Performance Comparison between OQAM and <i>N</i>-continuous OFDM

doi:10.4236/cn.2013.53B2071

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Communications and Network, 2013, 5, 390-393

http://dx.doi.org/10.4236/cn.2013.53B2071 Published Online September 2013 (http://www.scirp.org/journal/cn)

Performance Comparison between OQAM and

N-continuous OFDM

Guobing Cheng, Huilei Li, Shaoqian Li, Lisha Gong, Binhong Dong, Peng Wei

National Key Laboratory of Science and Technology on Communications,

University of Electronic Science and Technology of China, Chengdu, China

Email: [email protected]

Received August, 2013

ABSTRACT

Orthogonal frequency division multiplex/offset QAM (OFDM/OQAM) and N-continuous OFDM are both improved

multi-carrier modulation (MCM) techniques for the transmission of signals over multipath fading channels. In this pa-

per, we aim to compare these two techniques with respect to out-of-band radiation , bit error ratio (BER) and calcu lation

complexity. Analysis and simulation results show that, compared to the N-continuous OFDM, the OFDM/OQAM has

lower out-of-band radiation, calculation consumption and similar BER performance.

Keywords: OFDM/OQAM; N-continuous OFDM; Out-of-band Radiation

1. Introduction

Orthogonal frequency division multiplexing (OFDM) is

an efficient scheme and it has been some practical appli-

cations. However, the trad itional OFDM has some intrin-

sic drawbacks that the discontinuous phase between ad-

jacent symbols leads to high out-of-band radiations and

its robustness to multi-path propagation effect is acquired

by the insertion of a cyclic prefix (CP). To alleviate these

drawbacks, another MCM schemes such as N-continuous

OFDM and OFDM/offset QAM (OFDM/OQAM) are

proposed in [1,2] respectively. Compared to traditional

CP-OFDM, OFDM/OQAM may provide a higher useful

bit rate since it operates without CP and N-continuous

OFDM has less out-of-band radiation since it has several

continuous order of derivatives at the edge of adjacent

OFDM symbols.

For OFDM/OQAM system, pulse shapes with good

time-frequency localization (TFL) can be introduced.

Among these, a pulse shape named extended Gaussian

functions (EGF) is widely used and its TFL can be ad-

justed by the time and frequency real parameters [3].

Through selecting a suitable parameter, an OFDM/

OQAM signal with very low out-of-band radiation can

be acquired [4]. On the other hand, in the traditional

OFDM system, each OFDM symbol is independently

and the transmitted signals are no t continuous, leading to

high out-of-band radiation. In order to overcome the dis-

continuities between consecutive OFDM symbols, N-

continuous OFDM scheme is proposed at the price of

increasing calculation complexity and/or system per-

formance. Therefore, we have to comprise between these

aspects for practical application.

In this paper, we compare the performance of OFDM/

OQAM and N-continuous OFDM. Firstly, the system

models of them are given in section II. And then we ana-

lyze the out-of-band radiation, bit error ratio (BER) and

calculation complexity of these two schemes in section

III. The simulation results are shown in section IV. Brief

conclusion is given in section V. The analysis and simu-

lation results show that, compared to the N-continuous

OFDM, the OFDM/OQAM system has similar system

performance, lower out-of-band radiation and less calcu-

lation consumption.

2. System Model

2.1. System Model of OFDM/OQAM System

The baseband version of a continuous-time OFDM/

OQAM transmitting signal can be written as [2]





Mjjmt

staeegt n







 





 (1)

with M an even number of sub-carriers, ,mn the real-

valued symbol conveyed by the sub-carrier of index m

during the symbol time of index n0



the subcarrier

spacing and 0



the time offset between the adjacent real

part and imaginary part of an OFDM/OQAM symbol.

