Application of Frequency-Shift Filtering to the Removal of Adjacent Channel Interference in VLF Communications J.F. Adlard, T.C. Tozer, A.G. Burr. Communications Research Group, Department of Electronics University of York, York YO10 5DD United Kingdom. Email:
[email protected] Fax: +44 (0) 1904 432335
A BSTRACT The use of frequency-shift (FRESH) filtering for the rejection of adjacent channel interference (ACI) in GMSK modulated VLF communications is investigated. A range of scenarios based on a high powered interferer (up to 40 dB greater than the signal of interest (SOI)) in an adjacent channel to the SOI are tested, and the use of a FRESH filter for rejection of the interference is investigated. It is shown that a major improvement in BER performance over a fractionally spaced equaliser (FSE) is possible, and that only one interferer related frequency shift is required. This demonstrates that FRESH filters can be highly effective in ACI removal, with only a moderate increase in complexity over an FSE. 1. INTRODUCTION Very low frequency (VLF) radio provides a useful means of communication with submarines because it has stable and predictable propagation and can penetrate some distance through seawater. However there are a number of factors which can seriously degrade its effectiveness, such as impulsive noise from lightning strikes, and interference from other users of the frequency band. VLF communication often uses Gaussian Minimum Shift Keying (GMSK) to modulate the carrier, as transmit antenna bandwidths are limited. As VLF is used for long range communications, land based transmitters may use very high powers. This paper is concerned with the scenario where a receiver is physically relatively close to another user’s transmitter, operating on an adjacent channel. Despite the use of GMSK which minimises the out-of-band energy of the signal, the difference in power levels at the receiver between a signal of interest (SOI) from a distant transmitter and a local interferer can make the interferer’s GMSK side lobes a significant problem. We propose here the use of frequency shift filters (FRESH filters) [1, 2, 3, 4], also known as periodically time-varying filters, to excise such interference. These filters exploit
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Fig. 1. Spectrum of interference scenario used (example)
the spectral correlation which is a manifestation of the cyclostationarity of digitally modulated communications signals. They are particularly useful in the case of high powered interferers, because the spectral correlation of the interferer can be used to remove itself from the SOI frequency band. 2. D ESCRIPTION
OF
S CENARIOS
Two interference scenarios were explored here. The first has a SOI transmitting at a baud rate of 100 Hz (200 bits per second) and an interferer with a baud rate of 114.29 Hz at a carrier frequency 210 Hz higher than that of the SOI. In the simulations, the SOI was modelled at baseband (the filter performance is independent of the carrier frequency). The second scenario uses a baud rate of 100 Hz for both signals, with a carrier frequency separation of 200 Hz. The first scenario was chosen to have similar interference to the second, but in the first case the cyclic frequencies of the two signals are all distinct. This allows a close examination of how the FRESH filter exploits frequency shifts related to the properties of the SOI and interferer. In the second case, which is more likely to occur in practice, some cyclic frequencies are common to both the SOI and the interference. It is assumed that the interference baud rate and carrier frequency can be determined, or are known, at the receiver. GMSK modulation was used for both signals, which were
GMSK SOI FRESH filter
matched filter
data detector
FIR out
in
GMSK interferer
complex conjugate
frequency shift
FIR
Fig. 2. Structure of simulation Fig. 3. FRESH filter with 2 frequency shifts
carrying independent identically distributed data; the data carried on each signal were not mutually correlated. Both signals used identical Gaussian shaping filters, which had a bandwidth-time product of 2.5. This filter introduces a small amount of intersymbol interference. Normally an equaliser would be used to remove this, however as its effect is small compared to the ACI it has been omitted here. White noise was added to the signals to give a SOI Eb =N0 between 0 and 15 dB. Interferer powers from 0 to 40 dB relative to the SOI were used. The spectra of the signals with the interferer at 30 dB are shown in figure 1. The filters were implemented as trained adaptive filters. The LMS algorithm was used to adapt the filters to a steady state then adaptation was stopped while bit errors were counted. The SOI power was 1 and the LMS feedback coefficient, , was 0.001. It was found that lower values of than this made practically no difference to the final BERs calculated. 3. F REQUENCY S HIFT F ILTERING The use of the frequency shift filter (FRESH filter or periodically time-varying filter) has been described by Gardner and others [1, 2, 3, 4] although its use with carrier related spectral correlation is effectively the same as the conjugate filtering proposed in [5]. Communications signals can be cyclostationary with cyclic frequencies related to the carrier frequency or the baud rate, or certain combinations of the two [1]. In the frequency domain this cyclostationarity manifests itself as spectral correlation, that is, the signal is correlated with itself after frequency shifting by one of its cyclic frequencies. Often the complex conjugate of the shifted signal must also be taken to reveal the correlation, which is then referred to as conjugate spectral correlation [6]. This spectral correlation effectively provides a form of frequency diversity in the signal, and the FRESH filter exploits this to reduce the effect of additive noise and interference. The structure of a single shift FRESH filter is shown in figure 3. It is assumed the shift is one which exploits conjugate correlation so is followed by taking the complex conjugate of the signal. If a cyclostationary interferer is present, then its spectral correlation can also be exploited by a FRESH filter, if its cyclic frequencies are known or can be found. By using a filter which exploits the properties of the interference and
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Fig. 4. Spectral correlation of GMSK
