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978-1-4577-1343-9/12/$26.00 ©2013 IEEE

Comparisons of Filter Bank Multicarrier Systems

Juan Fang1, Zihao You2, I-Tai Lu5

ECE Department

Polytechnic Institute of NYU

Brooklyn, NY, USA

jfang1985@gmail.com1, zyou01@students.poly.edu2,

itailu@poly.edu5

Jialing Li3, Rui Yang4

InterDigital Communications, Inc.

Melville, NY, USA

Jialing.Li@interdigital.com3, Rui.Yang@interdigital.com4

Abstract—In this paper, we compare three filter bank

multicarrier (FBMC) techniques, i.e., Orthogonal Frequency

Division Multiplexing (OFDM), OFDM-Offset Quadrature

Amplitude Modulation (OFDM-OQAM) and wavelet packet

modulation (WPM), based on multiple criteria, including

bandwidth efficiency, computational complexity, latency, out-of-

band emission, peak-to-average power ratio, and sensitivity to

timing and frequency offsets. An efficient implementation of

OFDM-OQAM is also proposed for a special case.

Keywords-Multicarrier; OFDM; OFDM-OQAM; Wavelet

Packet Modulation

I. INTRODUCTION

Multicarrier modulation (MCM) techniques enable

transmission of a set of data over multiple narrow band

subcarriers simultaneously. With an advanced wideband

modulation and coding scheme (MCS), a system with MCM

can achieve much higher spectral efficiency in frequency

selective channels compared to those using single carrier

modulation techniques. Filter bank multicarrier (FBMC)

modulation is a family of MCM techniques in which a

prototype filter is designed to achieve a certain goal, such as

minimizing inter-symbol interference (ISI), inter-carrier

interference (ICI) and/or stop band energy. The well-known

Orthogonal Frequency Division Multiplexing (OFDM) can be

considered a type of FBMC whose time domain prototype

filter is a simple rectangular pulse. From the complexity

perspective, the main advantage of OFDM over other FBMC

techniques is that it is very easy to be implemented. However,

large sidelobes of the rectangular pulse in OFDM create

challenging issues in practical systems. For example, the

performance of the systems at the physical (PHY) layer is very

sensitive to frequency offset. In addition, in systems such as

those in TV white space and heterogeneous networks with

small cells, multiple radio links coexist in congested spectral

bands, but are loosely controlled or coordinated in resource

usage (frequency, timing and power). In such a network,

strong adjacent channel interference may be generated from

large out-of-band emissions partially contributed from large

sidelobes at the baseband. Another drawback of OFDM is that

the modulated signal exhibits large peak-to-average power

ratio (PAPR) which usually leads to low efficiency power

amplifiers (PAs). To overcome the aforementioned drawbacks,

researchers have been looking into different FBMC techniques,

including OQAM-OFDM [1]-[4] and Wavelet Packet

Transform (WPT) [5]. In OQAM-OFDM, subcarriers of the

signal overlap each other to achieve a high spectral efficiency.

Different from OFDM, the real and imaginary parts of the

QAM symbols are processed separately with 2×symbol rate. A

prototype filter needs to be carefully designed to minimize or

zero out ISI and ICI while keeping the sidelobes small. On the

other hand, wavelet packet modulation (WPM), which uses the

wavelet packet transform (WPT) instead of the discrete

Fourier transform (DFT), is receiving growing attention

because of some of its interesting features in terms of

spectrum usage and signal construction flexibilities [5]. Some

studies have also shown that the WPM signal exhibits smaller

PAPR than OFDM [6]. Little about the out-of-band leakage

from WPM waveforms is found in the literature.

In this paper, we compare OFDM with other FBMC

techniques including OFDM-OQAM and WPM in terms of

several metrics that are commonly considered when designing

a communication system. The metrics include bandwidth

efficiency, computational complexity, latency, out-of-band

emission, PAPR, and bit error rate (BER). Sensitivity to

frequency and timing offsets is also measured and compared.

An efficient implementation of the OFDM-OQAM synthesis

and analysis filter banks when the prototype filter is of odd

length is also proposed.

II. FILTER BANK MULTICARRIER SYSTEMS

Fig.1 shows a block diagram for a general FBMC

system.The transmitted signal, x[n], can be expressed as

ݔሾ݊ሿ ൌ ݏ,݃ሾ݊ െ ݈ܮ௦ሿ

ெିଵ

ୀ

(1)

where M is the number of subcarriers, s, is the lth symbol in

the kth subcarrier, Ls is the number of samples per transmit

symbol spacing, and ݃ሾ݊ሿ is the synthesis filter for the kth

subcarrier. At the receiver, the estimated lth symbol sො, in the

kth subcarrier is

̂ݏ, ൌ ሺݕሾ݊ሿ כ ݂ሾ݊ሿሻୀೞ (2)

where y[n] is the received signal and ݂ሾ݊ሿ is the impulse

response of the analysis filter for the kth subcarrier. Define the

number of samples per symbol duration as L, where ܮ ܯ.

