paper open-loop correlation reduction precoding in...
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202IEICE TRANS. COMMUN., VOL.E99–B, NO.1 JANUARY 2016
PAPER
Open-Loop Correlation Reduction Precoding in OverloadedMIMO-OFDM Systems
Hikari MATSUOKA†a), Yoshihito DOI†b), Tatsuro YABE†c), Student Members,and Yukitoshi SANADA†d), Senior Member
SUMMARY This paper proposes an open-loop correlation reductionprecoding scheme for overloaded multiple-input multiple-output (MIMO)orthogonal frequency division multiplexing (OFDM) systems. In over-loaded MIMO-OFDM systems, frequency diversity through joint maxi-mum likelihood (ML) decoding suppresses performance degradation ow-ing to spatial signal multiplexing. However, on a line-of-sight (LOS) chan-nel, a channel matrix may have a large correlation between coded symbolstransmitted on separate subcarriers. The correlation reduces the frequencydiversity gain and deteriorates the signal separation capability. Thus, inthe proposed scheme, open-loop precoding is employed at the transmitterof an overloaded MIMO system in order to reduce the correlation betweencodewords transmitted on different signal streams. The proposed precodingscheme changes the amplitude as well as the phase of the coded symbolstransmitted on different subcarriers. Numerical results obtained throughcomputer simulation show that the proposed scheme improves the bit errorrate performance on Rician channels. It is also shown that the proposedscheme greatly suppresses the performance degradation on an independentRayleigh fading channel even though the amplitude of the coded symbolsvaries.key words: open-loop precoding, overloaded MIMO, rician fading channel
1. Introduction
With the popularity of mobile phones and mobile ter-minals, the enlargement of capacity and the improve-ment of throughput are expected in wireless communica-tions. A multiple-input multiple-output (MIMO) transmis-sion scheme has been extensively studied to resolve thesedemands [1], [2]. MIMO increases the communication ca-pacity by using multiple transmit and receive antenna el-ements and improves the reliability of the communicationlinks through diversity [3], [4].
However, due to the requirements of a form factor, thenumber of antenna elements that can be implemented in amobile terminal is limited. In [5]–[7], overloaded MIMOin which the number of receive antennas is less than thatof transmit antennas has been investigated. Although thereare several signal separation schemes for MIMO, the max-imum likelihood (ML) detection that searches the round-robin candidate points of the signal shows the best perfor-mance in theory. Nevertheless, each additional transmission
Manuscript received March 14, 2015.Manuscript revised August 9, 2015.†The authors are with the Dept. of Electronics and Electrical
Engineering, Keio University, Yokohama-shi, 223-8522 Japan.a) E-mail: [email protected]) E-mail: [email protected]) E-mail: [email protected]) E-mail: [email protected]
DOI: 10.1587/transcom.2015EBP3104
signal stream deteriorates the performance in the overloadedMIMO. It has been shown in [8] that it is possible to sup-press the amount of performance degradation through diver-sity in a receiver. Therefore, by using an error correctioncode instead of increasing the number of receive antennas,spatially multiplexed signal streams can be separated with-out a large amount of bit error rate (BER) degradation.
The joint decoding scheme for overloaded MIMO sys-tems with error correction codes has been investigated [9]–[11]. If fading statistics among coded symbols are indepen-dent, the error rate approaches to a lower bound through fre-quency diversity on multipath channels. Nevertheless, onRician channels which include a line-of-sight (LOS) com-ponent, the performance of joint decoding deteriorates be-cause of correlations among the elements of a channel ma-trix [12], [13].
Precoding schemes for MIMO systems in order to re-duce the correlation of received signal streams have beenproposed. A precoding scheme in [13], [14] uses channelstate information (CSI). When the precoder uses the CSI,the signal covariance is optimized and the channel capacityis maximized. However, the receiver needs the feedback ofthe CSI before transmission. Open-loop precoding MIMOhas also been proposed in [15]. Nevertheless, this precod-ing scheme can be applied only to MIMO systems in whichthe numbers of transmit and receiver antennas are the same.Hence, this scheme is not applicable to overloaded MIMOsystems. In [16], a precoding scheme for joint decoding inthe overloaded MIMO system has been investigated. Thisscheme needs to detect the random precoding coefficientswith preamble sequences.
