Multiband software radio modem using turbo codes and OFDM Walter AKMOUCHE (*) - Didier LE RUYET (**) (*) D´el´egation G´en´erale pour l’Armement - [email protected] (**) Conservatoire National des Arts et M´etiers - [email protected]

Abstract— This article deals with OFDM transmission associated with turbo codes, in order to realize a software radio modem with several waveforms. Except for the frequency transposition, we show that all the functions can be implemented as software. This modem is adapted for HF, VHF and UHF transmission, depending on the chosen waveform. Simulations and tests in real condition achieve a bit error rate of 10−7 for SNR equal to 13 dB for VHF channel and of 10−9 for SNR equal to 13 dB for VHF channel. Index Terms— OFDM, military transmission, turbo-coding, software radio.

I. I NTRODUCTION

Most of the contributions concerning software radio deal with digital-analog conversion, in order to obtain large bandwidth, and then high baudrate. This paper deals with modulation and coding strategy in the case of a military dedicated software modem. Actually, specifications seem to prove that baudrate between 5 and 80 kBit/s are sufficient for most of the necessary applications (mail, data transfer, . . . ). In this paper, we describe a low cost software radio modem for military tactical applications, with minimum hardware and easy changes of configuration. Actually, military applications like mailing or data transfers (like mapping or imaging) use only few kbit/s, with a performing compression algorithm. We have to ensure reliability of the transmission and eventually to prevent interception, deception and jamming. A PC with soundboard and a cheap transmitter-receiver are enough to realize these functions. All the source code has been implemented with classical C++ language. Besides, an all-software architecture implies that the waveform can easily be changed in order to despite any interception program. In the case of civil applications, that means regular and easy update eventually using Internet download. Section 2 explains the problem statement, then section 3 gives the synoptic of the software radio modem and the four different types of waveform. Section 4 is dedicated to the synchronization and reception problems. Section 5 shows the results and the performances of the modem in the case of real tests in VHF and UHF channels. Section 5 gives the conclusion and the perspectives.

II. P ROBLEM STATEMENT

The conception and development of a modem for military application come up against many difficulties and constraints. This modem is specifically dedicated to tactical transmission, with a range between 0.5 and 40 kilometers (0.3 and 25 miles). That means that reliability and security of the communication are important, whereas the baudrate should remain sufficient to allow mail and data applications, which are absolutely necessary nowadays for military operations. Spread spectrum has been studied in that context, for propagation and discretion purpose, but is still not implemented. Besides, we have chosen a specifical strategy to prevent interceptions as far as possible.

III. S YNOPTIC AND DESCRIPTION OF THE TRANSMITTER / RECEIVER .

A. Synoptic and description of the transmitter For data transmission, a packet protocol (like IP) is adapted. The sending file is carved into IP datagrams, then compressed, coded and modulated. The soundboard converts the digital signal to the analog one before sending it on HF, VHF or UHF channels. Source compression is ensured with the Lempel-Ziv algorithm. Two versions of the modem have been developed and evaluated. The first one uses an error correcting code based on the concatenation of the Reed-Solomon RS(255, 223) code and the convolutional code CC(133, 171), with a scrambler assuring the operation s(k) = e(1+[(k−1)mod(7)]2040+(k− 1)divL). The second solution uses a turbo-code with two non recursive systematic (13,15) convolutional codes as constituent codes. The interleaver is a maximum spread interleaver of size 9216 bits. The rate 1/2 is obtained by puncturing the output of the convolutional encoders. Depending on the available bandwidth an orthogonal frequency division multiplex (OFDM) modulation with 128, 256 or 512 subcarriers is then generated. Four types of symbol modulation are possible for the data subcarriers: BPSK, QPSK, QAM-16 or QAM-64 depending on the properties of the channel. The guard time represents 10 or 25 % of the symbol-duration, and completed with a cyclic prefix (CP).

