PERFORMANCE COMPARISON OF SPREAD. Gunnar Andersson. Radio Communication Systems Lab., Royal Inst. of Technology

Transcription

1 PERFORMANCE COMPARISON OF SPREAD SPECTRUM METHODS IN AN HF INTERFERENCE ENVIRONMENT Gunnar Andersson Radio Communication Systems Lab., Royal Inst. of Technology c/o FOA, P. O. Box 65, S-58 Linkoping, Sweden ABSTRACT Since the interfering signals from other users of the spectrum is a main problem in HF communication, it is necessary to consider them when evaluating HF radio systems. Based on the Laycock-Gott congestion model, a statistical HF interference model is derived and briey compared to real measurements. The two basic methods to apply spread-spectrum modulation in radio communication are frequency-hopping (FH) and direct-sequence (DS) modulation. In this work we compare these two methods, with respect to the uncoded bit error probability, on an interference-limited HF channel. The results show that the FH system performs better than the DS system on this channel. The FH system is inherently well suited for the HF environment with predominantly narrowband interferers. The interference rejection capabilities of the DS system are not sucient to handle the high dynamic range of the interfering power. Additional narrowband rejection capabilities would be required to create useful DS systems. INTRODUCTION In the area of military radio communication, it has during the past decade been an increasing interest in using spread-spectrum (SS) techniques in the HF spectrum, mainly due to the inherent jamming protection and the stealth properties connected with SS technology. Additionally, SS modulation enhances the transmission reliability on frequency-selective channels, such as the HF channel. SS radio systems are traditionally divided into frequency-hopping (FH) and direct-sequence (DS) systems []. When evaluating SS systems on the HF channel, it is essential to consider the severe interference in the HF band. Actually, for an HF radio system, the performance is in most situations limited by the narrowband strong interfering signals, created by other This work has been supported by the National Defence Research Establishment (FOA) and the National Defence Materiel Administration (FMV) in Sweden.

2 users of the HF spectrum. Therefore, we need a statistical model of the HF interference. In 982 a long-term measurement program of the HF interfering signals began in England [2], and is still running. Similar measurements have also been carried out in Sweden [3]. Results from these measurements have been generalised to a congestion model, the Laycock-Gott model [4]. The aim of this paper is to describe a statistical HF interference model, based on the Laycock-Gott congestion model, and apply it to the calculations of the bit error probabilities of an FH and a DS spread-spectrum radio system. 2 INTERFERENCE STATISTICS The measurements cited above, are performed by measuring the received average interfering power over khz bandwidth and second, and comparing it with a threshold. By stepping the communication receiver in frequency with khz increment for every second, data over the whole HF spectrum is collected. A specic khz channel is declared occupied, at a particular threshold level, if the average received interfering power in the one second observation period exceeds the threshold. The congestion Q of a specic frequency band is then dened as the probability that a khz channel is occupied, and it is estimated as the fraction of occupied channels for the specic frequency band and chosen threshold. On the basis of extensive numerical analysis of the collected data, Laycock, Gott et al. have proposed a model for the spectral occupancy in the HF spectrum [4]. The model tries to predict the congestion Q k for the kth ITU band (according to the enumeration in [4]), for the particular receiving frequency, threshold and other parameters. The general model is according to Q k = + exp f?y k g ; where y k = X i Z i X i ; () and Z i are coecients to be tted to the measured data and X i are functions of the chosen parameters. The transformation of y k into Q k is called the logit transformation. In the original Laycock-Gott model, the expression for y k is a function of the centre frequency f k of the actual ITU band, the sunspot number R and the threshold x in dbm. These parameters and a number of coecients that have been tted to the measured data are combined to yield y k = A k + Bx + R(C 0 + C f k + C 2 f 2 k ) : (2) The coecients A k are characterised by 95 dierent values, one for each ITU band and they basically represent the median congestion in the kth band. For instance, the broadcast bands, which generally are quite congested, have shown to have relatively large values of A k. The coecients B, C 0, C and C 2 do not depend on the actual ITU band, and are thus valid for the whole HF spectrum. Now we dene a stochastic variable I k to be the average received power in dbm, over khz in the kth ITU user band. The Laycock-Gott model yields Q k = Pr [I k > x] = + exp f?y k g = + exp f? k? Bxg ; (3) 2