Note that Ls and L are not necessarily the same. For an ideal

channel where ݕሾ݊ሿ ൌ ݔሾ݊ሿ, a QAM symbol sො, in OFDM and

WPM will be the same as the input symbol s, if the filter

satisfies the orthogonal condition:

ۃ݃ሾ݊ െ ݉ܮ௦ሿ, ݂ሾ݊ െ ݈ܮ௦ሿۄ ൌ ߜߜ (3)

where ߜ is the Kronecker delta. Define the lth input symbol

vector along all subcarriers as

ܛ ൌ ሾݏ, ݏଵ, ڮ ݏெିଵ,ሿ், (4)

978-1-4577-1343-9/12/$26.00 ©2013 IEEE

the corresponding output signal vector from the transmitter as

ܠൌ ሾݔሾሺ݈ െ 1ሻܮሿ ݔሾሺ݈ െ 1ሻܮ 1ሿ ڮ ݔሾ݈ܮ െ 1ሿሿ், (5)

the corresponding received signal vector at the receiver as

ܡൌ ሾݕሾሺ݈ െ 1ሻܮሿ ݕሾሺ݈ െ 1ሻܮ 1ሿ ڮ ݕሾ݈ܮ െ 1ሿሿ், (6)

and the estimated lth symbol vector as

ܛො ൌ ሾ̂ݏ, ̂ݏଵ, ڮ ̂ݏெିଵ,ሿ். (7)

In the following subsections, we give the synthesis and analysis

filters for three different MCM schemes in details.

[ ]kg n

[ ]0g n

[ ]1Mg n−

0,s l

1,sM l−

,sk l

0,ˆ ls

1,sˆM l−

,sˆk l[ ]kf n

[ ]0f n

[ ]1Mf n−

[ ]x n [ ]y n

Figure 1. General structure for an FBMC system.

A. OFDM

In OFDM, the input symbols ݏ, are QAM symbols and

ܮ௦ ൌ ܮ. The synthesis and analysis filters are defined as

݃ሾ݊ሿ ൌ ݂ሾ݊ሿ ൌ ሾ݊ሿ ܹି (8)

where ܹ ൌ ݁ିଶగ/ . The prototype filter ሾ݊ሿ ൌ 1/√ܮ for ݊ ൌ 0,1, … , ܮ െ 1 and 0 elsewhere. Substituting (8) into (1),

after some math manipulations, the transmitted signal for the

lth symbol is obtained as

ܠ ൌ

1

√ܮ ۴

ுሾ۷ெ ெൈሺିெሻሿ்ܛ (9)

where the (i,j)th element of the ܮ ൈ ܮ DFT matrix ۴ is

ሺ۴ሻ ൌ ܹሺିଵሻሺିଵሻ, ݅, ݆ ൌ 1, … , ܮ (10)

and the inverse DFT (IDFT) matrix is given by ۴ு/ܮ . ۷ெ

stands for the ܯ ൈ ܯ identity matrix. Similarly, substituting (8)

into (2), after some math manipulations, the estimated lth

symbol is obtained as

ܛො ൌ

1

√ܮ ሾ

۷ெ ெൈሺିெሻሿ۴ܡ (11)

The OFDM transmitter can be implemented by using zero-

padding, inverse fast Fourier transform (IFFT) and parallel-to-

serial (P/S) conversion; the OFDM receiver can be

implemented by using serial-to-parallel conversion (S/P)

conversion and fast Fourier transform (FFT). For multipath

channels, cyclic prefix (CP) is usually used in OFDM.

B. OFDM-OQAM

In OFDM-OQAM, the input symbols ݏ, are OQAM

symbols and ܮ௦ ൌ ܮ/2. The OQAM symbols are defined as

ݏ, ൌ ݆ାݏ,ோ (12)

where ݏ,ோ is the real input sequence:

ݏ,ோ ൌ ൝

ݏҧ,′ூ , ݈ ൌ 2݈′

ݏҧ,′ொ , ݈ ൌ 2݈′ 1

(13)

where ݏҧ,′ூ and ݏҧ,′ொ are the real and imaginary parts of the ݈′th

input QAM symbol ݏҧ,′ , respectively. In (12), the ݆ା factor

introduces the π/2 phase shift between any pair of adjacent

OQAM symbols (in both the frequency and time) to ensure

orthogonality. In OFDM-OQAM, (3) is not satisfied.