B. Synoptic and description of the receiver The receiver has the inverse functions of the transmitter, associated with synchronization and equalization. C. On the packet protocol For data transmission, a packet protocol is adapted. IPdatagram has a datagram number which gives the order in the file. This number can be used to identify the erroneous datagrams. We consider two protocols. In the first protocol, the receiver makes only one acknowledgement for the global transmission : the incorrect datagrams are listed and the receiver sends back the list of datagrams which should be retransmit. For the next transmission of the uncorrected datagrams, the used waveform is automatically the most robust one, even if that implies a low data rate. The second protocol exploits powerful erasure codes such as digital fountain codes. Using such a code, the transmitter generates encoded packets until he receives an acknowledgment. The receiver generates this acknowledgment after receiving enough packets without error in order to be able to completely decode the stream. This protocol is also particularly interesting in case of a common message to be transmitted to several users. IV. M ODULATION AND TRANSMISSION TECHNIQUES

problems, we use two factors : first, the real and complex parts of modulated symbols are converted using the 2x32-bit of the soundboard, giving a good range. Second, since we are in the case of tactical transmission, low power of emission are sufficient and we accept a power-margin of about 10 dB compared to the maximum power of the emitter (that means emission of 10 W maximum, in our case with an emitter of 100W).

V. T HE WAVEFORMS AND BAUD RATE OF THE TRANSMISSION

A. The four ways of transmission Four ways of transmission are planned, in order to reach the maximum baudrate : •

•

•

A. The choice of the OFDM modulation Many OFDM properties could be very interesting for software radio applications : • •

•

it is known that OFDM pulse shape has a very good resistance to inter-symbol interferences (ISI). OFDM has a very good spectral efficiency since if the size of the modulation alphabet is 2a , the baudrate is equal to N ·a Db = Tpu , in bit/s and the spectral efficiency is equal Np to : η = Db /B = a · (Np +3) , bit/s/Hz , where B is the bandwidth, Np is the number of sub-carriers and Tu the duration of the OFDM-symbol. With its good spectral efficiency, we can obtain a satisfying effective baud rate after adding the guard interval of duration Tg and channel coding. Besides, due to its robustness, no complex filter should be designed and implemented. the implementation of OFDM with Cooley-Tuckey algorithms remains ”easy”. By using 2p subcarriers, we can use FFT algorithms, which are well known, optimized and very performing. It is much more simple to implement than a complex waveform (like Raised cosine filter with low roll-off, for example).

These properties can be exploited for transmitting high rate transmission, even in the case of bad channels. B. How we deal with the classical PAPR statement... Due to its gaussian properties, OFDM leads to power peaks which can imply saturation phenomena. To prevent such

•

for an a priori bad severe channel (some HF channels , corresponding to CCIR4 model for example), the modem uses a robust waveform, with a low bandwidth (3 kHz), low baud rate (only 3 kbit/s, useful). in the case of a quite good channel (in the case of HF-channel 28-29.7 MHz, or corresponding to CCIR 3 model), the waveform remains the same except the fact that BPSK or QPSK are used for data subcarriers. for good channels (In the case of VHF channels or channels corresponding to COST 207 Rural Area for example), symbol modulation is BPSK to QAM-16, with bandwidth varying between 5 and 7 kHz. for a good channel (the ISM channel, 802.16 channel , or channels corresponding to ETSI/BRAND model for example), the modem uses BPSK to QAM-64 modulations for the data subcarriers.

There are three categories of subcarriers. 65 % of the subcarriers are dedicated to information data. 10 % of the subcarriers are frequency-synchronization subcarriers, which contain the information concerning the modulation on the data subcarriers. Finally, last 25 % of subcarriers contain pattern synchronization.

B. Bandwidth and associated baudrate Considering the necessary baud rate (for data and mail applications), four kinds of bandwidths and associated baud rate are implemented. The bandwidths are B = 3 kHz for HFchannels (useful baud rate is about 3 kBit/s), B = 7 kHz for VHF channels (baud rate between 7 and 10 kBit/s), B = 12 kHz for some other VHF channels (baud rate of about 20 kBits/s) and, finally, B = 10 or 20 kHz in the case of UHF channels (which allows about 60 kBit/s useful baud rate). In practice, the timer is cadenced at 1 GHz (frequency of the PC-processor). The main limit is the analog-digital conversion of the soundboard which is performed at 44.100 kHz. Considering the imperfection of the low-pass filter and some error margin, the signal bandwidth should remain less than 20 kHz. However it is satisfying for our applications.