3 pdf of Ik x (dbm) Figure : The probability density function of Ik with B =?0:0 and k =?2. where we have set k = A k + R(C 0 + C f k + C 2 f 2 k ) : (4) Thus, k is compounded of all parameters, except the threshold x, in the input function (2). We can now deduce the probability distribution function of the stochastic variable I k as F Ik (x) = Pr [I k x] =? Pr [I k > x] =? Q k = + exp f k + Bxg : (5) Dierentiating (5) with respect to x yields the probability density function (pdf) of I k, f Ik (x) = df I k (x) dx =?B exp f k + Bxg ( + exp f k + Bxg) 2 : (6) In gure, a plot of f Ik (x) with typical values of k and B is presented. As we can see, the pdf of I k is very wide. For large interference levels x, one can deduce from (5) that there is a linear dependence between the received interference power (in dbm) and the logarithm of Pr[I k > x]. This is in accordance with another HF interference model by Perry and Rifkin [5]. Furthermore, one can easily show that f Ik (x) is symmetric around x =? k =B, which hence is the expected value of I k. The value of B decides the spread of I k, i.e., roughly the variance of I k. A lower value of B (B is negative) gives a narrower probability density function of I k. According to the measurements mentioned above, B is about?0:0 for the whole HF spectrum. Given B, the value of k determines the average of I k. Typical values of k are between?6 and?9, depending on the actual band k and the parameters included in k. In the example of f Ik (x) in gure, k is set to?2. To make the congestion model more accurate, Gott et al. have during the past few years expanded the input function (2) of the logit transformation with more parameters [6], [7]. Basically, they have added some dependence of the week and the location of the congestion measurement to the original expression. However, since the logit 3

4 transformation () and the dependence of the threshold x (i.e., the value of B) have not been changed, this does not aect the shape of f Ik (x) in gure. It only inuences the factor k and hence the expected value of the interference power I k, which we will use as a parameter in the forthcoming calculations. Therefore, the fact that we used the original parameter function (2), and not the rened models, when deriving f Ik (x), is of no importance. Let us denote the stochastic process, modelling the interference over an arbitrary khz HF frequency gap, as I(t). Thus, we now have a model for the time-averaged power of I(t). However, to compute the performance of the radio systems, the amplitude and phase distributions of I(t) must also be known. Assuming that the interference is created of a number of sources, each with perhaps a number of paths of propagation, a reasonable approach is to approximate the interference process I(t) by a Gaussian random process. When receiving radio signals, there is always a noise oor, which stems from the background noise, such as the atmospheric and the thermal noise, that we can not exclude in the receiver. In the forthcoming calculations, we will assume that the HF channel is interference-limited and hence neglect the impact of the noise oor. But now, when we will show the similarities between the measured power levels and the HF interference model, we will include the noise oor in the statistical description of the received power. Firstly, we let P k denote the total received time-averaged power (in dbm) over the khz channel in the kth ITU band, and we let N be the constant noise power (also in dbm) received in every khz channel, i.e., the noise oor. Furthermore, if we let P 0 k, N 0 and I 0 k be the same as P k, N and I k but in linear measures (mwatt), we have that P 0 k = I 0 k + N 0 () P k = 0 logfi 0 k + N 0 g : (7) We can now derive the probability distribution function of the total received average power P k, F Pk (x) = Pr [P k x] = Pr [0 logfi 0 k + N 0 g x] = Pr [I 0 k + N 0 0 x=0 ] = = Pr [I 0 k 0x=0? 0 N=0 ] = Pr [I k 0 logf0 x=0? 0 N=0 g] = = F Ik (0 logf0 x=0? 0 N=0 g); for x > N ; (8) where F Ik (x) is given in (5). For x N, the probability distribution function F Pk (x) is nought, since the total received power cannot be lower than the noise oor N. One can notice that if we let N!?, F Pk (x) converges to F Ik (x), as it should do. In gure 2, we have carried out two comparisons between the modelled probability distribution function F Pk (x) from (8) (dashed lines) and a measured realization of F Pk (x) (solid lines), for two dierent parts of the HF spectrum. The measurements are performed outside of Linkoping in June 994 with a measurement system that is very similar to the one used by Gott et al. The two left curves are for ITU bands 28 and 29 (7 300 { 8 95 khz), which are intended for xed and mobile HF services. It is obvious that the noise oor of the measurements is about?27 dbm, which hence is used as the value of N when plotting the modelled F Pk (x). Evaluating (4) with the values of A k, C 0, C and C 2 according to [7], we nd that k =?2, which is used in the plot of the modelled F Pk (x) for band 28 and 29. 4