Several literature have also investigated phase rotationbetween two signal streams [17]–[19]. The assumed systemin these references transmits multiple signal streams fromone antenna. Thus, the optimum amount of phase rotationbetween the signal streams can be found. On the other hand,each signal stream is transmitted from different antenna el-ement in the proposed scheme. Thus, the relative phase be-tween the signal streams cannot be fixed at the receiver.
This paper proposes an open-loop precoding schemewith predetermined coefficients for overloaded MIMO sys-tems with repetition codes. This precoding scheme changesthe phases of coded symbols with the predetermined coeffi-cients. It then reduces the correlation between coded sym-bols transmitted on different signal streams. In the proposedscheme the number of transmit antennas is limited by the
Copyright c© 2016 The Institute of Electronics, Information and Communication Engineers
MATSUOKA et al.: OPEN-LOOP CORRELATION REDUCTION PRECODING IN OVERLOADED MIMO-OFDM SYSTEMS203
correlation between the signal streams instead of the de-sign of the precoding coefficients since the orthogonality be-tween the coefficient sequences for different signal streamsis not assumed. Furthermore, pilot-based channel estima-tion as well as preamble-based channel estimation can beapplied with this scheme. However, the ill-condition of thechannel matrix that leads to the overlap of signal constella-tion points cannot be avoided if only the phase of the codedsymbols is rotated [20]. Thus, amplitude variation in ad-dition to the phase rotation is applied through multiplyingwindowing coefficients.
This paper is organized as follows. Section 2 explainsthe system model and the joint decoding scheme. Proposedprecoding scheme is described in Sect. 3. In Sect. 4, numer-ical results obtained through computer simulation are pre-sented. Finally, conclusions are presented in Sect. 5.
2. System Model
2.1 Overloaded MIMO-OFDM System
An MIMO-OFDM system with NT transmit antennas andNR receive antennas is shown in Fig. 1. The overloadedMIMO is the case when NT > NR. Information bits are de-multiplexed to NT transmit antennas in a bit-by-bit fashion.On each antenna branch, a transmit 2M QAM symbol is gen-erated with M information bits through Gray coding. Witha rate 1/L repetition code, the ith transmit symbol, Ci
p, isreplicated and assigned to L subcarriers. That is, on the pthbranch, the data subcarrier index assigned to the lth codedsymbol of the ith transmit symbol is given as
kl = (l − 1)ND/L + (i − 1) + (1 + Δ) (1)
where ND is the number of data subcarrriers in OFDM mod-ulation and Δ is the number of null subcarriers on channeledges and N = ND + 2Δ. Thus, the transmit symbol on theklth subcarrier of the pth branch is given as S p[kl] = Ci
p forl = 1...L where kl is calculated with i and l by Eq. (1). FromNT antenna branches, NT OFDM signal streams are trans-mitted. The received signal model of the overloaded MIMOsystem using a repetition code is presented in Fig. 2.
The OFDM signal of the pth branch is given as
up[n] =N−1∑k=0
Pp[k]S p[k] exp
(j2πnk
N
)(2)
where Pp[k] is the precoding coefficient on the kth sub-carrier, S p[k] is the coded symbol on the kth subcarrier,n(n = 0, 1, ...,N − 1) is the time index, and N is the sizeof the inverse discrete Fourier transform (IDFT). The lastpart of the OFDM symbol is replicated and inserted at thebeginning as a guard interval (GI). The generated OFDMsignal passes through a transmit filter. Therefore, the trans-mit signal in the baseband is given as
xp(t) =N−1∑
n=−NGI
up[n]pt(t − nTs) (3)
Fig. 1 Overloaded MIMO-OFDM system (NT=4, NR=1).