VI. R ECEIVER : SYNCHRONIZATION AND EQUALIZATION Synchronization is a major problem when using OFDM. We assume that the baseband signal OFDM is perturbed by an additive white gaussian noise (AWGN) and with limited time and frequency offset : frequency offset δf0 ≤ 0, 1 × B and time offset δf t0 ≤ 0, 2 × Tu .

A. Equalization Fig. 1.

We implemented the ZF criterion for the per tone equalizer : k.τ H ∗ (k) E(k) = · e2πj· N (1) 2 |H(k)| where H(.) is the impulse response of the channel. Due to the guard time, the equalization function is simple since each sub-channel is flat.

Sample block to estimate the correlation.

The minimization of Λ is independent of the additive or multiplicative constant. After simplifying and according to [2], we have : ·Y ¸ Y Λ(θ, ε) = log p[s(k), s(k + Np )] · p[s(k)] k∈I1

=

log

·Y

k∈I1

1) Synchronization algorithm using a likelihood function: We use the maximum likelihood algorithm proposed in [2]. We T consider a 2 × Np + Ng block of samples where Ng = Tug Np . We generate the sample-vector :

=

log

k6∈I1

p[s(k), s(k + Np )] · p[s(k)] · p[s(k + Np )]

· θ+N g −1 Y k=θ

S

I2

Y

¸ p[s(k)]

k

p[s(k), s(k + Np )] p[s(k)] · p[s(k + Np )]

¸

− → s = [s(1)s(2) . . . s(2Np + Ng )]T

Since k is independent of θ, and assuming the signal is gaussian, equations can be written as :

Moreover, let θ be the value of the sample with frequencyoffset δf0 and ε the sample value of the time offset. Let :

Λ(θ, ε) = |γ(θ)| · cos(2πε + arg(γ(θ)) − ρ · β(θ)) with :

I1 = {θ . . . (θ + Ng − 1)}

k=θ+Ng −1

X

γ(θ) =

and

s(k) · s∗ (k − Np ),

k=θ

I2 = {(θ + Np ) . . . (θ + Np + Ng − 1)} be respectively the vectors of sample indexes contained in the CP and the vector of sample indexes of useful duration. Samples during the useful duration and their copies during the CP are correlated and, then, we can deduce that ∀k ∈ I1 : E{s(k) · s∗ (k + m)} = σs2 + σb2 , for m = 0

1 · 2

k=θ+Ng −1

and ρ=

X

|s(k)|2 + |s(k + Np )|2

k=θ

σs2 SN R = σs2 + σb2 SN R + 1

We can notice that the ML-function depends on the signal-tonoise ratio (SNR). This knowledge is a limit of the algorithm since it means that the channel should be partially estimated.

E{s(k) · s∗ (k + m)} = σs2 · e2πjε ,for m = Np and E{s(k) · s∗ (k + m)} = 0 , otherwise with σs2 is the variance of the useful signal and σb2 the noise variance. For all other values k, there is no correlation, since we assume that the emitted symbols are independent. 2) Maximum likelihood function: We use the log-function of the maximum likelihood function of θ and ε, which is the log-function of the probability density function p(.) of the → sample-vector − s depending on θ and ε :

Λ(θ, ε) = log[p(s|θ, ε)]

β(θ) =

(2)

The maximum value of Λ corresponds to the frequency and time offsets. Considering that θ and ε are independent, the maximization could be carried through two successive operations. max Λ(θ, ε) = max[max Λ(θ, ε)] = max Λ(θ, εb) θ

ε

θ

and εb is the value of ε maximizing the cosine term : 2πε + arg(γ(θ)) = 2nπ where n is an integer. With this method, we ensure good performance and quite high baudrate, whereas the implementation remains complex.

