HF MODEM DESIGN FOR EXTREMELY HIGH SIMULTANEOUS DOPPLER AND DELAY SPREADS

Transcription

1 HF MODEM DESIGN FOR EXTREMELY HIGH SIMULTANEOUS DOPPLER AND DELAY SPREADS Tim Giles Royal Institute of Technology (KTH) SE- 44 Stockholm Sweden SUMMARY High Frequency(HF) radio modems are required to operate over a broad range of adverse channel conditions such as severe multi-path, fading, partial-band and carrier-wave interference as well as impulsive noise. The only compensation for the HF modem designer is that the number of digital signal processing(dsp) operations available per bit is usually high. The design of both serial and parallel tone modems has advanced in recent years so that the user can now expect higher data rates and lower bit error rates than ever before over mid-latitude channels []. In recent years, HF propagation at high latitudes has been studied through the Doppler and Multi-path Sounding Network(DAMSON) project with results showing that Doppler and delay spreads can occasionally be extremely high. The results suggest that a robust modem should withstand 4 Hz Doppler spread and 2 ms delay spread [2]. Many currently available modems have a robust mode based on applying stronger coding to the basic waveform [3, 4]. The author believes that for extreme Doppler and delay spreads that this is not a good design since both serial and parallel tone modems rely, be it indirectly, on channel estimates in the decoding process. When there are extremely high simultaneous Doppler and delay spreads, channel estimates become outdated during the measurement period. The problem demands a new approach. The author proposes wide-spaced M-ary Frequency Shift Keying(MFSK) in conjunction with a robust receiver. This allows communications to be maintained under extreme conditions at the cost of low data rates. A number of 8-FSK modem designs were tested. Standard 8-FSK with normal spacing is ineffective in the extreme channel conditions. However, wide-spaced Gaussian pulsed 8-FSK in conjunction with a combiner receiver achieves low uncoded error rates. This modem also performs well on a Gaussian channel. INTRODUCTION HF modem design has always been a vexing problem due to the nature of the channel. It is usual to encounter multi-path, fading, interference from other users and impulsive noise. Furthermore, these phenomena display a great deal of variability, i.e. the channel is far from stationary. Today, a complete HF modem design will include features to combat all these channel effects. Impulsive noise and narrow band interference are particularly problematic on the HF channel while multi-path (or delay spread) and fading (or Doppler spread) are common on many mobile radio channels.

2 Currently, there are two competing design philosophies within the HF arena for dealing with delay and Doppler spread, serial-tone and parallel-tone or orthogonal frequency division multiplex (OFDM) [5]. When combined with interleaving and error control coding, high performance and high data rates can be achieved for the Doppler spreads and delay spreads usually experienced on HF channels. In low rate mode, serial-tone modems can cope with fairly difficult fading conditions [3]. Ionospheric propagation has been the subject of much investigation. Traditionally ionograms were collected showing the delay spread profile of the HF channel. More recently, extensive measurement campaigns, specifically DAMSON [6], have been undertaken to collect the Doppler and delay spread profiles of the channel which are usually recorded as channel scattering functions. On occasion, extremely large Doppler spread and delay spreads have been observed over auroral paths. The results suggest that a robust modem, designed for all conditions, should withstand 4 Hz Doppler spread and 2 ms delay spread [2]. These values are truly extreme and most certainly beyond the capability of standard HF modem designs. 2 THE EXTREMELY POOR CHANNEL To begin the investigation of how a modem should be designed for extreme channel conditions a channel simulator was built using the C programming language to simulate a channel with 4 Hz Doppler and 2 ms delay spread. This channel was labeled the extremely poor channel. A tapped delay line was used as is standard for a Watterson Simulator [7] (see Figure ). However, a large number of taps were used to generate the 2 ms delay spread. Gaussian functions were used for both delay and Doppler spreads with the standard deviation of the power being set to σ τ = 2 ms and σ f = 4 Hz respectively. The channel scattering function is shown in Figure 2 and defined in (): E[ G(τ,f) 2 ] = 2πσ τ σ f exp ( τ 2 2σ 2 τ + f2 2σ 2 f where G(τ,f) is the Fourier transform of the tap gain function g(τ,t) and E[.] is the statistical expectation. It is generally accepted that this channel represents extreme conditions and that a modem designed to cope with such a channel would only occasionally have an advantage over a less conservative design. ) () 3 SUITABILITY OF MODULATION SCHEMES A serial-tone modem sends a fast phase shift keyed signal over the HF channel. A training sequence is usually employed to measure the channel impulse response. The estimate of the channel impulse response is then used by an equaliser to decode the data. The channel measurement period needs to be at least the length of the delay spread. For an extremely poor channel, the channel impulse response has substantially changed by the end of the measurement period. This leads to large estimation errors and poor equalisation. A parallel tone modem sends slow, narrow-band tones to convey the data. It relies on