Fig. 2 Received signal model in overloaded MIMO-OFDM system usinga repetition code.
where xp(t) is the OFDM symbol in the pth signal stream,pt(t) is the impulse response of the transmit filter, Ts is thesampling interval, and NGI is the GI length. The receivedsignal goes through a receive filter and the sum of the re-ceived signals in the qth antenna is given by
yq(t) =NT∑q=1
yqp(t) + wq(t) (4)
where yqp(t) is the received signal from the pth transmit an-tenna to the qth receive antenna, which is calculated as
yqp(t) =N−1∑
n=−NGI
up[n]hqp(t − nTs) (5)
and wq(t) is the noise in the qth receive antenna, hqp(t) isthe impulse response of the composite channel includingthe transmit and received filters. In an A/D converter, thereceived signal is digitized to discrete samples as
yq[n] = yq(nTs). (6)
The signal on the kth subcarrier after removing the GI andtaking the DFT of N samples is given as
Zq[k] =N−1∑n=0
yq[n] exp
(− j
2πnkN
)
204IEICE TRANS. COMMUN., VOL.E99–B, NO.1 JANUARY 2016
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
Z1[k1]...
ZNR [k1]...
Z1[kL]...
ZNR [kL]
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦
=
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
P1[k1]H11[k1] P2[k1]H12[k1] · · · PNT [k1]H1NT [k1]...
.... . .
...P1[k1]HNR1[k1] P2[k1]HNR2[k1] · · · PNT [k1]HNRNT [k1]
......
. . ....
P1[kL]H11[kL] P2[kL]H12[kL] · · · PNT [kL]H1NT [kL]...
.... . .
...P1[kL]HNR1[kL] P2[kL]HNR2[kL] · · · PNT [kL]HNRNT [kL]
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣Ci
1...
CiNT
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ +
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
W1[k1]...
WNR [k1]...
W1[kL]...
WNR [kL]
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦
(8)
=
NT∑p=1
Hqp[k]S [k] +Wq[k]. (7)
Assuming that kl is the subcarrier index for the lth codedsymbol and is given in Eq. (1), the ith received codeword isexpressed in the vector form as Eq. (8) where Hqp[kl] is thefrequency response between the pth transmit antenna andthe qth receive antenna and is calculated as
Hqp[kl] =N−1∑n=0
hqp[n] exp
(− j
2πnkl
N
)(9)
and Wq[kl] is the noise in the qth receive antenna on the klthsubcarrier and is given as
Wq[kl] =N−1∑n=0
wq[n] exp
(− j
2πnkl
N
)(10)
where
hqp[n] = hqp(nTs), (11)
wq[n] = wq(nTs). (12)
2.2 Joint Maximum Likelihood Symbol Detection
In the joint ML decoding, the joint metrics are calculated forall the combinations of the coded symbol sequences over NT
signal streams. The joint ML decoding for the ith codewordis expressed as
CiJML = arg min
Ci1,C
i2,...,C
iNT∈Ω
L∑l=1
NR∑q=1
|Zq[kl]
−NT∑p=1
Pp[kl]Hqp[kl]Cip|2 (13)
where k is given in Eq. (1) with i and l, Ω is the set of can-didate codeword vectors, and
Cip =
[Ci
p Cip . . . Ci
p . . . Cip
]T. (14)
In the conventional scheme no precoding is assume, i.e.,Pp[kl] = 1 for any p and kl.
Fig. 3 System model with precoding scheme.
2.3 Rician Fading Channel Model
In Eq. (8), the channel response on the klth subcarrier be-tween the pth transmit antenna and the qth received antenna,Hqp[kl], is modeled as a Rician fading channel in whicha constant channel component path and a Rayleigh fadingcomponent path are assumed to reach the receiver with thesame delay. In this case, the channel response, Hqp[kl], isgiven in the frequency domain as
Hqp[kl] =
√K
K + 1HLOS
qp +
√1
K + 1Hqp (15)
where K is the k-factor and Hqp is the Rayleigh fading com-ponent between the pth transmit antenna and the qth receiveantenna [21]. The constant channel component, HLOS
qp , be-tween the pth transmit antenna and the qth receive antennaincludes an initial phase, θqp, as
HLOSqp = e− j2πθqp . (16)
The initial phase is assumed to be a random variable thatdistributes over [0, 2π).
3. Correlation Reduction Precoding Scheme
3.1 Precoding for Phase Rotation
On a line-of-sight (LOS) channel, the correlation between
MATSUOKA et al.: OPEN-LOOP CORRELATION REDUCTION PRECODING IN OVERLOADED MIMO-OFDM SYSTEMS205
the channel response on different subcarriers in Eq. (8) in-creases. It then increases the correlation between the code-words transmitted from different antennas. The correlationreduces frequency diversity gain and deteriorates the sepa-ration capability of the signal streams [13], [14]. Thus, theopen-loop correlation reduction precoding scheme is pro-posed in this paper.
