Int. J. Electron. Commun. (AEÜ) 66 (2012) 605–612

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International Journal of Electronics andCommunications (AEÜ)
journal homepage: www.elsevier.de/aeueDistributed antenna network for gigabit wireless accessFumiyuki Adachi ∗, Wei Peng, Tatsunori Obara, Tetsuya Yamamoto, Ryusuke Matsukawa, Masayuki Nakada
Department of Electrical and Communication Engineering, Graduate School of Engineering, Tohoku University 6-6-05, Aza-aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japana r t i c l e

i n f oArticle history:
Received 4 November 2011
Accepted 16 March 2012
Keywords:
Distributed antenna network
Single-carrier
Frequency-domain equalization
Relay
Beamforming
Multiplexinga b s t r a c t
For gigabit wireless data services, there are three important technical issues to be addressed: limited
bandwidth, severe frequency-selective fading, and limited transmit power. A distributed antenna network (DAN) is a promising solution to the above three technical issues. In DAN, each mobile user isserved by using multiple distributed antennas close to it. In this paper, recent advances in various
distributed multi-input/multi-output (MIMO) techniques combined with single-carrier (SC) frequencydomain signal processing are presented for DAN. Particular attention is paid to SC frequency-domain
MIMO diversity, relay, beamforming, and multiplexing jointly used with frequency-domain equalization(FDE) to signiﬁcantly improve the signal transmission performance.
© 2012 Elsevier GmbH. All rights reserved.

1. Introduction
The 3rd generation long term evolution (LTE) systems with apeak data rate of few hundreds Mbps are now deployed in many
countries [1]. A next step is the development of broadband (gigabit) wireless technology to be used in the 4th generation systems
with a peak data rate of around 1 Gbps. There will be three important technical issues to be addressed: severe frequency-selective
fading, limited transmit power, and limited bandwidth. The gigabit
wireless channel is severely frequency-selective and severe intersymbol interference (ISI) is produced. Frequency-domain signal
processing, e.g., frequency-domain equalization (FDE) [2,3], may
play an important role in achieving a good signal transmission
performance in such a severe frequency-selective channel. In addition to the above, the path loss and shadowing loss cause a severe
received signal power drop since the transmit power is limited.
Gigabit data services are available only near the base station (BS) if
the present wireless network architecture is employed with limited
transmit power. A distributed antenna network (DAN) [4], in which
many antennas are distributed over a service area, is a promisingsolution to the above three technical issues.
The concept of DAN is illustrated in Fig. 1. In DAN, the conventional BS is replaced by the signal processing center (SPC) and manyantennas or clusters of antennas are spatially distributed over theservice area so that some antennas can always be visible from a
mobile terminal (MT) with a high probability. Antennas or antenna∗ Corresponding author. Tel.: +81 22 795 7082; fax: +81 22 795 7083.
E-mail address: adachi@ecei.tohoku.ac.jp (F. Adachi).
1434-8411/$ – see front matter © 2012 Elsevier GmbH. All rights reserved.
doi:10.1016/j.aeue.2012.03.010

clusters are connected to nearby SPC by means of optical ﬁber links
or wireless links. It is desirable to use as many distributed antennas
as possible while the number of MT antennas is limited to one or
two since there is not enough space to equip too many antennas at
an MT. A number of distributed antennas cooperate and act as distributed multiple-input multiple-output (MIMO) diversity, relay,
beamforming, or multiplexing.
For the DAN downlink, either the single-carrier (SC) or multicarrier (MC) transmission can be used. However, for the uplinktransmission, SC is promising since it has a lower peak-to-average
power ratio (PAPR). Using a transmit power ampliﬁer with the same
peak power, SC provides longer communication range than MC.
Therefore, we have been investigating a potentiality of SC-DAN[4]. In this paper, recent advances in various distributed MIMO
transmission techniques combined with SC frequency-domain
signal processing are presented for DAN. Particular attention ispaid to SC frequency-domain MIMO transmission techniques, i.e.,
antenna diversity, relay, beamforming, and multiplexing, to significantly improve the transmission performance. It is quite difﬁcult
if not impossible to deal with the above technical issues theoretically. Therefore, in this paper, we resort to the computer
simulation method to evaluate the performances achievable with
SC frequency-domain MIMO signal transmission techniques. This
paper provides a comprehensive performance evaluation of DAN
by computer simulation.
The rest of the paper is organized as follows. In Section 2, distributed MIMO diversity implemented by the frequency-domain
space-time coded joint transmit/receive diversity (FD-STBCJTRD) combined with transmit FDE is presented. Section 3
presents the distributed cooperative amplify-and-forward (AF)606