3 Input Signal Delay-line g(τ,t) g(τ,t) g(τ n,t) Σ Output Signal Figure : Tapped Delay-line Simulator Structure a guard time to deal with the delay spread and a differential scheme is often used to deal with the Doppler spread. A sensible design for the extremely poor channel would be to use 2 ms long tones with 2 ms of guard time. This will effectively deal with the delay spread but, the change in amplitude and phase between successive symbols will be very large. Furthermore, the fading or Doppler spread removes the orthogonality between tones and would cause substantial inter tone interference, usually referred to as inter-channel interference(ici). A modem could also use very strong error control coding to deal with these problem. In this case the power of the error control coding is used in attempting to remedy the signal distortion. When faced with such difficult circumstances one may be led to believe that it is not possible to send data over an extremely poor channel at all. The application of coherent or even differential schemes certainly seems unfruitful. Non-coherent frequency shift keying(fsk) schemes have potential and some versions of FSK have been proposed to solve this problem [8] as well as to deal with interference [9]. It is important to note that if a pulse is sent through an extremely poor channel at a particular time and frequency it will be spread by roughly 4 Hz and 2 ms. This implies that if wide-spaced FSK is used where each pulse is well separated in time and frequency, then data can be successfully conveyed over the channel. Some possibilities are examined in the following sections. 4 BASIC MFSK The modem design for the extremely poor channel begins with a simple reference modem. There are many design options for an HF MFSK modem. The parameters chosen here are not necessarily optimum but a sensible starting point. An 8-FSK modem was constructed using 32 ms long rectangular pulses separated by 3.25 Hz. Using the band from 3 Hz to 27 Hz, 9 parallel 8-FSK signals could be accommodated giving a raw data rate of bits per second. The receiver correlates the signal with a rectangular filter, in time, and compares the power at each frequency. The modem has been tested against a Gaussian noise channel and provides standard 8-FSK uncoded performance as shown in Figure 6. Note that here, the relationship between energy per bit over noise spectral density E b /N and Signal to Noise Ratio SNR is SNR = E b /N 5.5 db with a noise bandwidth of 3 khz. When tested against the extremely poor channel, the error rate did not drop below.3

4 Relative Power (db) Frequency (Hz) Time (ms) 2 3 Figure 2: Channel Scattering Function of the Extremely Poor Channel (see Figure 7). This does not provide a good foundation on which to provide data communications. The errors were caused by the frequency pulses being spread in frequency and time to neighbouring positions. 5 WIDE SPACED MFSK A simple solution to the distortion problem is to move the frequency pulses apart in time and frequency. Figure 3 shows the design adopted, which gives a buffer of two slots in time and frequency between each possible transmit frequency pulse. An example transmit data sequence is shown in Figure 3 with the black rectangles indicating the corresponding transmit frequencies (a Gray code has been used). An interesting advantage of this design is that the transmit signal has a constant envelope. The design spreads the 8-FSK constellation over 9 times as much area (time frequency) as the standard 8-FSK. This leads to a much lower data rate of bits per second. The performance in Gaussian noise is the same as the standard 8-FSK (see Figure 6); however, there is a fold improvement in the error performance in the extremely poor channel resulting from the spacing in time and frequency (see Figure 7). Note that at lower data rates, the relationship between E b /N and SNR is SNR = E b /N 5. db with a noise bandwidth of 3 khz.

5 Time (ms) Frequency (Hz) Example Data Gray Code = {,,,,,,, } Figure 3: Wide Spaced 8-FSK Constellation 5. COMBINER RECEIVER Under extreme channel conditions, the Basic MFSK receiver ignored a lot of the received signal s energy. At the transmitter, the frequency pulse can be considered to occupy just one slot in frequency and time. However, due to channel distortion, the received pulse can be considered to be spread over the neighbourhood of the transmitted pulse. Hence a receiver was designed that adds the powers received at the expected time and frequency and all neighbouring times and frequencies, 9 slots in all (see Figure 3). This is not the optimal combining policy. However it is reasonable for non-coherent receivers. The combiner degrades performance for the undistorted channel (see Figure 6). This is to be expected as the receiver is combining samples containing noise and no signal. The degradation in undistorted channels is compensated for by a five fold improvement in error performance for extremely poor channels. 5.2 GAUSSIAN PULSED MFSK Basic MFSK uses rectangular transmit pulses, which are limited in time but have a sinc shape in frequency. Consequently there is potential for interference between frequencies despite the wide spacing used. To reduce ICI a transmitter was constructed that outputs Gaussian shaped pulses (see Figure 4). Gaussian pulses in time are Gaussian in frequency. A standard deviation of 2.8 ms corresponding to 2.4 Hz was chosen. When this transmitter was used in combination with the combiner receiver (still using rectangular correlation), there was a small improvement in performance. Note that the property of constant output power is lost if Gaussian pulsed transmission is used.