According to (12), the estimated real sequence is

̂ݏ,ோ ൌ ܴ݁ൣ݆ିሺାሻ̂ݏ,൧ (14)

And, according to (12), the estimated ݈′th QAM symbol is

ݏҧመ,′ ൌ ̂ݏ,ଶ′ோ ݆̂ݏ,ଶ′ାଵோ (15)

As in [3], the synthesis and analysis filters are

݃ሾ݊ሿ ൌ ݂ሾ݊ሿ ൌ ሾ݊ሿ ܹ ܹି (16)

where ܾ ൌ ൫ܮ െ 1൯/2, and the length-ܮ prototype filter ሾ݊ሿ

is a square-root Nyquist filter with roll-off factor not greater

than 1. The prototype filter should be designed to strike a

balance between minimizing structure based interference, and

channel/radio impairment mitigation. The prototype filter

design is out of the scope of this paper and we will report it in

the future. In this paper we use the frequency sampling based

prototype filters [3] in our simulation. We further assume ܮ ൌ

ܭܮ ݀ , where the integer K is the overlapping factor (the

number of symbol durations in the prototype filter length), and

݀ is an odd integer. So, ܾ is an integer in this case. The

synthesis and analysis filters can be implemented in different

ways. An efficient implementation of the OFDM-OQAM will

be presented in Sec. III.

C. WPT

WPM is a multicarrier modulation based on WPT. In WPM,

the input symbols ݏ, are QAM symbols and ܮ௦ ൌ ܮ . The

synthesis filter ݃ሾ݊ሿ in (1) is derived by having the input data

symbols go through several sub-stages where the input of each

sub-stage first gets upsampled by 2, and then goes through a

pair of filters ݑሾ݊ሿ and ݒሾ݊ሿ . A 2 sub-stage (4 subcarriers)

example is shown in Fig.2. Let ܩሺݖሻ, ܷሺݖሻ and ܸሺݖሻdenote

the Z-transform of ݃ሾ݊ሿ, ݑሾ݊ሿ and ݒሾ݊ሿ, respectively. Then,

ܩሺݖሻ ൌ ෑ ܷ൫ݖଶషభ൯

୪୭మ ெ

ୀଵ

,

ܩଵሺݖሻ ൌ ܸ ቀݖଶౢమ ಾషభቁ ෑ ܷ൫ݖଶషభ൯

୪୭మ ெିଵ

ୀଵ

, …,

ܩெିଵሺݖሻ ൌ ෑ ܸ൫ݖଶషభ൯

୪୭మ ெ

ୀଵ

.

(17)

Figure 2. Block diagram of a WPM transmitter example with M = 4.

If an additive white Gaussian noise (AWGN) channel is

assumed, the structure of the receiver is simply the reverse of

the transmitter, where the analysis filter ݂ሾ݊ሿ in (2) is

determined by another pair of half-band low-pass filter ݑොሾ݊ሿ

and half-band high-pass filter ݒොሾ݊ሿ, respectively, as shown in

Fig.3 (4 sub-carriers, i.e., 2 sub-stages, are drawn in this figure).

These two pairs of filters are jointly designed so that (3) is

ݑሾ݊ሿ↑2

ݒሾ݊ሿ↑2

ݑሾ݊ሿ↑2

ݒሾ݊ሿ↑2

↑2

↑2

ݑሾ݊ሿ

ݒሾ݊ሿ

ݔሾ݊ሿ

ݏ,

ݏଵ,

ݏଶ,

ݏଷ,

978-1-4577-1343-9/12/$26.00 ©2013 IEEE

satisfied. In this paper, we use Daubechies (Db) wavelets [7] of

different lengths as ݑሾ݊ሿ, ݒሾ݊ሿ, ݑොሾ݊ሿ and ݒොሾ݊ሿ.

Figure 3. Block diagram of a WPM receiver example with M = 4

III. EFFICIENT IMPLEMENTATION OF OFDM-OQAM

Efficient polyphase implementations of OFDM-OQAM

synthesis filter bank (SFB) and analysis filter bank (AFB) have

been investigated in [1]-[4] (IFFT-based SFB and AFB for

ܮ ൌ ܭܮ 1 [1] and for general ܮ [4], IFFT-based SFB and

FFT-based AFB [2]-[3]). To make a system operable using

with either OFDM or OFDM-OQAM, the IFFT-based SFB and

FFT-based AFB should be chosen. It has been shown in [2]-[3]

that the complexity of such implementation for the special case

of ܮ ൌ ܭܮ െ 1 has lowest complexity. In this section, we

extend it to a novel efficient implementation for the case when

ܮ is an arbitrary odd integer.