F. Adachi et al. / Int. J. Electron. Commun. (AEÜ) 66 (2012) 605–612

where WH (k) and DNmt (k) represent the transmit FDE matrix ofsize Ndan × Nmt having Wm,n (k) as its (m, n)th entity and the
STBC-JTRD encoding matrix of size Nmt × Q, respectively. CNmt = 1/2
Nc −1 Nmt −1 Ndan −1 Wm,n (k)2is the power normal-

Nc /

k=0

m=0

n=0

ization coefﬁcient. W(k) is given byW(k) = A(k) · H(k),(2)

where H(k) is the channel matrix of size Nmt × Ndan having Hm,n (k) as
its (m, n)th entity, and A(k) is the scaling factor. Assuming minimum
mean square error (MMSE) transmit FDE, A(k) is given by1

Nmt −1 Ndan −1 A(k) =(1/Nmt )

m=0

n=0

2

Hm,n (k) + ((Es /N0 ))

−1

,

(3)

Fig. 1. Concept of DAN.

where Es and N0 are the symbol energy and single-sided power
spectrum density of additive white Gaussian noise (AWGN), respectively. DNmt (k) for different values of Nmt can be found in [5]. When
Nmt = 2 and Q = 2, we haverelay. Distributed beamforming and spatial multiplexing are discussed in Sections 4 and 5, respectively. Some concluding remarks
are drawn in Section 6.



DNmt =2 (k) =2. Distributed MIMO diversity

D0 (k)
D1 (k)−D1∗ (k)D0∗ (k).

(4){S(k); k = 0∼Nc − 1} are transformed by an Nc -point inverse fast
Fourier transform (IFFT) into the time-domain Ndan streams of Q
encoded blocks to be transmitted from Ndan distributed antennas.
The received signals on Nmt receive antennas at MT can be
expressed in frequency domain as

For the downlink, frequency-domain space-time block coded
joint transmit/receive diversity (FD-STBC-JTRD) combined withtransmit FDE [5] can be used. It allows the use of an arbitrary number Ndan of distributed transmit antennas while the number of MT
receive antennas is limited to Nmt ≤ 6. Note that for the uplink,frequency-domain space time transmit diversity (FD-STTD) [6] ispromising since it allows the use of an arbitrary number Ndan of
distributed receive antennas. A combination of FD-STBC-JTRD for
downlink and FD-STTD for uplink is suitable for DAN.
Fig. 2 illustrates the transmitter/receiver structures using FDSTBC-JTRD for the downlink packet access with turbo-coded hybrid
automatic repeat request (HARQ) using type-II S-P2 strategy [7].
The FD-STBC-JTRD is applied to a sequence of J blocks of Nc symbols
each to generate Ndan streams of Q encoded blocks. A combinationof J and Q is found in [5]. The transmit symbol matrix S(k) of size
Ndan × Q at the kth frequency can be expressed as

R(k) =

2Pt H(k)S(k) + N(k),(5)

where R(k) represents the frequency-domain received signal
matrix of size Nmt × Q, N(k) represents the noise matrix of size
Nmt × Q, whose elements are i.i.d. zero-mean complex Gaussian variables having variance 2N0 /Ts with Ts being the symbol
length, and Pt = Es /Ts denotes the total transmit power. The
frequency-domain received signal vector D̂Nmt (k) after FD-STBCJTRD decoding [5] can be expressed in the vector form asD̂Nmt (k) =

Nmt −1Ndan −1

2Pt A(k)m=0S(k) = CNmt WH (k)DNmt (k),⎞⎛
D0 (k)
2.
Hm,n (k) ⎝ . ⎠ + N̂(k),

n=0

(1)

(6)

#Ndan−1#1+ CP

Nc-Point IFFT

STBC- JTRD
encoder

Nc-Point FFT

Data mod.

Tx buffer

Turbo encoder

ACK/NACK from MT

Information
bits#0
Ndan transmit antennas(a)SPC

Error detector

Turbo decoderRx buffer

LLR calculation

Nc-Point IFFT

STBC- JTRD
decoder

Nmt receive antennas

Nc-Point FFT

#0

− CP

ACK/NACK for SPC#Nmt−1.
DJ−1 (k)Est.
information
bits(b)Mobile terminal (MT)Fig. 2. Transmitter/receiver structures of FD-STBC-JTRD downlink. (a)SPC. (b)Mobile terminal (MT).