5 Band 28 and F(x) Band x (dbm) Figure 2: Two comparisons of the modelled and measured probability distribution functions of the total received power Pk over khz. The modelled FP k (x) is plotted with the dashed line and the measured FP k (x) is plotted with the solid line for both cases. Additionally, the two right curves in gure 2 are for the ITU band 42 ( 650 { khz), which is a broadcast band that is used by many powerful transmitters. Therefore, F Pk (x) is fairly \at" and nearly all measured values of P k are much larger than the noise oor. The value of k is for this case equal to?9:4, again evaluated from (4) with the coecients according to [7]. We can also notice that the receiver clips at approximately?67 dbm. Comparing the measurements with the modelled curves, we see that F Pk (x) in (8) seems to model the probability distribution function of the total received power over khz quite well. Naturally, there are also measurements that do not coincide this well with the model, but on the average, the model works properly. 3 PERFORMANCE COMPARISON In this section we compare the performance of a direct-sequence and a frequencyhopping system, with respect to the uncoded bit error probability (BEP). The channel is disturbed by HF interfering signals, modelled as described above. Since, we believe that the channel is interference-limited, we will neglect the impact of the noise oor. 3. THE DS SYSTEM In a traditional DS system employing binary phase shift keyed (BPSK) modulation [], the modulated signal is spread over the frequency band by multiplying it with a spreading function c(t). The function c(t) is composed of a pseudo-noise (PN) sequence fc n g 5

6 of binary numbers and a pulse function p() c(t) = X n c n p(t? nt c ) ; (9) where p(t) is assumed to be one in the interval [0; T c ] and zero otherwise. At the receiving side the PN sequence is known, so that the received signal r(t) can be despread by multiplying it with the same direct-sequence signal c(t). For a DS/BPSK system with data symbols d i =, the received signal for the ith data bit can be written as s 2Eb r i (t) = c(t) cos(2f c t + d i 2 ) + n I(t) ; (0) T b where E b is the received signal energy per bit duration T b, f c is the carrier frequency and n I (t) is the received interference. The chip rate of c(t) is L times greater than the data rate R b, i.e., L = T b =T c. Hence, the ratio L basically gives the processing gain (PG) of the DS system. In the calculations below, R b is equal to 500 bit/s and L is set to 00 or 000, giving a spread-spectrum bandwidth W ss of approximately 00 or 000 khz, respectively. The performance of the DS system depends on the total wideband received interference power, since the DS signal has a momentary bandwidth of the whole W ss. Therefore, we dene a stochastic variable k, which represents the wideband signal to interference ratio (SIR) over the W ss in the kth ITU band as, k = S? I k;tot. S is the received signal power, which here is assumed to be constant, and I k;tot is the total interference power received over W ss in the kth ITU band, and as S, measured in dbm. To get I k;tot, we have to add the linear powers of the L narrowband Gaussian interfering processes present in W ss (I (j) (t); j = [; : : : ; L]), where each of the L power levels are distributed according to f Ik (x) in (6). If L is large enough (in the order of 00), the central limit theorem will allow us to approximate that the error term caused by the received interfering signal n I (t), will be Gaussian distributed after de-spreading and demodulation []. Then, given a wideband SIR k, the probability of error P e, for a received data bit is p P e ( k ) = Q 2L 0 k=0 ; () where Z x Q(x) = p e?y2 =2 dy : (2) 2 To obtain the total bit error probability of the system, we take the average of P e with respect to k, BEP = Z? E[P e ( k ) j k = x] f k (x) dx = Z? Q p 2L 0 x=0 fk (x) dx : (3) An explicit expression of the pdf f k (x) has not been able to obtain. Therefore, simulation studies have given the results shown in gure 3. The solid and dash-dotted curves show the bit error probabilities for the cases of L equal to 00 and 000, respectively. To be comparable with the FH system, the expected value of SIR on the x-axis, refers to the narrowband SIR over khz (i.e., E[SIR] = E[S? I k ]), and not to the wideband signal to interference ratio k. 6

7 0 0 L=000 0 BEP L= L=00, int. rej E [SIR], (db) Figure 3: The BEP curves for the DS system with L = 00 (solid line) and L = 000 (dashdotted line). signals are totally rejected. The dashed line gives the BEP for L = 00 when the three strongest interfering A surprising result is that the performance of the DS system actually deteriorates with growing L. For larger L, the averaging of the interfering signals, which is what the DS system actually does, is carried out over a wider frequency band. This decreases the variance of the error term after de-spreading and demodulation. On the other hand, the probability of having some very strong interfering signals in the receiving bandwidth W ss, yielding a larger variance of the error term, grows with L. The second eect is evidently the dominant one when increasing L for this model of the interfering signals. From the simulation results, one can conclude that a \straightforward" DS system performs badly on the HF channel. To get acceptable performance, some type of interference suppression is necessary, see e.g. [8]. The dashed line in gure 3 shows the BEP of the DS system for L = 00, if we totally reject the three strongest interfering signals within W ss, and evidently, the gain is dramatic. 3.2 THE FH SYSTEM In an FH system, the carrier frequency of the modulated signal (in our case a BFSK signal) is changed according to a pseudo-noise (PN) sequence []. The system is assumed to have N numbers of frequencies to hop between, and hence, N roughly is the processing gain of the system. At the receiving side, the same PN sequence of carrier frequencies is stored, so that the received signal r(t) can be de-hopped and demodulated. For an FH/BFSK system with the data symbols d i =, the received signal for the ith data bit can be written as s 2Eb r i (t) = cos[2(f i + d i f)t] + n I (t) ; (4) T b 7