A. Synthesis Filter Bank (SFB)

The Z-transform’s of the synthesis filters are

ܩሺݖሻ ൌ ܹൣ1 ܹି ڮ ܹିሺିଵሻ൧ۯሺݖሻ܋ሺݖሻ (18)

where

ۯሺݖሻ ൌ ݀݅ܽ݃ሼܣሺݖሻ ܣଵሺݖሻ ڮ ܣିଵሺݖሻሽ (19) ܋ሺݖሻ ൌ ሾ1 ݖିଵ ڮ ݖିሺିଵሻሿ். (20)

The polyphase filters in (19) are defined as

ܣሺݖሻ ൌ ሾݍ ݉ܮሿݖି , ݍ ൌ 0,1, ڮ , ܮ െ 1. (21)

Define the Z-transform of the input symbols ܛ (the Z-

transform is performed along the symbol index l) as ܁ሺݖሻ .

Similar to [3], the Z-transform of ݔሾ݊ሿ can be written as

ܺሺݖሻ ൌ ܋்ሺݖሻۯሺݖሻ۴ுగሾ۷ெ ெൈሺିெሻሿ்܁ ൬ݖ

ଶ൰. (22)

where

గ ൌ ݀݅ܽ݃൛1 ܹ ڮ ܹሺିଵሻൟ (23)

Then, ܺሺݖሻ can be further rewritten as

ܺሺݖሻ ൌ ܋்ሺݖሻሼۯଶ۾గ۴ுሾ۷ெ ெൈሺିெሻሿ்܁ሽ ൬ݖ

ଶ൰ (24)

where

ۯଶሺݖሻ ൌ ۯሺݖଶሻ. (25)

and the permutation matrix

۾గ ൌ

ൈሺିሻ ۷

۷ି ሺିሻൈ൨ ൌ

1

ܮ ۴

ுగ۴ (26)

From (24), the OFDM-OQAM SFB can be implemented by

using zero-padding, IFFT, permutation ۾గ , polyphase filters ܣሺݖଶሻ, and P/S conversion (via upsampling by ܮ/2 and delay

chain). Its polyphase structure is given in Fig.4.

B. Analysis Filter Bank (AFB)

Define the Z-transform of the received signal ݕሾ݊ሿ as ܻሺݖሻ

and that of the estimated symbols ܛො (the Z-transform is

performed along the symbol index l) as ܁ሺݖሻ . Since the

analysis filters are the same as the synthesis filters, in an

AWGN channel, the IFFT-based AFB could be written as

܁ ൬ݖଶ൰ ൌ ሼሾ۷ெ ெൈሺିெሻሿ۴ு۾గ்ۯଶሽ ൬ݖ

ଶ൰ ܋ሺݖሻܻሺݖሻ. (27)

Note that the DFT and IDFT matrix could be related through

۴ு ൌ ۴۾గ (28)

where ۾గ is the permutation matrix

۾గ ൌ

ۏێ

ێێ

ۍ1 00 ڮ

ڮ ڮ 0

ڮ 0 1

0 ڮ

ڭ گ

0 1

0 1 0

گ گ ڭ

0 ڮ 0 ے

ۑۑ

ۑ

ې

. (29)

Substituting (28) into (27), we obtain

܁ ൬ݖଶ൰ ൌ ሼሾ۷ெ ெൈሺିெሻሿ۴۾గۯଶሽ ൬ݖ

ଶ൰ ܋ሺݖሻܻሺݖሻ, (30)

where the permutation matrix

۾గ ൌ ۾గ۾గ். (31)

Based on (30), the FFT-based OFDM-OQAM AFB can be

implemented by using S/P conversion (via delay chain and

downsampling by L/2), polyphase filters ܣሺݖଶሻ, permutation

۾గ , FFT, and discarding irrelevant outputs. Its polyphase

structure is given in Fig.5.

L-point

IFFT

A0(z2)

A1(z2)

A2(z2)

AL-1(z2)

↑L/2

↑L/2

↑L/2

↑L/2

Z-1

Z-1

Z-1

+

+

+ x[n]s0,l

s1,l

s2,l

sM-1,l

0

0

2

L-1

Polyphase

filtering

P/S conversion

Pπb

b

b+1

L-1

0

1

b-1

0

1

Figure 4. Polyphase implementation of the OFDM-OQAM SFB

Figure 5. Polyphase implementation of the OFDM-OQAM AFB

Note that the inputs to the SFB (resp. the outputs from the

AFB) are purely real or imaginary, and so, a L/2-point cosine

modulated filter bank and a L/2-point sine modulated filter

bank could be used to replace the IFFT at the SFB (resp. the

FFT at the AFB), as in the critically sampled exponentially

modulated filter bank [8]. As such, the AFB’s complexity

could be reduced almost by half. However, if the system

design strategy is to make it operable using either OFDM or

ݑොሾ݊ሿ ↓2

ݒොሾ݊ሿ ↓2

ݑොሾ݊ሿ ↓2

ݒොሾ݊ሿ ↓2

ݕሾ݊ሿ

̂ݏ,

̂ݏଵ,

̂ݏଷ,

̂ݏଶ,

↓2

↓2

ݑොሾ݊ሿ

ݒොሾ݊ሿ

978-1-4577-1343-9/12/$26.00 ©2013 IEEE

OFDM-OQAM, the IFFT-based SFB and FFT-based AFB

structure should be chosen.