F. Adachi et al. / Int. J. Electron. Commun. (AEÜ) 66 (2012) 605–612

607

Fig. 3. Models of DAN and CN. (a) DAN (b) CN.

where N̂(k) represents the noise vector whose elements are i.i.d.
zero-mean complex Gaussian variables having variance 2Nmt N0 /Ts .
It can be understood from Eq. (6) that FD-STBC-JTRD achieves theNmt × Ndan -order diversity. The time-domain soft decision symbol
vector is obtained by applying Nc -point IFFT to {D̂Nmt (k); k = 0∼Nc −1}.
Computer simulations are done to measure the throughput distributions of DAN and a conventional cellular network (CN), both ofwhich use FD-STBC-JTRD. Fig. 3 illustrates the models of DAN and
CN. Ntotal = 7 antennas are assumed. In the case of the DAN, 6 antennas are equidistantly distributed along a circle of normalized radiusr = 2/3 and one antenna is located the center of cell. Ndan antennas
are selected from Ntotal = 7 antennas, based on the local average
received signal power (i.e., the antenna selection is based on thepath loss plus shadowing loss). On the other hand, in the case of
the CN, Ndan antennas are selected from Ntotal antennas co-locatedat the BS, based on the instantaneous received signal power.
The downlink packet access using Rate-1/3 turbo coded HARQ
using type-II S-P2 strategy [7] is computer simulated. 16QAM data
modulation, Nc = 256, and Ng = 32 are assumed. A packet is composed of 1536 information bits. Rate-1/3 turbo coded type-II S-P2
strategy uses three bit sequences of equal length: the systematic
bit sequence, the ﬁrst interleaved parity bit sequence, and the second interleaved parity bit sequence. First, only the systematic bit
sequence is transmitted. If any errors are detected, the ﬁrst parity
bit sequence is transmitted. Still any errors are detected, the second
parity bit sequence is transmitted. The above transmission process

Fig. 5. 1%-outage throughput. (a) DAN (b) CN.

is repeated until the packet is correctly received by MT. An L = 16path frequency-selective block Rayleigh fading channel is assumed.
Fading is assumed to stay unchanged over the transmission of eachpacket (either systematic bit sequence, ﬁrst parity bit sequence,or second parity bit sequence), but changes packet-by-packet. The
throughput is measured by changing the MT’s location randomly to
ﬁnd the cumulative distribution function (CDF). The shadowing andpath losses are changed only when the MT’s location is changed.
The spatial distribution of the measured throughput in DAN
and CN is illustrated in Fig. 4 for (Ndan ,Nmt ) = (4,2) and the normalized transmit Es /N0 = 0 dB. It can be clearly seen from Fig. 4 that
DAN achieves much higher throughput in a cell. In the CN, all theantennas suffer from the same path loss and shadowing loss andtherefore, the throughput at the cell edge signiﬁcantly drops. The
throughput at the cell edge is about 2.6 (bps/Hz) in DAN while itis about 1.2 (bps/Hz) in CN. Fig. 5 plots the 1%-outage throughput, which is the 1% value of the CDF, with Ndan as a parameter for
DAN. It can be seen from Fig. 5 that increasing Ndan achieves higher
throughput due to its larger spatial diversity gain. By increasing
Ndan from 1 to 4, the transmit power can be reduced by about 6 dB.
However, the use of more than Ndan = 4 provides only a marginalincrease in the throughput. This is because as Ndan increases, moreantennas which are not close to MT are selected. They do not

Fig. 4. Spatial distribution of throughput (Ntotal = 7 antennas and 16QAM data modulation).

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F. Adachi et al. / Int. J. Electron. Commun. (AEÜ) 66 (2012) 605–612

Fig. 7. An example of SDASA when (Nc , Nb , Ns ) = (16, 2, 8).

where Cdc and Cicr are the channel capacities for the direct communication and the cooperative AF relay using RSi , respectively. The
channel capacity Cdc for the direct communication is given by [10]C dc =
Fig. 6. Cooperative AF relay.