6 Rectangular Pulse Gaussian Pulse Figure 4: Transmitted Pulse Shapes 5.3 GAUSSIAN PULSED MFSK WITH GAUSSIAN CORRELATOR RECEIVER AND COMBINER For optimum performance in an undistorted channel, a Gaussian pulsed transmitter should be matched to a Gaussian correlator receiver. This was implemented in conjunction with a combiner that summed the powers in the neighbourhood of the expected signal. The 9 Gaussian correlators were placed in time and frequency as shown in Figure 5. The correlators are represented by ellipses and the transmitted pulse is indicated by the shaded ellipse. This design led to a performance improvement for the undistorted channel since the Gaussian correlators overlap (see Figure 6). A small increase in performance for the extremely poor channel resulted as well (see Figure 7). This was the best design of all those evaluated. It achieved very close to the standard 8-FSK performance for undistorted channels and provided an uncoded error rate of approximately 4 3 in extremely poor channels. 6 DISCUSSION It is understood that the application of error control coding forms an essential part of all modern HF modems. This paper has simply outlined a basis on which to build a complete modem with error control coding. By using wide spacing, the self interference of the signal has been reduced to a level which makes error control coding very effective. The simulations have assumed perfect synchronisation since its implementation is not perceived to be difficult. Training pulses are necessary but the accuracy of the synchronisation is not critical as the Doppler and delay spreads are expected to be large. This paper has addressed the problem of conveying data under extreme channel conditions. This does not fully address how a modem would be designed. A worst case design is not

7 32 ms 3.25 Hz Figure 5: Placement of Gaussian Correlators necessarily the best average design. The key element is knowing the channel. 7 CONCLUSION The problem of modem design for extremely high simultaneous Doppler spread and delay spread has been addressed. For HF channels such conditions only occur occasionally on auroral paths and/or in aeronautical communications. The approach of adding extra error control coding and training to a serial or parallel tone modems seems futile under very extreme channel conditions. This paper therefore presented an 8-FSK modem with wide spacing in frequency and time that managed to cope with the extremely poor channel conditions. Using a Gaussian pulse at the transmitter and combining groups of Gaussian correlators at the receiver performed best of all methods evaluated. This method resulted in an uncoded error rate of 4 3 in a channel that causes an error rate of.3 for basic 8-FSK. This constitutes an excellent basis for applying error control coding to construct a very robust modem. The author intends to make the simulation software freely available at: list.html

8 REFERENCES [] A.F.R Gillespie and S.E. Trinder, Performance Characteristics of High Data Rate HF Waveforms, Proceedings of the Eighth International Conference on HF Radio Systems and Techniques, University of Surrey, Guildford, UK, -3 July 2. [2] T.J. Willink, N.C.Davies, M.J. Angling, V. Jodalen and B. Lundborg, Robust HF data communications at high latitudes, IEE Proceedings of Microwave, Antennas and Propagation, Vol. 46, No. 4, August 999. [3] M.W. Chamberlain, W.N. Furman and E.M. Leiby, A Scaleable Burst HF Modem, Conference Proceedings of the Nordic Shortwave Conference, Fårö, Sweden, -3 August 998. [4] M.C. Gill, S.C. Cook, T.C. Giles and J.T. Ball, A 3 to 36 bps Multi-Rate HF Parallel Tone Modem, Proceedings of the IEEE Military Communications Conference, San Diego, USA, 5-8 November 995. [5] J. Pennington, Techniques for medium-speed data transmission over HF channel, IEE Proceedings, Vol. 36, Pt., February 989. [6] N.C. Davies, P.S. Cannon and M.J. Maundrell, DAMSON-a system to measure multipath dispersion, Doppler spread and Doppler shift on HF communications channels, Proceedings of the IEE Colloquium on High Latitude Ionospheric Propagation, pp 2/ -2/4, 992. [7] CCIR, Ionospheric Channel Simulators, Report 549-2, Recommendations and Reports of the CCIR, 986, Volume III, pp 59-67, ITU Geneva. [8] M. Darnell, B. Honary, P.D.J. Clark, N. Horley, M. Maundrell and G. Vongas, Adaptive DSP-Based MFSK Modems for HF Aeromobile Channels, Proceedings of the IEEE Military Communications Conference, San Diego, USA, 2-5 October 992. [9] R.G. Wilkinson, A Modem for More Reliable Communications at HF, Proceedings of the IEE Second International Conference on HF Communications Systems and Techniques, London, UK, 5-7 February 982.

9 Probability of Bit Error Basic MFSK Wide Spaced MFSK Combiner Receiver Gaussian Pulsed MFSK Gaussian MFSK with Gaussian Receiver E b /N (db) Figure 6: Modem Performance in Gaussian Noise only Probability of Bit Error 2 3 Basic MFSK Wide Spaced MFSK Combiner Receiver Gaussian Pulsed MFSK Gaussian MFSK with Gaussian Receiver E b /N (db) Figure 7: Modem Performance in Extremely Poor Channel