1. Introduction. 2. OFDM Primer

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1 A Novel Frequency Domain Reciprocal Modulation Technique to Mitigate Multipath Effect for HF Channel *Kumaresh K, *Sree Divya S.P & **T. R Rammohan Central Research Laboratory Bharat Electronics Limited Bangalore *Member Research Staff **Senior Member Research Staff {, divya, trrmohan}@crlbel.ernet.in, 1_umar@yahoo.com Abstract Frequency domain reciprocal modulation (FDRM) is a new digital transmission technique that offers an advantage in High frequency (HF) radio channel afflicted with dynamic multipath. Adaptive equalizers allow high-speed bandwidth efficient communications through the channel with multipath. However, when the multipath is dynamic, bandwidth-efficient digital transmission is very difficult because the adaptive equalizers frequently cannot adapt fast enough. The proposed new modulation technique employs two blocs of correlated data to cancel the effects of all linear distortion. Cancellation of all linear distortion is an intrinsic property of this modulation technique. Additionally FDRM is useful for transmission of bursty data pacet because demodulation is simplified by using two blocs of data. This technology is similar to OFDM, but has the ability to tolerate much faster changes in the multipath distortion. The performances of proposed modulation technique is studied through simulations, and compare the performance with OFDM is described in this literature. 1. Introduction High frequency (HF) data communication lins remain relevant even in today s satellite era because they offer beyond line-of-sight, indeed, potentially worldwide coverage, without using third-party equipment s and with running cost relatively cheaper than the counter part. The disadvantage is that HF is a difficult medium to use, with significant channel distortion and bacground noise at any given frequency. This has severely limited the maximum data rate on HF data modems to usually less than 4800 bitsper-second (bps) in the standard 3 Hz voice band channel allocation. Multicarrier modulation techniques are recognized as efficient method to transmit data over spectrally shaped noisy channels. These techniques have become increasingly number of transmission environments because of their superior performance. The significance of the multicarrier modulation technique can be easily noticed from the fact that it was considered (and mainly adopted) for realization of many high speed communication systems, including both wireless and wired communication systems. It was successfully implemented in number of products (e.g., voice-band and cellular modem) and selected for several standards Asymmetric digital subscriber line ADSL, digital audio broadcasting (DAB), digital terrestrial television broadcasting, MIL-STD etc. The ey idea behind all multicarrier modulation techniques is the partitioning of a transmission channel into a set of orthogonal sub-channel, each with approximately flat transfer function and additive white Gaussian noise (AWGN). The data is transmitted in parallel on all subchannel, each of which of completely independent. One of ey challenge factor, which degrade the performance of high-speed digital signal, is linear distortion such as echoes or multipath. If the echo is mild, it will increase the bit error rate (BER) in the presence of random noise. If the echo is severe, the error rate may be so high that the data is useless even with no random noise added to the transmission. There are number of methods of eliminating or reducing the effects of the linear distortions. One method is the use of an adaptive equalizer, while another is the use of a transmission system that is naturally tolerant to linear distortion, Such as code division multiple access (CDMA) or frequency shift eying (FSK). This paper is organized as follows. Section 2 describes the OFDM Primer. Section 3 the proposed modulation techniques are described, and their performance are analysed. Section 4 describes advantage, application and conclusion. 2. OFDM Primer The OFDM signal is generated at baseband by taing the inverse fast fourier transform (IFFT) of quadrature amplitude modulated (QAM) or phase-shift eyed (PSK) subsysmbols c = a + jb (fig.1). In the figure, the bloc P/S represents a parallel-to-serial converter. The transmitted data bloc is made up of many harmonic carriers (HCs) at different frequencies that can be accurately distinguished from each other at the receiver site because the HCs are orthogonal to each other. An OFDM symbol has a useful period T and preceding each symbol is a cyclic