IV. SYMBOL DENSITY, COMPLEXITY AND LATENCY

A. QAM Symbol Density

Define the time and frequency spacings for transmitting one

QAM symbol (equivalently, two PAM symbols) as TQAM and

FQAM, respectively. The bandwidth efficiency [9] in terms of

QAM symbol/sec/Hz, is defined as

ߛ ൌ 1 ൫ ொܶெܨொெ൯⁄ (32)

Denote one symbol duration as ܶ (in seconds). In OFDM,

assuming using CP, ܨொெ ൌ 1/ܶ, and ொܶெ ൌ ܶ ܶ where

ܶ is the CP duration. In OFDM-OQAM, ܨொெ ൌ 1/ܶ, and

ொܶெ ൌ ܶ. In WPM [10], for each sub-stage of the transmitter,

the time resolution is doubled and the frequency resolution is

halved. Therefore the product of these two values remains 1.

The QAM symbol densities of the three FBMC systems are

summarized in Table 1. It is clear that, with CP, OFDM is less

bandwidth efficient than OFDM-OQAM and WPM.

B. Computational Complexity

Based on the FBMCs’ efficient implementations described

in the previous sections, we discuss their computational

complexities in the critically sampled scenario, i.e., ܮ ൌ ܯ .

We evaluate the complexity in terms of the number of real

multiplications (but multiplications with േ1 and േ݆ are not

included since they are flip of sign and/or flip of real and

imaginary parts) per M QAM input symbols.

For OFDM, note that the number of real multiplications of

an ܮ -point FFT/IFFT (via Split Radix FFT [11]) with L

complex inputs is ߤிி் ൌ ܮ logଶ ܮ െ 3ܮ 4 . Therefore, the

total number of real multiplications of OFDM per M QAM

symbols is ߤைிெ ൌ 2ߤிி் ൌ 2ܮ logଶ ܮ െ 6ܮ 8.

For OFDM-OQAM, note that, via Split Radix FFT [11], the

number of real multiplications of an ܮ -point IFFT with L

purely real or imaginary inputs is ߤிி்ோ ൌ ଶ logଶ

ଶ െ 3

ଶ 4.

Therefore, the total number of real multiplications of OFDM-

OQAM per M QAM symbols (equivalently, 2M PAM

symbols) is ߤைிெିைொெ ൌ 2൫ߤிி்ோ 2ܮ൯ 2൫ߤிி்

2ܮ൯ ൌ 3ܮ logଶ ܮ ሺ8ܭ െ 10ሻܮ 24.

According to [5], the total number of real multiplications of

WPM per M QAM symbols is ߤௐெ ൌ 4ሺܮ െ 1ሻܮ , where ܮ

denotes the length of filters ݑሾ݊ሿ and ݒሾ݊ሿ. For example, the

Dbx wavelet is of length 2x, where x is a positive integer.

The complexities in terms of numbers of real

multiplications in OFDM, OFDM-OQAM with typical K

values, and WPM with various filters (Db1 and Db7 [7]) are

shown in Table 2. We see that the computational complexities

of the OFDM-OQAM and WPM could be up to 6 and 7 times

higher than the OFDM, respectively. This more or less reflects

the difference in implementation cost (e.g., gate and memory

counts if implemented in ASIC) although they don’t map to

the cost directly. However, due to the decoder complexity, the

contribution of the MCM processor to the overall receiver

complexity is not as significant. Therefore the increased

complexity of the OFDM-OQAM or WPM processors relative

to the OFDM processor may not be of concern when

considered in the context of the entire baseband processor.

TABLE 1 QAM SYMBOL DENSITY (SYMBOL/SEC/HZ)