3) Pattern synchronization (pattern inprint): Let us quote the case of 256 subcarriers. Then we use a a specific mapping with 21 QPSK-modulated carriers. There are 3 groups of 7 subcarriers (number 7, 16, 25, 35, 44, 53, 63 - 61, 71, 81, 91, 100, 108, 113 - 185, 195, 202, 211, 219, 226, 230), carrying COSAC sequences, which give also information about the modulation on each subcarrier (sequence 1 means that the modulation is QPSK, and so on). The same method has been implemented in the case of 128 or 512 subcarriers, with different patterns.

VII. R ESULTS AND PERFORMANCES The implementation of the IP-protocol is very interesting for network transmission on the battlefield. During our experiments, there were only two modems and IP was not really useful. But we have implemented and tested IP in the case of our transmission with the selected waveforms. Not only the baudrate is enough to ensure data or mailing applications, but the IP-protocol can be efficiently implemented to guarantee network deployment.

Fig. 3.

Obtained results for UHF channel with modulation OFDM/QPSK.

Fig. 4.

Obtained results for VHF channel with modulation OFDM/QPSK.

HF simulations show good results but authorizations for real tests in HF-channel are still not received [7], [8]. Performances and results are given by figures 2, 3, 4, and 5. The given performances have been measured on real channels (VHF and UHF channels), with distance between emitter and receiver of about 1 mile. Omnidirectional antennas with gain of 8 dBi were used during these experiments. Performances are always good and sufficient for data transmitting or mail applications. By comparing figures 4 and 5, we can see that turbo codes achieve a gain of about 3 dB, compared to the RS+CC concatenated scheme. The results are the same for UHF channel. Optimization of the transmission scheme and code could probably lead to better results.

Fig. 2.

Obtained results for UHF channel with modulation OFDM/QAM.

Fig. 5. Obtained results for VHF channel with modulation OFDM/QPSK and TurboCoding.

VIII. C ONCLUSION AND PROSPECT Since the modem is a software radio modem, it is easy to modify the source code (in order to change the channel coding, the modulation,...), to add other functions (like spread spectrum or ciphering for example), etc. Obtained performances (between 3 and 80 kBits/s) and results (BER) are satisfying and then allow data transmission and mailing for military applications in HF, VHF or UHF channels. Some prospects could be foreseen. Compiled ciphering module could be inserted, only by respecting the implementation constraints (input/output variables). Moreover, spread spectrum implementation is in progress since it seems us to be the priority, in order to ensure propagation capability and protection of transmission. But, this prototype could give nowadays demonstration of software radio applications and lead to the necessary modifications, since it remains quite easy to change the source code.

R EFERENCES [1] J.G. Proakis, “Digital Communication.” Mac Graw-Hill. [2] J.-J. Van de Beek, M. Sandell, P. O. B¨orjesson “ML estimation of timing and frequency offset in multicarrier systems.” Lulea university report, April 1996. [3] W. Akmouche, “D´etection et caract´erisation des modulations OFDM.” th`ese de doctorat de l’Universit´e de Bretagne Occidentale, oct. 2000. [4] S.B. Weinstein, P.M. Ebert “Data transmission by frequency-division multiplexing using the Discrete Fourier Transform”, IEEE Trans. Comm. Techn., Vol. COM-19, Oct. 1971, pp. 628-634 [5] B. Hirosaki “An orthogonally multiplexed QAM system using the discrete Fourier transform”, IEEE Trans. on Comm., Vol. COM-29, July 1981, pp. 982-989 [6] J.G. Proakis, M. Salehi “Communication System Engineering”, 2nd Edition, Prentice Hall Inc. [7] UIT/CCIR (C OMIT E´ C ONSULTATIF I NTERNATIONAL DES R ADIOCOMMUNICATIONS ) “Recommandations and rapports du CIR. Simulateurs de voies ionosph`eriques sur ondes d´ecam´etriques”, Rapport 549-2, 1986 [8] UIT/CCIR (C OMIT E´ C ONSULTATIF I NTERNATIONAL DES R ADIOCOMMUNICATIONS ) “Recommandations and rapports du CIR. Utilisation de simulateurs de voie ionosph`erique en ondes d´ecam´etriques”, Rapport 520-1, 1986 [9] COST 207 - O FFICIAL P UBLICATIONS OF THE E UROPEAN C OMMUNITIES “Digital Land Mobile Radio Communications”, final report 1989