1
Ns



Nc −1

εdc
log2
k

1+

k=0

Prdc
|Hmt→spc (k)|2
Nspc



,

(8)

where Hmt→spc (k) and Nspc are respectively the channel gain for the
MT–SPC link and the noise power at SPC. Prdc is the received signal
power at SPC and is given as

contribute to the performance improvement since most part of
total transmit power is allocated to antennas close to the MT.

−˛
Prdc = P̄T · rmt→spc· 10−/10 ,3. Distributed cooperative relay

where P̄T = PT · R−˛ is the normalized MT transmit power with PT
being the MT transmit power and ˛ being the path loss exponent,
rmt→spc = Rmt→spc /R is the normalized distance between MT and
SPC, and  is the shadowing loss in dB. εdc
takes 0 or 1 (“εdc= 1”kkindicates that the kth subcarrier is used on the MT–SPC link and 0
otherwise).
The channel capacity Cicr of the cooperative AF relay using RSi isgiven by [10]The cooperative amplify-and-forward (AF) relay using 2-timeslots [8] is a powerful means to extend the coverage with limited
MT transmit power. Each distributed antenna is replaced by relay
stations (RSs). Fig. 6 illustrates a DAN with 6 distributed RSs and
SPC equipped with the single antenna. The cell radius is denoted
Cicr =

1
2

Nc −1Nc −1 cr
εi,k,k
k=0 k =0


1+

Ns

log2

cr

Pr,mt→spc

Nspc

Hmt→spc (k)2 +



2



2

cr
cr
(Pr,mt→i/NRSi )Hmt→i (k) · (Pr,i→spc/Nspc )Hi→spc (k )

Nc −1 Nc −1

cr(Pr,mt→i/NRSi )

j=0

j =0

by R. The distances between MT and SPC, between MT and the ith
RS (denoted by RSi ), and between the RSi and SPC are denoted by
Rmt→spc , Rmt→i , and Ri→spc , respectively. MT is assumed to havethe single antenna (Nmt = 1). The best RS (Ndan = 1) which provides
the maximum channel capacity is selected from 6 RSs. In the ﬁrst
time slot, MT broadcasts to SPC and RS; in the second time-slot, RS
transmits an ampliﬁed version of its received signal to SPC.
SC uplink block transmission of Ns symbols per block is considered. A total number Nc (>Ns ) of subcarriers used in the system
are divided into Nc /Nb resource blocks of Nb consecutive subcarriers each. It is assumed that an MT transmits an Ns -symbol block to
SPC. Spectrum division/adaptive subcarrier allocation (SDASA) [9]is considered. The frequency-domain signal of Ns -symbol block to
be transmitted is divided into D = Ns /Nb sub-blocks of Nb frequency
components each. They are adaptively mapped onto D different
resource blocks based on the channel conditions of MT–RS–SPC
and MT–SPC links to achieve the maximum channel capacity. An
example of SDASA with (Nc , Nb , Ns ) = (16, 2, 8) is illustrated in Fig. 7.
Relaying is not always effective. Sometimes, the direct communication provides higher capacity. In the direct/cooperative AF relay(D/AR) switching, the cooperative AF relay is used only if it provides
larger channel capacity than the direct communication. The channel capacity Csw of the D/AR switching using SDASA is expressedasC sw = max{C dc , Cicr },

(9)

(7)



2



2

cr
(εcr
/Ns )Hmt→i (j) + (Pr,i→spc/Nspc )Hi→spc (k ) + 1
i,j,j

,(10)

where Hmt→i (k) and Hi→spc (k) are the channel gain for the MT–RSilink and the RSi –SPC link, respectively. NRSi is the noise power at RSi .
crcrcrPr,mt→spc, Pr,mt→iand Pr,i→spc
are respectively the received signal
powers at SPC and RSi in the ﬁrst time slot and SPC in the sec−˛cr= P̄t,mt · rmt→spc· 10−/10 ,ond time slot and are given as Pr,mt→spc
−˛
−˛
cr
cr
= P̄t,mt · rmt→i· 10−/10 , and Pr,i→spc= P̄t,i · ri→spc· 10−/10 ,Pr,mt→iwhere P̄t,mt = Pt,mt · R−˛ and P̄t,i = Pt,i · R−˛ are respectively thenormalized MT transmit power with Pt,mt being the MT transmit
power and the normalized RSi transmit power with Pt,i being theRSi transmit power. rmt→i = Rmt→i /R and ri→spc = Ri→spc /R are thenormalized distances. εCR
in Eq. (10) takes 0 or 1 (“εCR= 1”i,k,k
i,k,k
indicates that the kth subcarrier and k th subcarrier are respectively used in the ﬁrst and second time slots, and 0 otherwise). For
the fair performance comparison between cooperative relay anddirect communication, the MT transmit power of direct communication is assumed to have the same total transmit power given byP̄T = P̄t,mt + P̄t,i .
The channel capacity of the D/AR switching using SDASA is measured by computer simulation. 6 RSs are distributed equidistantly
along a circle of the normalized radius 2/3 (ri→spc = 2/3) similar to
Fig. 3. Fig. 8 shows the spatial distribution of the 10%-outage capacity of the D/AR switching (note that SDASA is not used). 6 RSs and
SPC are respectively illustrated by black dots and triangle. It canbe seen from Fig. 8 that the D/AR switching can achieve larger 10%outage capacity than the direct communication and the cooperative
AF relay over an entire area. When the D/AR switching is used, theF. Adachi et al. / Int. J. Electron. Commun. (AEÜ) 66 (2012) 605–612