00 0

1 2T1







, with 0 the duration of the complex-

valued symbols. T

,mn



is an additional phase term given

G. B. CHENG ET AL. 391



,0()mod

mn mn









  (2)

where 0



can be arbitrarily chosen.



t is the pulse

shape that can be different from the rectangle shape of

conditional OFDM system. The EGF shape is often used

in OFDM/OQAM system and its out-of-band character-

istic can be adjusted by the Gaussian parameter



. In

the following, the adaption and compromise between

BER performance and out-of-band radiation are dis-

cussed.

For a distortion-free channel, perfect reconstruction of

real symbols is obtained owing to the following real or-

thogonal condition



 



,,, ,,

mnpqmnpqmpnq

gggtgt,



 

 (3)

where is the taking real part operator.



,1





if and

mp,0



 if mp



2.2. System model of N-continuous OFDM

System

The baseband equivalent OF DM symbol can be given as





0isg

sts tiTT











(4)

where

T is the OFDM symbol duration and

T is the

CP length. In order to make the transmitted signal





and its first N derivatives continuous, the following

equation should be satisfied that

 

itTi tT

sts t

dt dt

 

 (5)

for all and n=0, 1,…, N [1 ,5 ] .

1i

The realization of N-continuous OFDM symbol is to

pre-coder the set of information symbols (taken

from some complex-valued symbol constellation ) in

each OFDM symbol such that



,ki





t becomes

N-continuous. Concretely, the OFDM symbol





t can

be expressed as [1]



iki g

tde TtT











(6)

where and the complex numbers



01 1

,,..., K

kk k





,ki

d are the result of pre-coding information symbols

,ki. For OFDM symbols, the characterization (5) be-

comes

njk n

ki ki

ke dkd





 





(7)

where 2





 . An equivalent form of vector is

that

,

Ad Ad

-1

(8)

where





01 1

,, ,

, ,...,,

ki kiki

dd d





d (9)





, ,...,,

jk jk jk

diag eee





 1

(10)

and

01 1

11...1

... .

... ......

...

NN N

kk k













A (11)

Finally, we can get 1

()



 H

dIPdPΦd, where

. The deducing detail can be

referred to [1].



HH 

H

PΦAAA AΦ

3. Comparison of the OFDM/OQAM and

N-continuous OFDM System

3.1. Comparison of the Out-of-band Radiation

Because the pulse shape with lower side lobe such as the

EGF shape is used in the OFDM/OQAM system, the

final transmitting signal has very low out-of-band radia-

tion naturally. The EGF shape is defined as [6]



00 0

,, ,,

000

,1 ,

cos2

aka

ztdgt gt

 

































































(12)

where







is the Gaussian function defined by

 

gte a









.



is the frequency paramr, 0

ete



is the time

parameter and 00 12







. For ifferent a, we can get

different transmitting signal and the larger the value of

a is, the lower out-of-band radiation

will be.

For N-continuous OFDM system, the out-of-band

radiation is determined by the number of orders that

having continuous derivatives. And the larger is, the

lower out-of-band radiation will be.

In contrast to OFDM/OQAM, increasing of leads

to not only the decrease of BER performance but also the

rapid increasing of calculation complexity. Therefore, the

compromise should be made between calculation con-

sumption and system performance.

3.2. Comparison of the BER Performance

In OFDM/OQAM system, since the pulse shape that

having immunity to the inter-symbol interference (ISI) is

introduced, the CP is not necessary. Then it can provide

higher bit rate or equivalently higher bit energy.

While for the N-continuous OFDM, the using of CP

cannot be avoided. Furthermore, since the maximum-

likelihood detector of N-continuous is prohibitively

G. B. CHENG ET AL.

392

complex, suboptimal iterative detector is usually used

and there is a certain performance loss when the iterative

time is less than 4.

3.3. Comparison of the Calculation Complexity

In the OFDM/OQAM system, the complex data sources

are divided into real and image part and carried out FFT

calculation respectively. Then a pulse shape with the

duration of 0c is met. Finally these two paths

signals are added and we get the transmitting OFDM/

OQAM signal [4]. Therefore the OFDM/OQAM system

calculation consumption comprises of

TmT

2log 4

MmM



real multiplications and



2log4 1

MmM real

additions.

