streams on carrier c and therefore assures that the t

j,c

do not interfere with the previously allocated subchannels on carrier c.Interference

on later allocated subchannels is suppressed by DPC. With this kind of zero-forcing,

several Quality-of-Service (QoS) constrained optimization problems can be solved

at reduced computational complexity, where the optimum can be achieved quite

closely. Such optimization problems can be the weighted sum rate maximization

under minimum and maximum rate requirements with a transmit power constraint

or the transmit power minimization for the fulﬁllment of minimum rate require-

ments. As zero-forcing ﬁlters are applied together with DPC, the subchannels are

interference-free and the optimum powers p

i,c

can be determined by water-ﬁlling

alike solutions. For the details of the power and user allocation the reader is re-

ferred to [9] for the pure sum rate maximization, to [4] for the weighted sum rate

maximization under a power constraint and [1] for QoS constrained optimization

problems.

4.9.4 Approximation of the Ergodic Sum Rate with Large

System Analysis

In this section we will present approximations for the subchannel gains λ

i,c

with

results from large system analysis. For the large system analysis the number transmit

antennas and receive antennas go to inﬁnity at a ﬁnite ﬁxed ratio β, i.e., N →

∞,R→∞,β=

, ﬁnite. Then the empirical eigenvalue distributions of the

matrices in (4.13) and (4.11) converge almost surely to an asymptotic limit. For ﬁnite

systems, we propose to use the a.e.d. f

(x) of a matrix A to ﬁnd an approximation

for the i-th strongest eigenvalue as follows. Let A be a L × L matrix with ﬁnite

L, then the i-th eigenvalue of this matrix is approximated by these two implicit

equations.

(A)=L



i−1

(x) d x, where



(x) d x =

L −i +1

4.9 Large System Analysis 153

Hence the x domain is divided into L intervals, where in each interval [m

i−1

; m

] the

integral



i−1



) d x



is equal to 1/L. The centroid of each interval then repre-

sents one eigenvalue. Using these approximations for the computation of eigenvalues

in (4.11) and (4.13), the user and power allocation is afterwards done as originally

proposed for ﬁnite systems. The a.e.d.s f

(x) can be computed from the Stielt-

jes transformation S

(z) as described for example in [10]. In the following we will

therefore present equations for the Stieltjes transforms.

SESAM with MMSE Filters

As a direct computation of the Stieltjes transforms of the matrices in (4.11) seams to

be diﬃcult, we ﬁrst introduce the following approximation of the subchannel gains.

i,c

≈ ρ

i,c



(i),c



I +

i,c



−1

(i),c



, (4.14)

where n

i,c

denotes the number of subchannels assigned to the user π

(i) in previous

steps on carrier c. V

i,c

∈ C

N×i−1−n

i,c

is a matrix with orthonormal columns, i.e.,

i,c

= I, independent of H

(i),c

. Hence the eﬀect of the interfering subchannels

allocated to other users is taken into account by the matrix V

i,c

, which consists of

as many orthonormal columns as subchannels assigned to other users than user

(i) interfere with the i-th subchannel on carrier c. The eﬀect of interference

of subchannels allocated to the same user is considered by taking the n

i,c

+1-th

largest eigenvalue in (4.14), denoted as ρ

i,c

. Due to the independence between

the matrices H

(i),c

and V

i,c

, the Stieltjes transform S

i,c

(z) of the matrix

i,c

(i),c



I +

i,c



−1

(i),c

∈ C

R×R

can be derived from [10, Theorem

2.39] and is given by the implicit equation

β =

1+zS

i,c

(z)

1 −

1+S

i,c

(z)

N−(i−1−n

i,c

)

−

i,c

(z)

i−1−n

i,c

For details the reader is referred to [3].

SESAM with ZF Filters

As the matrix H

(i),c



I −



i−1

j=1

j,c



(i),c

has the same nonzero eigenvalues as

i,c

= V

i−1,c

(i),c

i−1,c

,whereV

i−1,c

contains the N − i − 1 orthonormal

basis vectors of the projector I −



i−1

j=1

j,c

, we derive an implicit equation for the

Stieltjes transform S

i,c

(z) of the latter matrix in the following. The computation

of S

i,c

(z) works recursively, as it requires the a.e.d. f



i,c

(x),where

i,c

denotes

the last step before step i, in which a subchannel has been assigned to the user π

(i)

on carrier c. S

i,c

(z) is given implicitly by





i,c

(x)

1 −

β +(x − z)

βS

i,c

(z)

d x =

N − 

i,c

− 1

N − 

i,c

154 4 System Level Aspects for Single Cell Scenarios

where





i,c

(x) d x =

N − 

i,c

−1

N − 

i,c

For details the reader is referred to [2].

4.9.5 Numerical Results

Figure 4.20 exhibits the sum rate averaged over 1000 channel realizations versus the

number of transmit antennas, where the sum rate maximization under a transmit

power constraint is considered. The ratio β has been ﬁxed to β =2.Eachcross

for the SESAM approaches corresponds to the sum rate achieved with one channel

realization and the line goes through the average sum rates. Figure 4.20 (a) com-

0 10 20 30 40 50 60

100

120

Number of transmit antennas

Sum rate (bpcu)

Asymptotic Computation

Average Gain

(a) Sum rate averaged over 1000 channel re-

alizations compared to asymptotic sum

rate in a system with K =2users,

β = N/R =2

0 10 20 30 40 50 60

Number of transmit antennas

Sum rate (bpcu)

Sum Capacity

SESAM

SESAM large system

BD DPC large system

BD large system

(b) Large system approximation of sum

rates for diﬀerent algorithms with K =

5, P

= 10, β =2

Figure 4.20: Numerical Results

pares the approximated sum rate with the average sum rate for SESAM with MMSE

ﬁlters in a system with 2 users, one carrier, and at a transmit power of P

= 100,

which corresponds to a transmit SNR of 20dB. In Fig. 4.20 (b) the same compar-

ison is made with SESAM and ZF ﬁlters at 10 dBandinasystemwith5 users.

Additionally, Fig. 4.20 (b) exhibits the average sum capacities and the large system

approximations of Block Diagonalization [7] with and without DPC, which have also

been derived in [2]. From both ﬁgures we can conclude that the presented approxi-

mations match the average sum rate quite well, already with reasonable numbers of

transmit and receive antennas.

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