An Implementation of CPFSK-OFDM Systemsby using Software Defined Radio

Kazuyuki Morioka∗†, Naoki Kanada∗, Shunichi Futatsumori∗,Akiko Kohmura∗, Naruto Yonemoto∗ Yasuto Sumiya∗ and David Asano†

∗Electronic Navigation Research Institute 7-42-23, Jindaiji-higashi, Chofu, Tokyo, 182-0012, Japan.Email: {morioka, kanada, futatsumori, kohmura, yonemoto, sumiya}@enri.go.jp

†Shinshu University, 4-17-1, Wakasato, Nagano, 380-8553, Japan.Email: {s09t255,david}@shinshu-u.ac.jp

Abstract—In this paper, CPFSK-OFDM systems which useCPFSK (Continuous Phase Frequency Shift Keying) as the firstmodulation scheme of OFDM (Orthogonal Frequency DivisionMultiplexing) are considered. We implemented CPFSK-OFDMsystems by using software defined radio and evaluated them inan AWGN (Additive White Gaussian Noise) channel. We foundthat the performance is better when the modulation index ofCPFSK is 0.75. In the future, we will evaluate our system in afading environment.

I. Introduction

In Orthogonal Frequency Division Multiplexing (OFDM),a high-rate data stream is split into a number of lower ratestreams which are simultaneously transmitted on a number oforthogonal subcarriers. As the symbol duration is increased forlower rate parallel streams, the relative amount of dispersion intime caused by multipath delay spread decreases. Therefore,OFDM is a widely used modulation scheme for broadbandmobile wireless communication systems. In commonly usedOFDM systems, each subcarrier is modulated by using PhaseShift Keying (PSK) or Quadrature Amplitude Modulation(QAM).

On the other hand, Continuous Phase Modulation (CPM)has an attractive property of fast decaying side-lobes due toits continuous phase transitions [1][2]. When CPM is usedas the first modulation scheme of OFDM, this property canmitigate the effects of phase noise and carrier frequencyoffset (CFO), and thus reduces the Inter-Carrier Interference(ICI). Also, CPM can be interpreted as a coded modulationscheme due to its restricted phase transitions. Therefore, thebit error rate can be improved by using multi-symbol detectionand error correction. As CPM has such desirable properties,a combination of OFDM and CPM has been studied in[3][4][5][6][7][8][9][10][11][12][13][14].

OFDM systems combined with CPM can be divided intotwo types. One is that OFDM modulated signals are inputinto a CPM modulator to generate constant envelope signals[3][4][5]. In this paper, we call this type of system an OFDM-CPM system because the CPM modulator is cascaded after theOFDM modulator. The Peak to Average Power Ratio (PAPR)of this system becomes 0dB while the bit error rate becomesworse due to the loss of orthogonality of the subcarriers.

The other type of system is where CPM is usedas the first modulation scheme of an OFDM system

[6][7][8][9][10][11][12][13][14]. The OFDM modulator is cas-caded after the CPM mapper, so we call this type of systema CPM-OFDM system in this paper. As mentioned above,this type of system can mitigate the effects of CFO and ICIresulting in better bit error properties while the PAPR remainsas high as conventional OFDM systems.

In this paper, we focus on the latter type of CPM-OFDMsystem, especially CPFSK-OFDM systems which are a specialtype of CPM. Originally, CPM-OFDM systems were proposedby Tasadduq and Rao[6] then Yang, et.al [10] and Weng,et.al[11] extended them. Also, some experimental results ofCPM-OFDM systems in the area of optical communicationswere reported recently [15][16][17][18][19].

This paper is organized as follows. In section 2, we definethe model of CPM-OFDM systems that we use. We describeour prototype CPFSK-OFDM system in section 3 and showsome results in section 4. Finally, we conclude this paper insection 5.

II. SystemModel

A system model of CPM-OFDM can be described asfollows [6]. At first, the first modulation signals of subcarriern becomes

Xn(t) = e jΦn(t,a). (1)

Here, the phase Φn(t, a) can be divided into three parts asfollows [20],

Φn(t, a) = θn(t, an,k) + θn,k + ϕ0. (2)

θn(t, an,k) is the instantaneous phase which is determined bythe latest L symbols and described as

θn(t, an,k) = 2πhk∑

i=k−L+1

an,iq(t − iTs). (3)

Also, θn,k is the cumulate phase which is cumulated until the(k − L)-th symbol and described as

θn,k = [hπk−L∑

i=−∞an,i] (mod 2π), (4)

The last part ϕ0 is the initial phase of CPM.