OFDM OFDM-OQAM WPM

ܶ/ሺܶ ܶሻ 1 1

TABLE 2 COMPUTATIONAL COMPLEXITY

ܮ ߤைிெ ߤைிெିைொெ (ܮ ൌ ܭܮ 1) ߤௐெ

K = 3 K = 4 K = 5 Db1 Db7

128 1032 4504 5528 6552 1016 7112

512 6152 21016 25112 29208 4088 28616

2048 32776 96280 112664 129048 16376 114632

TABLE 3 OFDM LATENCIES

TCP 0 5.2μs 4.7μs 16.7μs

߬ைிெ 0.0667ms 0.0719ms 0.0714ms 0.0834ms

TABLE 4 OFDM-OQAM LATENCIES

K 3 4 5

߬ைிெିைொெ 0.3000 ms 0.3667 ms 0.4334 ms

TABLE 5 WPM LATENCIES (ASSUMING ܮ ൌ ∞ሻ

Dbx Db1 Db4 Db7

߬ௐெ 0.1333 ms 0.5333 ms 0.9333 ms

C. Latency

The latency discussed in this sub-section is the inherent

latency introduced in FBMC’s structure from the input of the

SFB to the output of the AFB. The latency due to the

arithmetic operations (e.g., multiplication) is ignored since

they depend on hardware or DSP implementation. Let the

sample duration be ௦ܶ ൌ ܶ/ܮ. In OFDM, latency comes from

the P/S and S/P conversion pair and CP (of duration ܶ). The

latency due to an L:1 P/S and 1:L S/P conversion pair is

ܮ ௦ܶ ൌ ܶ. The total latency is ߬ைிெ ൌ ܶ ܶ.

In OFDM-OQAM, the prototype filter support is ൫ܮ െ

1ሻ ௦ܶ ൌ ܭܶ . Latency comes from the OQAM modulation

(which is T/2), P/S and S/P conversion pair, and filtering. The

total latency is ߬ைிெିைொெ ൌ ்ଶ ܶ ܭܶ ൌ ቀܭ

ଷ

ଶቁ ܶ.

In WPM, latency comes from the P/S and S/P conversion

pair and filtering. The latency caused by filtering is ൫ܮ െ

1ሻሺܮ െ 1ሻ ௦ܶ ൌ ൫ܮ െ 1൯ሺܶ െ ௦ܶሻ , then the total latency is

߬ௐெ ൌ ൫ܮ െ 1൯ሺܶ െ ௦ܶሻ ܶ ൌ ܮܶ െ ൫ܮ െ 1൯ ௦ܶ.

Assuming the symbol duration T = 66.7μs, the latencies of

OFDM for three different CP durations used in 3GPP LTE, of

OFDM-OQAM for typical K values, and of WPM for various

filters (Db1, Db4 and Db7 [7]) are shown in Table 3, Table 4

and Table 5, respectively. Note that Table 5 shows the latency

upper bounds by assuming ܮ ൌ ∞. It is clear that the latency

from MCM for OFDM-OQAM and WPM is much higher than

that for OFDM with CP. However, comparing to the latency

requirement in IMT-Advanced (100ms for control plane and

10ms for user plan), such an increase in latency should still be

manageable, especially for OFDM-OQAM.

V. EVALUATION OF TRANSMITTED SIGNAL

Simulations are carried out for a system with 64 subcarriers.

Assuming subcarrier spacing ∆݂ ൌ 15݇ܪݖ or the symbol

duration T = 66.7μs, the total bandwidth of the system is 960

kHz. Let the number of samples per symbol, L, be 128 unless

978-1-4577-1343-9/12/$26.00 ©2013 IEEE

specified. Then, the sample duration is 0.52μs. QPSK symbol

modulation is assumed unless specified. In OFDM, CP is not

used. In OFDM-OQAM, the frequency sampling prototype

filters (with three typical K values) that minimize the total

structure based interference [3] are used. In WPM, two

Daubechies wavelets, Db1 and Db7, are used.

A. PAPR

The PAPR of the lth transmitted symbol is defined as

PAPR ൌ

݉ܽݔሺିଵሻஸஸିଵ|ݔሾ݊ሿ|

ଶ

1

ܮ ∑ |ݔሾ݊ሿ|ଶିଵୀሺିଵሻ

(33)

where ݔሾ݊ሿ is defined in (1). Fig.6 shows the complementary

cumulative distribution function (CCDF) of PAPRs for

different MCM signals when L = 64. The PAPR performance

of OFDM-OQAM does not depend on the K value so that only

the results of K = 3 is shown for simplicity. It is observed that

the PAPR performance depends primarily on the number of

subcarriers and is insensitive to the type of FBMC schemes

considered in this paper.

Figure 6. CCDF of the three FBMC systems.

B. Power Spectral Density (PSD)

Fig.7 shows the PSDs of the three types of FBMC signals.

The OFDM-OQAM has the largest stopband attenuation

because its prototype filter has small sidelobes. In addition, the

stopband attenuation for K = 4 is about 20dB larger than that

for K = 3. The WPM has the worst out-of-band leakage

because its overall synthesis filters have large sidelobes. The

WPM with Db7 has smaller out-of-band leakage than the

WPM with Db1 since the former uses longer filter than that of

latter. Note that in this simulation, the impact from nonlinear

PA was not considered. With nonlinear PA, the out-of-band

emission for all MCM schemes will increase and difference

among them could be reduced. The investigation of the

performance using nonlinear PA will be left as future work.

VI. PERFORMANCE EVALUATION AT RECEIVER

In this section, the simulation parameters are the same as

those in Section V.