2 prefix of length T g, which is longer than the channel impulse response so that there will be no intersymbol interference (ISI) [4]. The frequencies of the complex exponentials are f = / T, and the useful part for 2N+1 subcarriers is given by u ( t) c exp( j2π f t),0 t T. (1) = N = N The baseband signal is quadrature modulated, up-converted to the radio frequency (RF) and transmitted through the channel. At the receiver (fig 2) the signal is down converted to an intermediate frequency (IF), and quadrature demodulated. The bloc S/P represents a serial-to parallel converter. A carrier frequency offset of f causes a phase rotation of 2 πt f. If uncorrected this causes both a rotation of the constellation and a spread if the constellation points similar to additive white Gaussian noise (AWGN). A symboltiming error will have little effect as long as all the samples taen are within the length of the cyclically extended OFDM symbol. 3. Proposed Modulation Technique The proposed FDRM modulation is based on two consecutive blocs of data that contain the same information but use different encoding. The first is similar to normal (N) OFDM with the restriction that low-valued magnitudes are not used for HCs. The second bloc is a reciprocal (R) in the frequency domain to the first bloc. A reciprocal bloc is formed by a complex division of the magnitude and phase of each HC in a normal OFDM bloc into 1.0 at an angle of 0 degrees. The computed reciprocal coefficients are used for the corresponding same frequency HCs in the reciprocal bloc. The two blocs are sent out in adjacent time slots so that approximately the same echo is applied to both blocs. At the receiver site each HC from a reciprocal bloc is divided into the corresponding HC in the normal bloc, and a square root is performed on the quotient. This process yields the transmitted data without linear distortion, as will be explained. Thus, echo cancellation is an inherent property of FDRM. Mathematical description Assume a transmitted signal bloc is U(f) in the frequency domain and a channel s frequency response in H(f). The transmitted signal bloc may be burst of OFDM modulation, which is comprised of multiple harmonically related carriers. The normal received signal is X ( f ) = (2) If a reciprocal signal bloc is 1 R ( f ) = (3) and sent through the same channel the received reciprocal signal will be Y ( f ) = R( f ) = (4) The estimated transmitted signal at the received is X ( f ) = = = Y ( f ) (5) Liewise, the estimated channel frequency response is = X ( f ) Y ( f ) = Note that to avoid a division by zero problem, it is necessary that the coefficients in the normal bloc not have zero or near zero magnitudes. If a signal such as a burst transmission of conventional 16 QAM were examined in the frequency domain, some of the coefficients would liely have very low valued magnitudes. Thus some of its reciprocal coefficients would be huge, maing an impractical signal for transmitting over physical channels. OFDM has the property of controlled magnitudes in the frequency domain. Square Root at Transmitter FDRM Another way to use FDRM is to perform the square root function at the transmitter prior transmission. Therefore the estimated transmitted signal at the receiver is = 1 Performance Analysis 2 2 (6) (7) To illustrate the performance of the proposed method, we have performed simulation for an OFDM/FDRM system with N=1024 sub carrier & QPSK symbol. In changing echo environment To enforce the condition that approximately the same echo be applied to both blocs, the bloc length may need to be reduced if the antenna s travel velocity is high. If a wide bandwidth channel is available, the bloc time can be shortened. In practice this typically not a problem.

3 For the channel with rapid flat fading, FDRM wors very well because fade affects both the normal and reciprocal blocs. Hence the affect of fade is cancelled automatically. Thus an automatic gain control circuit does not need a fast response or an accurately set level. In Deep fades The HCs that are unfortunate enough to be located in the portion of the spectrum that is deeply faded will be hopelessly contaminated by any noise in the channel, and must be discarded. In this case, the use of well-nown forward error correction techniques will allow the transmitted data to be received without error. Performance Near Threshold One might thin that sending the same signal twice in a different form would reduce the channel capacity by onehalf. However the information in both bloc of data is same wand when the two blocs are processed together the signals add in a voltage basis while the noise contaminating each bloc of data is uncorrelated and adds on a power basis. Thus the signal to noise ratio of the processed signal should be 3dB better that either the signals in the N bloc or R bloc ( refer figure 4-6). The estimated received processed signal in the presence of noise is: = + Nn ( f ) + Nd ( f ) Where N n is the random noise disturbing the first bloc and N d is the uncorrelated random noise disturbing the second bloc. Near threshold one might expect that the performance of FDRM may be poor because the N d term could cancel the signal from the second reciprocal bloc. Simulation shows that the division by almost zero problem at low carrier to noise ratios is not a severe problem. (8) Figure 4 6, the result of SER versus E b /N 0 for AWGN, Rayleigh channel with Doppler frequency of 25Hz and 100Hz. 4. Advantage and Conclusion There are a number of advantage associated with the demodulation of FDRM that of OFDM. 1. Equalization is automatic 2. Phase Locing is not required. A simpler angular estimator is sufficient to correct the frequency error. 3. No accurate automatic gain control (AGC) is required. 4. FDRM wors well in environment with fast fades. Conclusion FDRM has immunity to dynamic multipath. It is well suited to HF channel condition. It find application to wireless internet traffic, mobile data communications, wireless video and audio entertainment, microwave and home networs using AC power lines and home phone lines at frequencies above audio. References [1] John A.C. Bingham, Multicarrier Modulation for Data Transmission: An Idea Whose Time Has Come, IEEE Comm. Magazine Pg May [2] Y. Wu, et.al., COFDM: An Overview, IEEE Trans. on Broadcasting, Vol. 41 No. 1 Pg. 1-8, March [3] Thomas H. Williams, A Digital Transmission System with Very High Immunity to Dynamic Multipath, IEEE transactions on Broadcasting, March 1999, Vol 45, No.1. [4] B.Le Floch, R. Halbert-Lassalle, and D. Castelain, Digital Sound Broadcasting to Mobile Receivers, IEEE Trans. Consumer Electron., Vol. 35 pp Aug Figure 3 is a set of three simulated constellation plots of a single harmonic carrier. These plots compare FDRM, normal OFDM and square root at the transmitter FDRM. Single HCs with the magnitude of 1.0 at 45 0 at the transmitter are contaminated with equal levels (-20 db) of randomly distributed noise. Note that FDRM has a tighter constellation than conventional OFDM. Square root at the transmitter (SR_FDRM) suffers a noise performance penalty relative to both OFDM and FDRM since the noise is not reduced by performing the square-root operation at the receive site.

4 Figure. 1. Bloc diagram of OFDM transmitter. Figure. 2. Bloc diagram of OFDM receiver. Figure 3 Comparative SER Vs Carrier to Noise

5 Figure 4 SER Vs Carrier to Noise for AWGN Figure 5 SER Vs Carrier to Noise for Rayleigh F d =25Hz Figure 6 SER Vs Carrier to Noise for Rayleigh F d =100Hz