978-1-4799-4609-9 / $31.00 ©2014 IEEE

Fig. 1. Structure of CPM-OFDM transmitter.

Also, q(t) in equation (3) is the continuous phase functiondefined as

q(t) =∫ t

−∞g(τ)dτ. (5)

Here, an,i ∈ (−1,+1) is the i-th transmitted symbol of the n-thsubcarrier. Moreover, h is the modulation index of CPM andL is the memory length, which means that the instantaneousphase is dependent on the past L-th symbols [20].

If g(t) is the rectangular pulse as described bellow andL = 1, the signals are called Continuous Phase FrequencyShift Keying (CPFSK) [20].

g(t) ={ 1

2LTs, 0 ≤ t ≤ LTs

0, otherwise(6)

Especially, CPFSK signals becomes Minimum Shift Keying(MSK) when h = 0.5 [20].

Finally, CPM-OFDM signals S (t) are obtained by perform-ing an IFFT on the CPM signals Xn(t) as follows.

S (t) =N−1∑n=0

Xn(t) × e j 2πntNTs , 0 ≤ t ≤ T. (7)

Here, T = NTs, N is the number of subcarriers and Ts isthe OFDM symbol interval. Fig. 1 shows the structure of theCPM-OFDM transmitter.

III. Evaluation System

We focus on CPFSK which is a special type of CPMin this paper. Here, we describe our evaluation system forCPFSK-OFDM. CPM is a general term for continuous phasemodulation and it includes CPFSK, MSK, GMK and so onaccording to the CPM parameters such as modulation index,pulse wave form and pulse duration time. As it is requiredto vary these parameters flexibly in order to evaluate CPMsystems, we use software defined radio to evaluate our system.

Fig.2 shows our evaluation system for CPFSK-OFDM.As shown in the figure, we insert a variable attenuator tochange the signal strength. Also, splitted signals go into aspectrum analyzer to measure the spectra of the signals. The

Fig. 2. Evaluation system of CPM-OFDM.

Fig. 3. System block diagram of our evaluation system.

0.0001

0.001

0.01

0.1

1

1 2 3 4 5 6 7 8

Sym

bol E

rror

Rat

e

Received SNR (dB)

CPFSK, h=0.5CPFSK, h=0.625CPFSK, h=0.75

Fig. 4. SER of CPFSK-OFDM systems in an AWGN Channel.

constellation of the CPM signal is shown in the figure. Aswe used software defined radio, the development cost of ourevaluation system is very low.

We used Ettus Research, USRP N210 as the front endof the software defined radio. Fig.3 shows a block diagramof USRP 210. A 100MSPS AD converter and 400MSPS DAconverter are built into the USRP. Also, a daughter board witha frequency range of 4.9GHz to 5.9GHz is used. The personalcomputer for signal processing and the USRP are connectedby a gigabit ethernet and baseband signals go through them.All of the OFDM signal processing is done on the personalcomputer. We used National Instruments, LabVIEW as ourprogramming language.

IV. Performance Evaluation in AWGN Channel

In this section, the evaluation results for CPFSK-OFDMsystems in an AWGN channel are shown. We added AWGNat the receiver digitally for simple evaluation. The centerfrequency is 5.1GHz and the number of subcarriers is 128.Fig.4 shows the results of our experiment. The horizontalaxis is the SNR (Signal to Noise Ratio) measured at thereceiver and the vertical axis is the SER (Symbol Error Rate).The modulation indexes we used are h = 0.50.625, 0.75 andshown in Fig.4. We found that the performance is better whenh = 0.75 for CPFSK-OFDM systems.

V. Conclusions

In this paper, CPFSK-OFDM systems which use CPFSKas the first modulation scheme of OFDM were considered.We implemented a CPFSK-OFDM system prototype by usingsoftware defined radio and evaluated it. We measured theperformance of the prototype CPFSK-OFDM system in anAWGN channel. The results show that a modulation indexof 0.75 is better for CPFSK-OFDM systems. In the future, wewill evaluate our system in a fading environment.

Acknowledgment

Part of this work was supported by JSPS KAKENHI GrantNumber 25889076.

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