A ZCMT Precoding Based STBC MIMO-OFDM

System with Reduced PAPR

Imran Baig, Varun Jeoti and Micheal Drieberg

Electrical and Electronic Engineering Department,

Universiti Teknologi PETRONAS, Tronoh, 31750, Perak, Malaysia

imran_baig_mirza@yahoo.com, {varun_jeoti, mdrieberg}@petronas.com.my

Abstract—Orthogonal frequency division multiplexing (OFDM) is

a strong candidate for 4G wireless networks, due to its high data

rate and ability to combat frequency selective fading. OFDM

may be combined with multiple-input multiple-output (MIMO)

to increase the diversity gain and system capacity over the time-

variant frequency-selective channels. However, a major

drawback of MIMO-OFDM system is that the transmitted

signals on different antennas might exhibit high peak-to-average

power ratio (PAPR). The high PAPR leads to nonlinear

distortion of the high-power-amplifier (HPA) and results in

inter-carrier-interference (ICI) plus out-of-band radiation. In

this paper, we present a Zadoff-Chu matrix transform (ZCMT)

based space-time-block-coded (STBC) MIMO-OFDM system

with reduced PAPR. Extensive simulations have been performed

to analyze the PAPR of the proposed system with root-raised-

cosine (RRC) pulse shaping. Simulation results show that, ZCMT

precoded STBC MIMO-OFDM system has low PAPR when

compared to both the Walsh-Hadamard transform (WHT)

precoded STBC MIMO-OFDM systems and the conventional

STBC MIMO-OFDM systems.

Keywords-component; orthogonal frequency division

multiplexing (OFDM); multiple-input multiple-output (MIMO);

Zadoff-Chu matrix transform (ZCMT); root-raised-cosine (RRC);

space-time-block-coded (STBC)

I. INTRODUCTION

Multiple-input multiple-output with orthogonal frequency

division multiplexing (MIMO-OFDM) system has been

receiving great attention, as one of the solutions for achieving

high speed, efficient, and high quality service for the 4G

wireless networks. OFDM is a multicarrier transmission

scheme that has become the technology of choice for next

generation wireless and wireline digital communication

systems because of its high speed data rates, high spectral

efficiency, high quality service and robustness against narrow

band interference and frequency selective fading [1]. OFDM

thwarts Inter Symbol Interference (ISI) by inserting a Guard

Interval (GI) using a Cyclic Prefix (CP) and moderates the

frequency selectivity of the Multipath (MP) channel with a

simple equalizer [2]. OFDM is widely adopted in various

communication standards such as Digital Audio Broadcasting

(DAB), Digital Video Broadcasting (DVB), and even in the

beyond 3G Wide Area Networks (WAN). On the other hand,

the MIMO configuration promises to increase capacity and

performance proportionally with the number of antennas [3]–

[6]. OFDM can be combined with the MIMO architecture to

increase diversity gain and to enhance system capacity on the

wireless channel.

However, among others, the Peak to Average Power

Ratio (PAPR) is still one of the major drawbacks in the

transmitted OFDM signal [7]. A large number of PAPR

reduction techniques have been proposed in the literature [8]-

[14]. The precoding based techniques, however, show great

promise as they are simple linear techniques and do not

require any side information.

In this paper, we present a PAPR analysis of the ZCMT

precoding based (space-time-block-coded) STBC MIMO-

OFDM system for 4G wireless networks with root-raised-

cosine (RRC) pulse shaping. The system shown is based on

two transmit antennas. However, the proposed scheme can be

extended to systems with more transmit antennas. The rest of

the paper is organized as follows: Section II describes the

basics of the STBC MIMO-OFDM system and PAPR, In

Section III we present the proposed scheme, Section IV

presents simulation results and section V concludes the paper.

II. STBC MIMO-OFDM SYSTEM AND PAPR

Fig. 1 illustrates the general block diagram of a STBC

MIMO-OFDM system. Baseband modulated symbols are

passed through serial-to-parallel (S/P) converter which

generates complex vector of size N. We can write the complex

vector of size N as X = [X0, X1, X2… XN-1]T. The complex

vector, X is then passed through the STBC encoder (2×2)

which generates two sequences: ���= [���,�, ���,�, ���,�

… ���,��]T and ���= [���,�, ���,�, ���,� … ���,��]

T. Both these

sequences are then passed through each IFFT block for

antenna 1 and antenna 2 respectively.