In the proposed scheme, the precoding coefficients aremultiplexed to the coded symbols of the codeword. The co-efficients are selected from a DFT matrix. The precodingcoefficient for the klth coded symbol of the ith codeword inthe pth signal stream, Pp[kl], is given as
Pp[kl] = exp
(− j
2π(l − 1)(p − 1)NT
)(17)
where k is given by Eq. (1). Because of the length of the co-efficient sequence, that is expresses as
[Pp[k1] Pp[k2] · · ·
Pp[kL]], the coefficient sequences are not orthogonal each
other. Even though the coefficient sequences are not orthog-onal, it can still reduce the correlation between the code-words transmitted on different streams. Since the precodingcoefficients are derived from the parameters of i, l, and p, itis also known to the receiver. From Eq. (13), the metric forthe joint ML decoding is given as
L∑l=1
NR∑q=1
|Zq[kl] −NT∑p=1
Pp[kl]Hqp[kl]Cip|2
≈NR∑q=1
L∑l=1
⎛⎜⎜⎜⎜⎜⎜⎝NT∑p=1
Pp[kl]Hqp[kl]Cip −
NT∑p′=1
Pp′ [kl]Hqp[kl]Cip′
⎞⎟⎟⎟⎟⎟⎟⎠
×⎛⎜⎜⎜⎜⎜⎜⎝
NT∑p=1
Pp[kl]Hqp[kl]Cip −
NT∑p′=1
Pp′ [kl]Hqp[kl]Cip′
⎞⎟⎟⎟⎟⎟⎟⎠∗
=
NR∑q=1
L∑l=1
⎛⎜⎜⎜⎜⎜⎜⎝NT∑p=1
|Pp[kl]Hqp[kl](Cip − Ci
p)|2 + IC (18)
where * indicates complex conjugate, IC is the sum of thecross correlation term among the signal streams and is givenas
IC =
NR∑q=1
L∑l=1
⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝NT∑p=1
NT∑p′=1p′�p
Pp[kl]Pp′ [kl]∗Hqp[kl]Hqp′ [kl]
∗
×(Cip − Ci
p)(Cip′ − Ci
p′ )∗). (19)
The approximation in Eq. (18) is because the noiseterm, Wq[kl], in Eq. (8) is neglected for simplicity. IfHqp[kl]Hqp′ [kl]∗ is almost constant over all the subcarri-ers due to the constant channel component, the cross cor-relation term may increases when Ci
p � Cip. Thus, the
correlation between the precoding coefficient sequences,∑Ll=1 Pp[kl]Pp′ [kl]∗, should be small to reduce the total
amount of interference by the cross correlation.
3.2 Precoding for Amplitude Variation
Even though the pulse of each symbol is rotated, the ill-condition of the channel matrix cannot be avoided [20]. Thisis because the channel response includes the constant chan-nel component whose phase is random owing to propagationconditions. Thus, the amplitude of each symbol should alsobe varied with the coefficient. In order to further reduce thecorrelation, window coefficients based on an optimized bet-ter than raised-cosine (OBTRC) pulse is applied [22].
From Eq. (17), if the codeword length, L, is the sameas the number of signal streams, the correlation of the code-words on the pth and p′th (p � p′) streams diminishes withorthogonal precoding coefficient sequences. However, if lreaches only up to L (< NT ), the precoding coefficient se-quences for the pth and the p′th streams are not orthogonal.The cross correlation of the precoding coefficient sequencesis equivalent to the amount of inter-carrier interference (ICI)of OFDM subcarriers with the frequency offset. This crosscorrelation is given as
L∑l=1
Pp[kl]P∗p′ [kl]
=
L∑l=1
exp
(− j
2π(l − 1)(p − p′)NT
). (20)
The OBTRC pulse has been proposed to reduce the ICI ofthe OFDM subcarriers with the frequency offset.