of the SOI a highly effective interference rejection filter can be constructed. 4. S PECTRAL C ORRELATION
OF
GMSK
SIGNALS
GMSK signals are generated from linear filtering of MSK, and so exhibit the same form of correlation as MSK signals. It is shown in [6] that conjugate correlation exists under frequency shifts of = 2fc Tk0 for odd values of k and non-conjugate correlation for = Tk0 for even k, where k are integers, fc is the carrier frequency, and T0 is the baud period. When the signal is modelled at complex baseband, the useful correlation occurs at = Tk0 with k odd for conjugate correlation and k even for non-conjugate correlation. This is illustrated in figure 4. Here the spectrum of GMSK is shown from -350 Hz to 350 Hz. The baud rate is 100 Hz. The arrows on the graph, and the a and b labels indicate which frequencies are correlated. For example the central region (-50 to 50 Hz) is correlated with the regions at frequency shifts of -200 Hz and at 200 Hz (that is, frequency shifts of -2 and 2 times the baud rate). However correlation of the centre with the region from 50 to 150 Hz occurs only after reflection about the y-axis and then shifting by 100 Hz, in other words, this is conjugate correlation under a baud rate frequency shift. This can be clarified with the example that the signal component at 49 Hz exhibits correlation with the components at -151 and 249 Hz, and conjugate correlation with the components at -349, -149, 51 and 251 Hz. (Larger shifts are neglected for simplicity). If the carrier frequency is not zero then an extra 2fc must be added to the shifts exploiting conjugate correlation. Table 1 shows the frequency shifts used in the first scenario (SOI and interferer with different baud rates), and how they are derived from the signals’ properties. These 10 shifts (5 SOI related and 5 interferer related) were chosen as the most likely to be effective
Ranking of frequency shifts (SOI/interferer different baud rates)
SOI
Frequency shift (Hz) 305.71 -228.57 534.28 228.57 77.14 200 -200 100 -100 -300
Relation to signal properties
2fi ? bi ?2bi 2fi + bi 2bi 2fi ? 3bi 2bs ?2bs
1
2
rank
Related to which signal Interferer
3
bs
?bs ?3bs
Table 1. Frequency shifts tested (bi =symbol rate of interferer, bs =symbol rate of SOI, fi =interferer carrier)
305.7 −228.6 77.1 534.3 228.6 −300 −200 200 100 −100
by inspection of figure 1.
frequency shift (Hz)
0 dB
40 dB 30 dB 20 dB 10 dB
interferer power
5. R ESULTS Fig. 5. Ranking of frequency shifts for effect on BER
5. . 1 First scenario - different baud rates Simulations of the VLF system were designed to identify first of all which frequency shifts should be used in the FRESH filter and how many different shifts should be used. Initially, a system using a single shift was constructed, and the BER was measured for different values of that single shift. This was repeated for interferer powers from 0 dB to 40 dB relative to the SOI. Figure 5 shows the ranking of the best three frequency shifts for each interferer power; the highest column indicates the most effective shift in reducing BER. This graph shows that with higher powered interferers more of the best frequency shifts are related to the interferer properties. At lower interferer powers the best frequency shifts are SOI related. Figure 6 shows the actual improved error rates that result from the use of four of these frequency shifts. The best two SOI related and interferer related shifts were used, and the resulting BERs plotted against white noise power for each interferer power. The interferer related shifts are more us eful for all interferer powers greater than that of the SOI. Of course the actual error rate is higher when the interferer power is higher, but the benefit in using a FRESH filter also increases, as is shown below. The previous two graphs were based on a FRESH filter with two branches and one frequency shift. The effect of combining several different frequency shifts in a multibranch filter were also measured. Figure 7 shows the performance of filters with between zero and four frequency shifts. Zero shifts is equivalent to a fractionally spaced equaliser; four shifts require a structure with 5 branches and subfilters. The frequency shifts were added in order of their effectiveness in a single shift filter, that is 305.7,
-228.6, 77.1, 534.3 Hz. It is clear that there is little advantage in using more than one frequency shift. This shows that only a moderate increase in complexity is required: a filter with one frequency shift has two branches, and two subfilters, so the filtering computational load is double that of the corresponding FSE. Having confirmed that overall the most effective and efficient FRESH filter for high interference powers is one using a single frequency shift of 305.7 Hz (for this interference scenario), it was tested against a FSE with various interferer powers and white noise levels. These results are shown in figures 8 to 12. It is clear that even with very high powered interferers, which give unusably high error rates with a FSE, a major improvement is possible by using a single shift FRESH filter. The performance is dependent on the white noise level: with a high signal to noise level, the bit error rate approaches that with no interferer presen t. This means that in some circumstances the FRESH filter comes close to perfect removal of the interferer. 5. . 2 Second scenario - equal baud rates The comparison of the effectiveness of individual frequency shifts was repeated for the second interference scenario where the SOI and interference have the same baud rate and have carrier frequencies separated by twice the baud rate. In this case the cyclic frequencies (corresponding to those tested above) are as shown in table 5. . 2. Clearly, some of these cyclic frequencies can be interpreted as either SOI or interferer related. The ranking of these frequency shifts is shown in figure 13. For compar-
BER of GMSK with GMSK ACI at equal power − different baud rates Effect of SOI and Interferer frequency shifts in filter
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−100 Hz +100 Hz −228 Hz 305.71 Hz
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The actual BERs achieved with this scenario, using a single shift of 300 Hz and an interference power of 30 dB, are shown in figure 14 along with the data from figure 11. This shows the change in interference scenario has little effect in BER so figures 8 to 12 also illustrate performance under the second interference scenario.