For N-continuous OFDM, the system calculation con-

sumption comprises of 2

real multiplications and

M real additions. Because both multiplications

and additions calculation are directional proportional to

the square of the number of subcarriers M. Therefore the

calculation consumption increases rapidly for a large M.

Taking the number of subcarriers and the

length the of pulse shape is four times of the length of

OFDM symbol, i.e., , for example, the numerical

comparison of calculation complexity is listed in Table 1.

It is shown that the calculation complexity of N-con-

tinuous OFDM is far more than that of the OFDM/

OQAM system.

256M

4m

4. Simulation Results

In this section, it aims to compare the out-of-band radia-

tion and BER performance of OFDM/OQAM with the

N-continuous system. Unless other wise stated, the

simulation parameters are: the number of subcarriers is

M = 512, sampling time Ts = 1/15 ms, CP length Tg =

144Tsamp, the data is modulated by 16QAM. A 3GPP

EVA fading channel is combined without carrier fre-

quency offset and synchronization errors. The power

spectrum is estimated by Welch’s averaged periodogram

method with sampling duration Tsamp, a 4096-sample

Hanning window and 512-sampleoverlap. And the simu-

lation results are shown in Figure 1 and Figure 2.

Figure 1 shows the results of BER performance of N-

continuous OFDM and OFDM/OQAM, and the results of

original OFDM are also given. It can be seen that N-

continuous OFDM has poorer performance than original

Table 1. Numerical comparison of calculation complexity.

scheme real multiplication addition real

OQAM/OFDM 8192 7168

N-continuou

Figure 1. Comparison of BER performance of N-continuous

OFDM and OFDM/OQAM.

Figure 2. Comparison of out-of-band radiation of N-con-

tinuous OFDM and OFDM/OQAM.

OFDM and the situation is more serious when the N is up

to 10. On the other hand, for OFDM/OQAM system, it

has similar performance with origin OFDM, and the per-

formance loss is negligible even for 2



.

In Figure 2, it sh ows the power spectral density of N-

continuous OFDM and OFDM/OQAM, together with the

results of original OFDM. The results imply that the N-

continuous OFDM has lower out-of-band radiation than

original OFDM. And the larger N is, the lower out-of-

band radiation will be. While for OFDM/OQAM system,

it has a sharp decay at the edge of the main lobe, which is

better for transmission in means of avoiding adjacent

interference. And the parameter



has a certain effect

on the out-of-band radiation. When N = 10, N-continu-

ous OFDM is a little better than that of OFDM/OQAM

with 0.5





. But at same time, the calculation con-

sumption is very large.

5. Conclusions

524288

OFDM 523776

In this paper, the performance of OFDM/OQAM and

G. B. CHENG ET AL.

393

N-continuous OFDM are compared with respect to out-

of-band radiation, BER performance and calculation

complexity with different system parameters. We show

that N-continuous OFDM is only designed to suppress

the out-of-band radiation, but this benefit is acquired

with large calculation consumption increase. The advan-

tages of OFDM/OQAM lie in that it has not only the na-

ture advantage of low out-of-band radiation, but also the

strong immunity to ISI and inter-carrier interference si-

multaneously. When the length of pulse shape is suitable

selected, while with moderate complexity increase. In

whole, OFDM/OQAM system outperforms the N-con-

tinuous OFDM system.

6. Acknowledgements

This work is supported in part by the National Science

Foundation of China under Grant number 61101101,

National Grand Special Science and Technology Project

of China under Grant No. 2010ZX03006-002-02,, Pro-

gram for New Century Excellent Talents in University of

China ((NCET110058), the Foundation Project of Na-

tional Key Laboratory of Science and Technology on

Communications under Grant 9140C020404120C0201,

and Key Laboratory of Universal Wireless Communica-

tions, Beijing university of Posts and Telecommunica-

tions, Ministry of Education, P.R.China (No. KFKT-

2012102).

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