The coefficients for odd-numbered streams are given as
Podd[kl] =⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩1, l < α
exp(− ln 2
(l−αβ
)n), α ≤ l ≤ α + β
12 , α + β < l
(21)
and those for even-numbered streams is
Peven[kl] = Podd[k(L−l+1)]. (22)
The coefficient for the klth coded symbol in the pth signalstream is then given as follows;
Pp[kl] =
⎧⎪⎪⎨⎪⎪⎩Podd[kl] exp
(− j 2π(l−1)(p−1)
NT
), p is odd
Peven[kl] exp(− j 2π(l−1)(p−1)
NT
), p is even
.
(23)
4. Numerical Results
4.1 Simulation Conditions
Simulation conditions are presented in Table 1. Some of thespecifications such as the bandwidth or the number of sub-carriers follow the IEEE 802.11a/g standards. A coded sym-bol is modulated with QPSK on each subcarrier and multi-plexed with OFDM. The number of data subcarriers is 48
206IEICE TRANS. COMMUN., VOL.E99–B, NO.1 JANUARY 2016
Table 1 Simulation conditions.
Modulate scheme QPSK/OFDMNumber of subcarriers 64
Number of 48 (Δ=8)date subcarriers
Bandwidth 312.5 [kHz]of subcarrier
Guard interval 16 sampleslength
Number of 4, 6, 8transmit antennas
Number of 1receive antennas
Parameters of window α = 1, β = 3coefficients n = 1
Block coding Repetition codeCoding rate 1/4Interleaver Block interleaver (8×6)
Rician fadingChannel model 1 path Rayleigh fading
Independent Rayleigh fadingChannel estimation Ideal
and the DFT size is 64. Thus, the number of null subcarri-ers, 2Δ, is 16. The guard interval length is set to 16 sam-ples. The bandwidth of each subcarrier is 312.5 kHz. Thenumber of transmit antennas is 4, 6, and 8 while the num-ber of receive antennas is set to 1. Thus, the number ofsignal streams is 4, 6, and 8. The coding rate of the rep-etition code is 1/4. A block interleaver with the size of(8 × 6) is employed to spread the coded symbols over thesubcarriers. In order to show the validity of the proposedscheme, a Rician fading channel, a 1 path Rayleigh fadingchannel, and an independent Rayleigh fading channel areassumed. These channels corresponds to a flat fading chan-nel in LOS environment, that in NLOS environment, anda frequency-selective fading channel in NLOS environmentwithin the OFDM bandwidth, respectively. On the indepen-dent Rayleigh fading channel model each coded symbol issubject to independent Rayleigh fading distribution. Perfectchannel estimation in the receiver is assumed. In the per-formance figures, Eb is the bit energy and N0 is the noisespectrum density.
4.2 Numerical Results
4.2.1 Design of Precoding for Amplitude Variation
The parameters of window coefficients for amplitude vari-ation are set as n = 1, α = 1, and β = 3, in this paper.With these parameters the window coefficients are given asFig. 4. The correlation between coefficient sequences for thepth and p′th streams are given in Table 2. Here, the numberof signal streams is assumed to be NT = 8. The correlationis calculated with the following equation;
ρpp′ =
∑Ll=1 Pp[kl]P∗p′ [kl]√∑L
l=1 |Pp[kl]|2√∑L
l=1 |Pp′ [kl]|2. (24)
Fig. 4 Window coefficients based on OBTRC pulse.
Table 2 Example of cross correlation of window coefficient sequences(NT = 8).
(a) W/O amplitude variation���pp’
1 2 3 4 5 6 7 8
1 1.000 - - - - - - -2 0.653 1.000 - - - - - -3 0.000 0.653 1.000 - - - - -4 0.271 0.000 0.653 1.000 - - - -5 0.000 0.271 0.000 0.653 1.000 - - -6 0.271 0.000 0.271 0.000 0.653 1.000 - -7 0.000 0.271 0.000 0.271 0.000 0.653 1.000 -8 0.653 0.000 0.271 0.000 0.271 0.000 0.653 1.000
(b) With amplitude variation���pp’
1 2 3 4 5 6 7 8
1 1.000 - - - - - - -2 0.574 1.000 - - - - - -3 0.313 0.574 1.000 - - - - -4 0.238 0.313 0.574 1.000 - - - -5 0.227 0.238 0.313 0.574 1.000 - - -6 0.238 0.227 0.238 0.313 0.574 1.000 - -7 0.313 0.238 0.227 0.238 0.313 0.574 1.000 -8 0.574 0.313 0.238 0.227 0.238 0.313 0.574 1.000
MATSUOKA et al.: OPEN-LOOP CORRELATION REDUCTION PRECODING IN OVERLOADED MIMO-OFDM SYSTEMS207
Fig. 5 BER vs. Eb/N0 (QPSK, Rician fading K=10, 8 transmit anten-nas).