978-1-4577-1884-7/11/$26.00 ©2011 IEEE

Figure 1. STBC MIMO-OFDM (2×2) system

The complex baseband STBC MIMO-OFDM signal for

antenna i with N subcarriers can be written as:-

��, = �√� ∑ ���, . ������������ , n=0, 1, 2... N-1 (1)

where (� = 1, 2) denote the antenna number, j=√−1 and the

PAPR of the STBC MIMO-OFDM signal for antenna i in (1)

can be written as:-

PAPR = ��� ���,! "

#[ ���,! "] (2)

where E [.] denotes expectation.

III. PROPOSED ZCMT PRECODED SCHEME

A. Zadoff-Chu (ZC) Sequences and Zadoff-Chu Matrix

Transform (ZCMT)

Zadoff-Chu (ZC) sequences are class of poly phase

sequences having optimum correlation properties. ZC

sequences have an ideal periodic autocorrelation and constant

magnitude. According to [15], ZC sequences of length L can

be defined as:-

&� = ' �(")*+ ,-"" ./�0 123 4 #56� .�(")*+ 7-8-9:;" ./�< 123 4 =>> ? (3)

where k = 0, 1, 2… L-1, q is any integer and r is any integer

relatively prime to L. The kernel of the ZCMT is defined in

(4). For @ = A × A and j=√−1, the ZCMT, A, of size @ = A × A = A� is obtained by reshaping the ZC sequence by C = DA + F as hereunder:-

G = HIIJ

&�� &�� … &�84�;&�� &�� … &�84�; ⋮ ⋮ ⋱ ⋮ &84�;� &84�;� … &84�;84�; NOOP. (4)

Here m is the row variable and l the column variable. In other

words, the L2 point long ZC sequence fills the kernel of the

Matrix Transform row-wise.

B. Alamouti Space-Time Block Code (STBC)

The STBC achieves a full diversity gain by performing a

simple maximum-likelihood (ML) decoding algorithm.

According to [16], the 2×2 orthogonal STBC can be defined

as:-

� = Qs� −s�∗s� s�∗ T (5)

Alamouti encoded signal is transmitted from the two transmit

antennas over two symbol periods. During the first symbol

period, two symbols s1 and s2 are simultaneously

transmitted from the two transmit antennas. During the second

symbol period, these symbols are transmitted again, where

-s2* is transmitted from first transmit antenna and s1* is

transmitted from the second transmit antenna.

C. ZCMT precoded MIMO-OFDM system

Fig. 2 shows the ZCMT precoded STBC MIMO-OFDM

system. In this system, the kernel of the ZCMT, A acts as a

precoding matrix of dimension @ = A × A and is applied to

the constellations symbols before the STBC encoding and

IFFT to reduce the PAPR.

Figure 2. ZCMT precoded STBC MIMO-OFDM (2×2) system

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In the ZCMT precoded STBC MIMO-OFDM system, the

baseband modulated data is passed through the S/P converter

which generates a complex vector of size L that can be written

as X = [X0, X1, … XL-1]T. Subsequently, ZCMT precoding is

applied to this complex vector which transforms this complex

vector into a new vector of length L that can be written as

Y=AX= [Y0, Y1, Y2… YL-1] T, where A is a precoder matrix of

size @ = A × A and Ym can be written as:-

U� = ∑ &�,V . �V4�V�� D = 0,1, … A − 1 (6)

where &�,V refers to the mth row and l

th column of the precoder

matrix. Expanding equation (6), using row wise sequence

reshaping C = DA + F and putting q=0, r=1 in equation (3) we

get:-

U� = ∑ 8��)8X+9Y;"+" ;. �V4�V�� (7)

where D = 0, 1, 2 . . . A − 1. Equation (7) represents the

ZCMT precoded constellations symbols. The U� is then

passed through the STBC encoder (2×2) which generates two

sequences: U��8�;= [U��8�,�;, U��8�,�;, U��8�,�; … U��8�,��;]T and U��8�;= [U��8�,�;, U��8�,�;, U��8�,�; … U��8�,��;]T. Both these

sequences are then passed through each IFFT block for

antenna 1 and antenna 2 respectively. The complex baseband

ZCMT precoded STBC MIMO-OFDM signal for antenna i

with N subcarriers can be written as:-

��, = �√� ∑ U��8 ; . ������������ , n=0,1,2,...,N-1 (8)