Bit Error Rate
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ison with figure 5, the frequency shifts with two interpretations are plotted twice. We see that there is no significant change in the rankings from figure 5 - shifts related to both the SOI and the interferer do not become significantly more effective.
Effect of number of frequency shifts in filter
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Fig. 8. Filter performance with 0 dB interferer
Fig. 6. BER with best SOI and interferer shifts
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FSE 1 shift 2 shifts 3 shifts 4 shifts
6. C ONCLUSIONS
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E /N b
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Fig. 7. BER with different numbers of shifts in filter
Related to which signal Interferer
SOI
Frequency shift (Hz) 300 -200 500 200 100 200 -200 100 -100 -300
Relation to signal properties
2fi ? b ?2b 2fi + b 2b 2fi ? 3b 2b ?2b
b
?b ?3b
Table 2. Frequency shifts tested with equal baud rates (b=baud rate of interferer and SOI, fi =interferer carrier)
We have shown that the use of FRESH filters can give a major improvement in BER in the reception of a GMSK signal with severe adjacent channel GMSK interference, when compared to a fractionally spaced equaliser. We have also shown that most of the improvement in the high powered interference case can be achieved by using only one frequency shift, and that this shift should be one which exploits the properties of the interferer. The increase in complexity required to use this technique is not severe: the filter computational load is doubled. R EFERENCES [1] William A. Gardner, “Cyclic Wiener filtering: Theory and method”, IEEE Transactions on Communications, vol. 41, no. 1, pp. 151–163, January 1993. [2] William A. Gardner and William A. Brown, “Frequency-shift filtering theory for adaptive cochannel interference removal”, in Proceedings of the 23rd Annual Asilomar Conference on Signals, Systems and Computers, 1989, pp. 562–567.
BER of GMSK with GMSK ACI at 10 dB higher power − different baud rates
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BER of GMSK with GMSK ACI at 40 dB higher power − different baud rates −2
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Fig. 9. Filter performance with 10 dB interferer −6
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BER of GMSK with GMSK ACI at 20 dB higher power − different baud rates
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Fig. 12. Filter performance with 40 dB interferer
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Ranking of frequency shifts (SOI/interferer same baud rate)
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Fig. 10. Filter performance with 20 dB interferer BER of GMSK with GMSK ACI at 30 dB higher power − different baud rates
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Fig. 13. Ranking of frequency shifts for effect on BER
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Fig. 11. Filter performance with 30 dB interferer
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BER of GMSK with GMSK ACI at 30 dB higher power
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Fig. 14. Comparison of filter performance with interferer at same and different baud rates
[3] William A. Gardner and S. Venkataraman, “Performance of optimum and adaptive frequency-shift filters for cochannel interference and fading”, in Proceedings of the 24th Annual Asilomar Conference on Signals, Systems and Computers, 1990, pp. 242–247. [4] Jeffrey H. Reed and Tien C. Hsia, “The performance of time dependent adaptive filters for interference rejection”, IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 38, no. 8, pp. 1373–1385, August 1990. [5] W. M. Brown and R. B. Crane, “Conjugate linear filtering”, IEEE Transactions on Information Theory, vol. IT-15, no. 4, pp. 462–465, July 1969. [6] William A. Gardner, Prentice Hall, 1988.
Statistical Spectral Analysis,
c British Crown Copyright 1998/DERA Published with the permission of DERA on behalf of the Controller HMSO.