Fig. 6 BER vs. Eb/N0 (QPSK, 1 path Rayleigh, 8 transmit antennas).
The maximum correlation value reduces to 0.653 or 0.574with or without amplitude variation while it is 1.0 in theconventional overloaded MIMO.
The correlation is smaller if the window coefficient foreach stream have larger variation. However, larger variationin the coefficients means larger variation in the amplitude ofthe coded symbols. As explained in the following section,the variation in the amplitude reduces diversity gain on theindependent Rayleigh fading channel [23], [24]. Thus, it is atrade-off between the correlation and the diversity gain. Asit has been shown in [24] that the symbol error rate degrada-tion is less significant, the maximum difference in the am-plitude of the coded symbols is set to 1/2.
4.2.2 BER Performance
The BER performance curves on a Rician fading channel(K=10) and a 1 path Rayleigh fading channel with the pro-posed precoding scheme are shown in Figs. 5 and 6. Thenumber of transmit antennas is 8. While the receiver can
Fig. 7 BER vs. number of transmit antennas (QPSK, Rician fadingK=10, Eb/N0=13 dB).
Fig. 8 BER vs. Eb/N0 (QPSK, Rician fading K=∞, 8 transmit antennas).
decode almost no codewords in the absence of precoding,the proposed scheme achieves the BER of 10−3 at Eb/N0 of13 dB or 26 dB. On the other hand, the BER performanceshow almost the same with and without the coefficients foramplitude variation. This is because the Rayleigh fadingcomponent changes the amplitude of the coded symbols.The BER versus the number of signal streams on the Ricianfading channel (K = 10) is shown in Fig. 7. Eb/N0 is set to13 dB. As it is shown that the BERs grow as the number ofsignal streams increases. However, the BER degradation issuppressed with the proposed precoding schemes.
The BER performance on the Rician fading channel(K=∞) with the proposed precoding scheme is shown inFig. 8. The number of transmit antennas is 8. When thetransmitter does not use the precoding, the BER is close to0.5. In contrast, by using the proposed precoding for phaserotation, the BER improves to 2 × 10−2. However, an er-ror floor appears. Since the coded symbols in all streamshave the same amplitude, the candidate signal constellationpoints overlap with a certain probability [16]. With the pre-
208IEICE TRANS. COMMUN., VOL.E99–B, NO.1 JANUARY 2016
Fig. 9 BER vs. number of transmit antennas (QPSK, Rician fadingK=∞, Eb/N0=10 dB).
Fig. 10 BER vs. Eb/N0 (QPSK, independent Rayleigh, 8 transmit anten-nas).
coding for amplitude variation, the BER performance re-duces to 10−4 at Eb/N0 of 15 dB. The BER versus the num-ber of signal streams on the Rician fading channel (K = ∞)is shown in Fig. 9. Eb/N0 is set to 10 dB. It is also clearthat the precoding scheme with phase rotation and ampli-tude variation can suppress the BER degradation created bysignal multiplexing.
The BER performance on the independent Rayleighfading channel with the proposed precoding scheme isshown in Fig. 10. The number of transmit antennas is 8. TheBERs of these three schemes are almost the same. In [24], ithas been shown that the BER performance deteriorates if thesignal is received by multiple branches (antenna branches in[24] while L subcarriers in the proposed scheme) with un-equal powers. Since the proposed scheme varies the ampli-tude of the coded symbols over the L subcarriers with thewindow coefficients, it increases the BER especially whenthe subcarriers are subject to independent fading [23], [24].It can be observed through the BER curves with and with-out amplitude variation in Fig. 10 that the power difference
Fig. 11 BER vs. Eb/N0 (16QAM, Rician fading K=10, 6 transmit anten-nas).