A. Bit Error Rate (BER)

Fig.8 shows the BER performance comparison using QPSK

and 16QAM modulation in AWGN channel. The unit of the

abscissa, Es/No, stands for the symbol signal-to-noise ratio.

The three FBMC systems obtain almost the same BER

performances for each modulation scheme and they are

consistent with the theoretical results.

Figure 7. PSDs of OFDM, OFDM-OQAM (K = 3 & 4), and WPM (Db1 &

Db7).

Figure 8. BER performance of OFDM, OFDM-OQAM and WPM.

B. Sensitivity to Timing Offset (TO) and Carrier Frequency

Offset (CFO)

As OFDM and other multicarrier schemes, OFDM-OQAM

is sensitive to TO and CFO. Table 6 shows the real part of the

estimated input symbol for OFDM-OQAM. In Table 6, ݐ is

the TO in seconds, and

߶൫݊, ݂, ሺ݉ െ ݇ሻ൯ ൌ ܲሺ݂ െ ∆݂ሻܲሺെ݂ െ ∆݂ሻ ݁

ଶగ (34)

represents the interference of the signal modulated at the mth

subcarrier to that at the kth subcarrier due to CFO ݂ with

∆݂ ൌ బଶ ሺ݉ െ ݇ሻ

ଵ

ଶ and

ݍሺݔሻ ൌ ܲ ൬݂ െ 12ܮ൰ ܲ ൬െ

1

2ܮ െ ݂൰ ݁

ଶగ௫

(35)

where ܲሺ݂ሻ is the Fourier transform of ሺ݊ሻ. It is shown that

both ICI and ISI are generated when there is TO or CFO.

Since the stopband attenuation is large for OQAM-OFDM, the

TO-generated-ICI only exists between adjacent subcarriers.

This feature can be used in designing TO estimation.

Fig.9 and Fig.10 display the BER performance degradation

of the three FBMC systems due to TO and CFO, respectively.

For OFDM, CP was not included so that all MCM schemes

have the same bandwidth efficiency. Here we assume the

channel is noise free so that the only distortion to the signal is

from the ISI and ICI. For the case with CFO, pilots are

4 5 6 7 8 9 10 11

10-3

10-2

10-1

100

PAPR

reference value (dB)

CC

DF

OFDM

WPM(db1)

OFDM-OQAM(K=3)

WPM(db7)

-1000 -500 0 500 1000

-100

-80

-60

-40

-20

0

20

f(kHz)

PS

D

(dB

)

WPM-Db7

WPM-Db1

OFDM

OFDM-OQAM(K=3)

OFDM-OQAM(K=4)

4 6 8 10 12 14 16 18 20

10-4

10-3

10-2

10-1

100

Es/N0(dB)

BE

R

Theory

OFDM

OFDM-OQAM(K=3)

WPM-Db1

WPM-Db7

Dashed line: 16QAM

Solid line:QPSK

978-1-4577-1343-9/12/$26.00 ©2013 IEEE

inserted every 1ms for the receiver to correct the phase error

caused by the CFO. From Fig.9 and Fig.10, we see that WPM

(Db1) is least sensitive to TO and CFO, compared to others.

Compared to OFDM, OFDM-OQAM is more sensitive to TO

(or CFO) when TO (or CFO) is small but less sensitive to TO

(or CFO) when TO (or CFO) is large. The break point depends

on the constellation size. Besides, in asynchronous uplink or

cognitive radio OFDM-OQAM systems are more robust than

OFDM systems to misalignments among users because of its

sufficient stopband attenuation.

VII. CONCLUSION

In this paper we reviewed three different MCM techniques,

i.e., OFDM, OFDM-OQAM and WPM, and modeled them

under the same FBMC framework. For OFDM-OQAM, we

proposed an efficient implementation of the IFFT-based SFB

and FFT-based AFB by using simple permutations to avoid

complex multipliers. We compared these MCM techniques

using multiple metrics. In general, OFDM-OQAM and WPM

are more bandwidth efficient than OFDM since they don’t

need CP. OFDM-OQAM has much lower out-of-band

emission comparing to OFDM and WPM, which may make it

more suitable to cognitive radio systems. On the other hand,

for OFDM-OQAM the computational complexity is about 6

times greater and the latency is 5 times longer than OFDM,

but still in the manageable range for practical systems. For

WPM, those numbers could be even larger. In terms of PAPR,

the three MCM techniques with their nominal corresponding

parameters have very similar characteristics. Regarding the

timing and frequency offsets, WPM is least sensitive. OFDM-

OQAM is less sensitive to those offsets for large offset values,

but more sensitive for small values. So, for OFDM-OQAM, to

achieve better in-band performance, tighter time and

frequency error control is needed. Timing and frequency error

correction and the investigation into performance with a

nonlinear PA is left as future work.