609

Fig. 8. Spatial distribution of the 10%-outage capacity. (a) D/AR switching. (b) Cooperative AF relay. (c) Direct communication.

10%-outage capacity is 1.6(19.0) bps/Hz at the cell age (at the center of the cell) while it is about 0.9(19.0) bps/Hz and 1.5(9.0) bps/Hz
when the direct communication and the cooperative AF relay areused, respectively.
The throughput is measured by changing the MT’s location
randomly to ﬁnd the CDF of the channel capacity. Fig. 9 plots
the 10%-outage capacity, computed from the CDF, of the D/AR
switching without SDASA as a function of the normalized transmit
power-to-noise power ratio (SNR) i = P̄T /N. The D/AR switching
can reduce the transmit power compared to the direct communication and the cooperative AF relay. The transmit power required
for achieving a 10%-outage capacity of 1.0 bps/Hz can be reduced
by about 3 dB compared to the direct communication and by about
1 dB compared to the cooperative AF relay. An additional use of

Fig. 9. 10%-outage capacity of D/AR switching.

SDASA obtains the frequency diversity gain and can further reduce
the required transmit power compared to the D/AR switching
without SDASA. This is clearly seen from Fig. 10 which plots the
10%-outage capacity of the D/AR switching jointly used SDASA.
4. Distributed beamforming
The SC beamforming implemented by frequency-domain adaptive antenna array (FDAAA) [11] is effective to improve the received
signal power while suppressing own signal ISI and the other users’
co-channel interference (CCI) [4]. Distributed clusters of antennas
shown in Fig. 11 are considered. 7 antenna clusters are equidistantly distributed along a circle of normalized radius (2/3)R and one
antenna cluster is located at the center of cell, where each antenna

Fig. 10. Additional capacity improvement by SDASA.

610

F. Adachi et al. / Int. J. Electron. Commun. (AEÜ) 66 (2012) 605–612-3

10

1 active antenna cluster
Single-cell environment

CN

-4

m

10

-5

10

DAN

Fig. 11. Distributed cluster of antennas.
-6

10

cluster consists of Nr antennas with linear array conﬁguration. Four
frequency reuse patterns shown in Fig. 12 are considered.
Uplink performance of the distributed beamforming in DAN system are investigated by computer simulations assuming single cell
environment and cellular environment with the frequency reusefactor (FRF) = 1, 3, 4 and 7. It is assumed that each distributed cluster
has 4 antennas. Scheduling among clusters of antennas is considered and up to two (D = 1, 2) active clusters of antennas are used.
The cluster(s) of antennas which have shortest distance(s) to thedesired user will be used. The weight control is performed on thereceived signals of each cluster of antennas, given byR̃(k) = WT (k)R(k),(11)
Twhere R(k) = [R0 (k), . . . , Rn (k), . . . , RNr −1 (k)] is the frequency
domain received signal vector with Rn (k) representing the received
signal at the kth frequency on the nth antenna, n = 0∼Nr − 1, andW(k) = [W0 (k), . . . , WNr −1 (k)] is the beamforming weight vector.

0

1

2

3

4

5

6

7

8

9

10

Normalized transmit SNR (dB)
Fig. 13. 10% outage BER in single-cell environment.