Fig. 12 BER vs. Eb/N0 (16QAM, Rician fading K=∞, 6 transmit anten-nas).
among the L symbols does not lead to the significant BERdegradation.
4.2.3 BER Performance with Higher Order Modulation
The BER performance with 16QAM signals is presented inFigs. 11 and 12. The Rician fading channels with K = 10and K = ∞ are assumed in Figs. 11 and 12. The differ-ent from Fig. 5, the performance of the proposed precodingscheme for phase rotation shows the error floor on the Ricianchannel with K = 10. This is also because the candidatesignal constellation points overlaps even though the precod-ing scheme for phase rotation is applied. Since the numberof the candidate signal constellation points increases with16QAM symbols and the fading channel varies the ampli-tude of the received signal, more overlaps among the can-didate signal constellation points occur and the level of theerror floor increases. On the other hand, the error floor onthe channel with K = ∞ is lower with the proposed precod-
MATSUOKA et al.: OPEN-LOOP CORRELATION REDUCTION PRECODING IN OVERLOADED MIMO-OFDM SYSTEMS209
ing for phase rotation. On the channel with a fixed ampli-tude response, the different signal amplitudes in multi-levelmodulation reduces the probability of the overlaps amongthe candidate signal constellation points. On both channels,the proposed precoding scheme for amplitude variation andphase rotation reduces the BER level of the error floor effec-tively.
5. Conclusions
This paper has presented a correlation reduction precod-ing scheme that uses predetermined coefficients for phaserotation and amplitude variation over the codeword. Thephase rotation coefficients are derived by the DFT coeffi-cients while the amplitude variation coefficients are calcu-lated based on the OBTRC pulse. With the use of the pre-coding for phase rotation, the receiver is able to separate thesignal streams even those received on the Rician channels.Furthermore, with the use of the precoding for amplitudevariation, the proposed scheme eliminates the error floor ofthe BER performance curves that appear on the channel withonly the constant component. Even though the proposedscheme leads to the gain imbalance in the channel responseson different subcarriers, the performance on the independentRayleigh fading channel shows almost the same BER as theconventional scheme.
Acknowledgments
This work is supported in part by Ministry of Internal Af-fairs and Communications in Japan under the project nameof Strategic Information and Communications R&D Promo-tion Programme (SCOPE 141303004).
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210IEICE TRANS. COMMUN., VOL.E99–B, NO.1 JANUARY 2016
Hikari Matsuoka was born in Tokyo, Japanin 1992. He received his B.E. degree in elec-tronics engineering from Keio University, Japanin 2014. Since April 2013, he has been a gradu-ate student in School of Integrated Design Engi-neering, Graduate School of Science and Tech-nology, Keio University. His research interestsare mainly concentrates on MIMO-OFDM sys-tem.
Yoshihito Doi was born in Wakayama,Japan in 1989. He received his B.E. degreein electronics engineering from Keio University,Japan in 2013. Since April 2013, he has been agraduate student in School of Integrated DesignEngineering, Graduate School of Science andTechnology, Keio University. His research inter-ests are mainly concentrated on MIMO-OFDMsystem.
Tatsuro Yabe was born in Shizuoka, Japan,in 1990. He received his B.E. degree in electron-ics engineering from Keio University, Japan, in2013. Since April 2013, he has been a graduatestudent in the School of Integrated Design Engi-neering, Graduate School of Science and Tech-nology, Keio University. His research interestsare in MIMO systems.
Yukitoshi Sanada was born in Tokyo in1969. He received his B.E. degree in elec-trical engineering from Keio University, Yoko-hama, Japan, his M.A.Sc. degree in electri-cal engineering from the University of Victoria,B.C., Canada, and his Ph.D. degree in electricalengineering from Keio University, Yokohama,Japan, in 1992, 1995, and 1997, respectively. In1997 he joined the Faculty of Engineering, To-kyo Institute of Technology as a Research As-sociate. In 2000, he joined Advanced Telecom-
munication Laboratory, Sony Computer Science Laboratories, Inc, as anassociate researcher. In 2001, he joined the Faculty of Science and En-gineering, Keio University, where he is now a professor. He received theYoung Engineer Award from IEICE Japan in 1997. His current research in-terests are in software defined radio, cognitive radio, and OFDM systems.