REFERENCES

[1] P. Siohan, C. Siclet and N. Lacaille, "Analysis and design of

OFDM/OQAM systems based on filterbank theory," Signal Processing,

IEEE Transactions on, vol.50, no.5, pp.1170-1183, May 2002.

[2] A. Viholainen, T. Ihalainen, T. Hidalgo, M. Renfors and M. Bellanger.

“Prototype filter design for filter bank based multicarrier transmission,”

in Proc. of 17th European Signal Processing Conference, Aug. 2009.

[3] A. Viholainen, M. Bellanger and M. Huchard, “Prototype filter and

structure optimization,” Physical Layer for Dynamic Spectrum Access

and Cognitive Radio, Jan. 2009.

[4] B. Farhang-Boroujeny, "Tutorial: Filter Bank Multicarrier for Next

Generation of Communication Systems," 2010 Wireless Symposium and

Summer School at Virgina Tech, June 3, 2010.

[5] A. Jamin and P. Mahonen, “Wavelet packet Modulation for Wireless

Communications,” Wireless Communications & Mobile Computing

Journal, John Wiley and Sons Ltd., vol. 5, no. 2, p. 123–137, Mar. 2005.

[6] M. Gautier, C. Lereau, M. Arndt, and J. Lienard, “PAPR analysis in

wavelet packet modulation,” in Proc. of 3rd International Symposium

on Communications, Control and Signal Processing (ISCCSP), Mar.

2008.

[7] I. Daubechies, Ten Lectures on Wavelets, SIAM Publications, 1992.

[8] A. Viholainen, J. Alhava, and M. Renfors, “Efficient implementation of

complex modulated filter banks using cosine and sine modulated filter

banks,” EURASIP Journal on Advances in Signal Processing, vol. 2006,

Article ID 58564, 10 pages, doi: 10.1155/ASP/2006/58564, 2006.

[9] B. Farhang-Boroujeny and C. H. G. Yuen, “Cosine modulated and offset

QAM filter bank multicarrier techniques: A continuous-time prospect,”

EURASIP Journal on Advances in Signal Processing, vol. 2010, Article

ID 165654, 16 pages, doi: 10.1155/2010/165654, 2010.

[10] M. K. Lakshmanan and H. Nikookar, “A Review of Wavelets for Digital

Wireless Communication,” Wireless Personal Communications: An

International Journal, vol.37 no.3-4, p. 387-420, May 2006.

[11] H. S. Malvar, Signal Processing with Lapped Transforms, Artech House,

Boston, Mass, USA, 1992.

TABLE 6 ESTIMATED DATA AT THE RECEIVER

ݏҧመ,ூ

CFO

: ݂

Hz

ۉ

ۈ

ۈ

ۈ

ۈ

ۇ

ܿݏ ቆߨ ݂ሺ݃ ݈ሻܮ ߨሺ݉ െ ݇ሻ ൬݃ െ ݈

1

2൰ቇ

כ ݏ,ூ ߶൫ሺ݃ െ ݈ሻܮ, ݂, ሺ݉ െ ݇ሻ൯

ܿݏ ൬ߨ ݂ ൬݃ ݈

1

2൰ ܮ ߨሺ݉ െ ݇ሻሺ݃ െ ݈ 1ሻ

ߨ

2൰

כ ݏ,ொ ߶ ቆ൬݃ െ ݈ െ

1

2൰ ܮ, ݂, ሺ݉ െ ݇ሻቇ ی

ۋ

ۋ

ۋ

ۋ

ۊ

∞

ୀି∞

ெିଵ

ୀ

TO:

݊ ൌ

ݐܮ/

ܶ

ۉ

ۈۈ

ۈۈ

ۈ

ۇ

ܿݏ ቆሺ݉ െ ݇ሻ ߨ2 െ

ߨ

ܮ ሺ݉ ݇ሻ݊ ߨሺ݃ െ ݈ሻቇ

כ ݏ,ூ ݍ൫ሺ݃ െ ݈ሻܮ െ ݊൯

ܿݏ ቆ3ሺ݉ െ ݇ሻ ߨ2 െ

ߨ

ܮ ሺ݉ ݇ሻ݊ ߨሺ݃ െ ݈ሻቇ

כ ݏ,ொ ݍ ቆ൬݃ െ ݈ െ

1

2൰ ܮെ݊ቇ ی

ۋۋ

ۋۋ

ۋ

ۊ

∞

ୀି∞

ାଵ

ୀିଵ

Figure 9. BER performance as function of TO.

Figure 10. BER performance as function of CFO.

0 50 100 150 200 250 300

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Frequency Offset(Hz)

BE

R

OFDM-OQAM (K=3)

OFDM

WPM (Db1)

Dashed line: QPSK

Solid line:16QAM

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