The complex passband transmit signal, x(t) of the

proposed system after pulse shaping and digital-to-analog

(D/A) can be written as:-

8Z;= ��[\] ∑ ��, . ^8Z − _ a;����� (9)

where bc is carrier frequency, r(t) is baseband pulse, a = 7d�< . ` is compressed symbol duration after IFFT and T

is the symbol duration is seconds. The RRC pulse shaping

filter can be defined as:-

^8Z; = e �,)fgh 8�i;0.jifgh .c2e,)fgh 8�.i;0)fgh .,�:kl"f"gh" 0 (10)

0 ≤∝ ≤ 1, where ∝ is rolloff factor. The PAPR of ZCMT

precoded STBC MIMO-OFDM signal in (9) with pulse

shaping can be written as:-

oGop = |�8];|"rsfs�ghXtu:�gh v |�8];|">]�ghr (11)

It is important to note that the orthogonality of the symbols

after introducing precoding is maintained, as the precoding

matrix is cyclic auto-orthogonal [10].

IV. SIMULATION RESULTS

Extensive simulations in MATLAB® have been carried

out for the PAPR analysis of ZCMT precoded STBC MIMO-

OFDM systems with RRC pulse shaping. To show the PAPR

analysis of the proposed system, random generated data is

modulated by QPSK, 16-QAM and 64-QAM. We evaluate the

PAPR statistically by using complementary cumulative

precoded STBC distribution function (CCDF).

The CCDF of the PAPR for ZCMT MIMO-OFDMA

signal is used to express the probability of exceeding a given

threshold PAPR0 8wwxy = o^z{ 8oGop > oGop�;;. We

have compared the simulation results of the proposed system

with WHT Precoded STBC MIMO-OFDM and conventional

STBC MIMO-OFDM systems. To show the PAPR analysis of

the proposed system with RC pulse shaping in MATLAB®,

we have used RRC rolloff factor, α = 0.22 and with N = 512

system subcarriers. All the simulations have been performed,

with 105 random OFDM blocks. Simulation parameters used

are given in Table.1.

TABLE 1: SYSTEM PARAMETERS

Channel Bandwidth 5MHz

Oversampling Factor 4

System Subcarriers 512

MIMO Scheme 2×2

Precoding WHT and ZCMT

Modulation QPSK, 16-QAM and 64-QAM

Pulse Shaping Root Raised Cosine (RRC)

Roll Off Factor of RC α = 0.22

CCDF Clip Rate 10�

Figure 3. CCDF comparison of PAPR of ZCMT precoded

OFDM system, WHT precoded STBC MIMO-OFDM system and

MIMO-OFDM conventional, with N=512 for QPSK.

Figure 4. CCDF comparison of PAPR of ZCMT precoded

OFDM system with WHT precoded STBC MIMO-OFDM system and

MIMO-OFDM conventional, with N=512 for 16-

0 2 4 6 810

-2

10-1

100

PAPR0(dB)

Prob(P

APR > P

APR0)

RCC Pulse Shaping Factor Alpha= 0.22

MIMO-OFDM

WHT-MIMO-OFDM

ZCMT-MIMO-OFDM

0 2 4 6 810

-2

10-1

100

PAPR0(dB)

Prob(P

APR > P

APR0)

RCC Pulse Shaping Factor Alpha= 0.22

MIMO-OFDM

WHT-MIMO-OFDM

ZCMT-MIMO-OFDM

CCDF comparison of PAPR of ZCMT precoded STBC MIMO-

OFDM system and STBC

OFDM conventional, with N=512 for QPSK.

CCDF comparison of PAPR of ZCMT precoded STBC MIMO-

OFDM system and STBC

-QAM.