Computer simulations are done to measure the uplink bit error
rate (BER) in a single-cell environment and in a multi-cell environment with frequency reuse. The 10%-outage BER is plotted for the
1 active antenna cluster case in Fig. 13 as a function of the normalized transmit signal-to-noise ratio (SNR). In order to see whether
the beamforming technique can beneﬁt from the distributed natureof DAN, the 10%-outage BER of CN is also plotted in Fig. 13. In orderto make fair comparison, the number of antennas of CN is set to beequal to the total number of distributed antennas in use. It can beobserved that distributed beamforming in DAN can reduce the 10%
outage BER signiﬁcantly compared to CN.
The 10% outage BER in a multi-cell environment is plotted inFig. 14. It can be observed that beamforming in DAN is more robust
to the CCI. Even with FRF = 1 (strong CCI exists), better quality ofcommunication can be realized by using the distributed beamforming compared to the CN case. Due to the increased diversity order,

Multi-cell environment-3

10

10% outage BER

2 active clusters,
CN

1 active cluster,CN

1 active cluster,
DAN
-4

10

2 active clusters,
DAN
-5

10

FRF=1
FRF=3
FRF=4
FRF=7
-6

10

0

1

2

3

4

5

6

7

8

Normalized transmit SNR (dB)
Fig. 12. Cellular structure.

Fig. 14. 10% outage BER in a multi-cell environment.

910

F. Adachi et al. / Int. J. Electron. Commun. (AEÜ) 66 (2012) 605–612

611

Fig. 15. TS-SC MIMO multiplexing using QRM-MLBD.

the 10% outage BER performance with 2 active antenna clusters ismuch better than the one with 1 active antenna cluster.
In this study, perfect synchronization has been assumed andhow to synchronize the active antenna clusters remains as our
future work.
5. Distributed multiplexing
Multiple distributed antennas in DAN can be used not only for
spatial diversity but also for the spatial multiplexing to improve
the throughput [12]. The downlink transmission is consideredbelow. Ndan different antennas are selected from Ntotal distributed
antennas and simultaneously used for spatial multiplexing. A
training-sequence (TS) aided SC (TS-SC) and maximum likelihood (ML) block signal detection using QR decomposition andM-algorithm (QRM-MLBD) [13] is considered.
TS-SC MIMO multiplexing using QRM-MLBD is illustrated inFig. 15. The data-modulated symbol sequence to be transmitted is serial-to-parallel (S/P) converted to Ndan parallel symbol
sequences, each parallel symbol sequence is divided into asequence of symbol blocks of Nc symbols each. Before the transmission, the TS of length Ng symbols is appended at the end ofeach block. The block sn = [sn (0),. . .,sn (t),. . .,sn (Nc + Ng − 1)]T ([.]Trepresenting the transposition) to be transmitted from the nthTantenna is expressed using the vector form as sn = [dTn uTn ] , wheredn = [dn (0),. . .,dn (t),. . .,dn (Nc − 1)]T is the data symbol vector andun = [un (0),. . .,un (t),. . .,un (Ng − 1)]T is the TS vector which is identical for all blocks.
In order to let TS to play the role of cyclic preﬁx (CP), the discrete Fourier transform (DFT) size to be used at the receiver mustbe Nc + Ng symbols (the sum of data block length and TS in symbols). The use of TS instead of CP can reduce the required numberof surviving paths in the M-algorithm. At the MT, QRM-MLBD isapplied to the overall frequency-domain received signal by treating
a concatenation of the space and frequency-domain channel and
DFT as the equivalent channel. The Nmt Nc × 1 frequency-domainTreceived signal Yall = {Y1 }T · · · {YNmt }Twith Ym representing the frequency-domain received signal vector at the mth receive
antenna is given by [13]


Yall

=


=

⎡

⎤⎡

⎤ ⎡

⎤

H1,1 F · · · H1,Ndan F
s1
N1
2Es
.. ⎦ ⎣ . ⎦
..
..
⎣ ..
⎦
⎣
..
+
.
.
.
.
Ts
sNdan
NNmt ,
HNmt ,1 F · · · HNmt ,Ndan F
2Es
Hsall + Nall
Ts
(12)