8 0 0 0 DS, L=00 BEP 0 2 FH, const. signal FH, fading signal 0 3 Figure 4: E [SIR], (db) The bit error probability of the FH and DS systems, as a function of the expected value of SIR. The upper curve for the FH system is for Rayleigh fading signal amplitude. where E b is the received signal energy per bit duration T b, f is chosen such that orthogonal signals are obtained and n I (t) is the received interference. The system is assumed to transmit one data bit per hop (f i is changed for every T b ), which gives a desirable interleaving eect on the bit stream. Furthermore, T b is assumed to be larger than or equal to 2 ms, corresponding to a bit rate no higher than 500 bit/s. This ensures that the momentary bandwidth of the system does not exceed khz, i.e., the bandwidth over which I k is valid. We will not give the performance analysis of the FH system here, instead we refer to [9]. In gure 4, we present the resulting BEP curve for both constant received signal power S (dashed line) and Rayleigh fading signal envelope (dash-dotted line). In the same gure we also give the BEP of the DS system with L = 00 from section 3.. Obviously, the FH system performs better than the DS system on this interferencelimited HF channel. Intuitively, the dierence can be explained by the fact that in the FH case the strong interfering signals ruin the data bits that are hit, but many data bits are aected only by a small interfering signal and are received properly. On the other hand, in the DS system the strong interfering signals are all continuously received by the wideband receiver and increase the probability of erroneous detection for all data bits, and apparently, that eect is worse. Furthermore, the performance degradation in the FH system due to the fading is not very large. The variation of the SIR for the received bits is already so large, due to the interfering signals, that the introduction of the Rayleigh fading of the signal does not increase it to any great extent. 4 CONCLUSIONS By developing the Laycock-Gott congestion model, we have obtained a reasonable statistical description of the interference situation on HF, which has been used in the 8

9 evaluation of DS and FH systems on HF. The evaluation shows that the narrowband bit decisions the FH system performs, yields a lower BEP than the wideband detection of the DS system. Loosely speaking, the global average BEP of the FH system is the average of the BEP on every channel in W ss, but the BEP of the DS system depends on the average of the interference power in every channel. Evidently, that eect is worse for the total performance on the interference-limited HF channel we have examined. The results illustrate the importance of somehow dealing with the strong interfering signals when designing SS systems for the HF channel. In the case of DS systems, one can employ interference rejection techniques to suppress the strongest signals in W ss, since the gain of suppressing those signals is larger than the loss of loosing signal power in the suppressed frequency gaps [0]. In FH systems, one can adapt to the frequencyselective HF channel by introducing an adaptive frequency-hopping (AFH) scheme []. Such a system evaluates all the available channels continuously and performs the communication only on the best ones. These improvements of the SS systems will also improve the systems' stealth properties if they are combined with power control. REFERENCES [] M. K. Simon et al., Spread spectrum communications handbook, 2nd edition, McGraw-Hill Inc., 994. [2] N. F. Wong, G. F. Gott et al., \HF spectral occupancy and frequency planning", Proc. of the IEE, vol. 32, part F, no. 7, pp. 548{557, Dec 985. [3] M. Broms, \Results from measurements of occupancy in Sweden", Proc. HF 92, Nordic Shortwave Conf. in Sweden, 992. [4] P. J. Laycock, G. F. Gott et al., \A model for HF spectral occupancy", IEE Conf Pub. 284, London, UK, 988. [5] B. D. Perry, R. Rifkin, \Interference and wideband HF communications", Proc. 5th Ionospheric Eects Symposium, Springeld, VA, May 987. [6] G. F. Gott et al., \Recent work on the measurement and analysis of spectral occupancy at HF", IEE Conf Pub. 392, York, UK, 994. [7] S. K. Chan, G. F. Gott et al., \HF spectral occupancy a joint British/Swedish experiment", Proc. HF 92, Nordic Shortwave Conf. in Sweden, pp. 299{309, 992. [8] J. E. M. Nilsson, \Interference robustness of coded spread spectrum methods in an HF interference environment", Proc. HF 95, Nordic HF Conf. in Sweden, 995. [9] G. Andersson, \Performance of frequency-hopping radio systems on interferencelimited HF channels", IEE Conf Pub. 392, York, UK, 994. [0] B. Lagerquist, N. Hallqwist, \Interference rejection techniques in a DS spreadspectrum HF radio system", (in Swedish), FOA-R SE, National Defence Research Establishment, Linkoping, Sweden, Nov 994. [] J. Zander, \Adaptive frequency hopping in HF communications", Proc. MilCom 93, Bedford, MA, Oct