Figure 5. CCDF comparison of PAPR of ZCMT precoded

OFDM system with WHT precoded STBC

MIMO-OFDM conventional, with N=512 for

Fig. 3 shows the CCDF based comparison of the PAPR

for the conventional STBC MIMO

precoded STBC MIMO-OFDM systems and

precoded STBC MIMO-OFDM system respectively, with

RRC pulse shaping. At clip rate of

10.3 dB and 5.3 dB for the conventional

OFDM systems, WHT precoded STBC MIMO

systems and ZCMT precoded STBC MIMO

respectively, with the RRC pulse shaping

0.22), using QPSK modulation for

Fig. 4 shows the CCDF based comparison of the PAPR

for the conventional STBC MIMO

precoded STBC MIMO-OFDM systems and

precoded STBC MIMO-OFDM system respectively, with

RRC pulse shaping. At clip rate of

to 11.1 dB, 10.6 dB and 6.8 dB for the conventional

MIMO-OFDM systems, the WHT precoded STBC MIMO

OFDM systems and the ZCMT precoded STBC MIMO

OFDM systems respectively, with

(roll-off factor α = 0.22), using@ = 512.

10 12

RCC Pulse Shaping Factor Alpha= 0.22

MIMO-OFDM

WHT-MIMO-OFDM

ZCMT-MIMO-OFDM

10 12

RCC Pulse Shaping Factor Alpha= 0.22

MIMO-OFDM

WHT-MIMO-OFDM

ZCMT-MIMO-OFDM

0 2 410

-2

10-1

100

PAPR

Prob(P

APR > P

APR0)

RCC Pulse Shaping Factor Alpha= 0.22

CCDF comparison of PAPR of ZCMT precoded STBC MIMO-

STBC MIMO-OFDM system and STBC

M conventional, with N=512 for 64-QAM.

Fig. 3 shows the CCDF based comparison of the PAPR

conventional STBC MIMO-OFDM systems, the WHT

OFDM systems and the ZCMT

OFDM system respectively, with

. At clip rate of 10�, the PAPR is 11 dB,

dB for the conventional STBC MIMO-

WHT precoded STBC MIMO-OFDM

ZCMT precoded STBC MIMO-OFDM systems

C pulse shaping (roll-off factor α =

QPSK modulation for @ = 512.

shows the CCDF based comparison of the PAPR

conventional STBC MIMO-OFDM systems, the WHT

OFDM systems and the ZCMT

OFDM system respectively, with

. At clip rate of 10�, the PAPR is reduced

dB for the conventional STBC

WHT precoded STBC MIMO-

ZCMT precoded STBC MIMO-

OFDM systems respectively, with the RRC pulse shaping

, using 16-QAM modulation for

6 8 10 12

PAPR0(dB)

RCC Pulse Shaping Factor Alpha= 0.22

MIMO-OFDM

WHT-MIMO-OFDM

ZCMT-MIMO-OFDM

Fig. 5 shows the CCDF based comparison of the PAPR

for the conventional STBC MIMO-OFDM systems, WHT

precoded STBC MIMO-OFDM systems and ZCMT precoded

STBC MIMO-OFDM system respectively, with RRC pulse

shaping. At clip rate of 10�, the PAPR is reduced to 11.2 dB,

10.8 dB and 7.2 dB for the conventional STBC MIMO-

OFDM systems, the WHT precoded STBC MIMO-OFDM

systems and the ZCMT precoded STBC MIMO-OFDM

systems respectively, with the RRC pulse shaping (roll-off

factor α = 0.22), using 64-QAM modulation for @ = 512.

V. CONCLUSION

In this paper, we present an analysis of the PAPR for the

ZCMT precoded STBC MIMO-OFDM system with RRC

pulse shaping. Simulation results have shown that the ZCMT

precoded STBC MIMO-OFDM system with RCC pulse

shaping has much lower PAPR than the WHT precoded STBC

MIMO-OFDM systems and conventional STBC MIMO-

OFDM systems. Hence, it can be concluded that the ZCMT

precoded STBC MIMO-OFDM system is more favorable than

the WHT precoded STBC MIMO-OFDM and the STBC

MIMO-OFDM Conventional systems. Furthermore, the

proposed system does not require any power increase,

complex optimization and side information. Finally, the

proposed system also takes advantage of frequency variations

of the communication channel and can offer substantial

performance gain in fading multipath channels.

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