where Hm,n denotes the frequency-domain channel matrix
between the nth transmit antenna and mth receive antenna, F the
DFT matrix of size (Nc + Ng ) × (Nc + Ng ), Nm the frequency-domainnoise vector. In the second equation of Eq. (12), H denotes an equivalent channel matrix of size Nmt (Nc + Ng ) × Ndan (Nc + Ng ), which is aconcatenation of the space and frequency-domain channel and DFT,
sall the overall transmit symbol vector of size Ndan (Nc + Ng ) × 1, andNall denotes the overall noise vector of size Nmt (Nc + Ng ) × 1.
QRM-MLBD consists of three steps: ordering (TSs are
moved to the bottom of the vector), QR decomposition,and M-algorithm. The overall transmit symbol vector
sorder = [s1 (0), ..., sNt (0), ..., s1 (Nc + N g − 1), ..., sNt (Nc + N g − 1)]T
after ordering is expressed asTsorder = [dT (0), dT (1), ..., dT (Nc − 1), uT (0), ..., uT (Ng − 1)] ,(13)

where dT (t) and uT (t) denote the data symbol vector and TS vector at tth symbol of size Nt × 1, respectively. After ordering, theQR decomposition is applied to the ordered equivalent channel
matrix H to obtain H = QR, where Q is an Nmt (Nc + Ng ) × Ndan (Nc + Ng )unitary matrix and R is an Nmt (Nc + Ng ) × Ndan (Nc + Ng ) upper triangular matrix. The transformed frequency-domain received signal
TŶ = [Ŷ (1), ..., Ŷ (Ndan (Nc + Ng ))] is obtained as
HŶ = Q Yall =2Es orderRs+ QH Nall .
Ts

(14)

The MLD can be converted to the successive tree search problem
and the computational complexity can be reduced by introducing
the M-algorithm [14] into the successive tree search. In the case of
SC-MIMO block transmissions, the magnitude of a complex-valued
element closer to the lower right positions of matrix R may dropwith higher probability. The received signal powers associated withsymbols to be detected at early stages in the M-algorithm signiﬁcantly drop and hence, the probability of removing the correct pathat early stages may increase when a smaller number M of surviving
paths is used. In TS-SC MIMO multiplexing with ordering, the symbols to be detected at early stages in the M-algorithm are symbols
belonging to the known TSs. Therefore, the probability of removing
the correct path can be signiﬁcantly reduced.
Computer simulation is done to measure the throughput distributions of DAN and CN, both using Ntotal = 7. The same antenna
distribution pattern as in Section 3 is assumed. The single-user andsingle-cell SC-DAN is considered. Antenna selection is based on
the local average received signal power. TS-SC MIMO multiplexing(Nc = 64 and Ng = 16) using QRM-MLBD. Turbo-coded HARQ type-II
S-P4 strategy [7], and 16QAM are considered. Packet size is 2048.
The number M of surviving paths in the M-algorithm is set to 16.
An L = 16-path frequency-selective block Rayleigh fading channel
with uniform power delay proﬁle is assumed.
The throughput is measured by changing the MT’s location randomly to ﬁnd the CDF of the throughput for (Ndan , Nmt ) = (2,2).
Independent fading is assumed for each retransmission. The spatial distribution of the throughput is plotted in Fig. 16 for DAN
and CN when the normalized transmit Es /N0 = 5 dB. It can be seenfrom Fig. 16 that DAN achieves higher throughput than CN (notethat CN can achieve high throughput only near SPC). The cell edge
throughput is about 3 bps/Hz higher with DAN than with CN.

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F. Adachi et al. / Int. J. Electron. Commun. (AEÜ) 66 (2012) 605–612

Fig. 16. Spatial distribution of throughput. (a) DAN. (b) CN.

of MT antennas to one or two so as to alleviate the complexity problem of MT. It was conﬁrmed by the computer simulation that theDAN can be a promising future wireless network to provide gigabit wireless data services to mobile users. Theoretical analysis of
SC-MIMO transmission performance of DAN is left as an important
future study.
References

Fig. 17. 10%-outage throughput.

Fig. 17 plots the 10%-outage throughput for DAN and CN using
QRM-MLBD. For comparison, the 10%-outage throughput is alsoplotted for DAN and CN using MMSE detection. DAN can reduce
the normalized transmit Es /N0 required for achieving the same
throughput as CN. The Es /N0 reduction from CN for a 10%-outage
throughput of 5 bps/Hz is as much as about 10 dB. Furthermore,
QRM-MLBD can improve the throughput compared to the MMSE
detection. The Es /N0 reduction from MMSED for a 10%-outage
throughput of 5 bps/Hz is as much as about 9 dB in DAN.
6. Conclusion
In this paper, we have investigated the potentiality of DAN
combined with SC frequency-domain signal processing. Distributed
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the problems arising from the limited bandwidth, severe channel
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