These experiments show that pulsed systems can not only operate effectively without sideband energy, but can actually benefit in performance by removing the sidebands.
Traditional communications systems rely on sidebands as the means of transmitting modulated signals. But this is not necessarily true for ultranarrowband (UNB) modulation methods. In fact, it can be shown by means of amplitude-modulated (AM) pulse testing that the sidebands are not essential for transmission or reception of AM pulse-modulated signals. In pulsed radar systems, sidebands at the transmitter are necessary because available filters cannot remove them. But they are not necessary at the receiver, where zero-group-delay filters having very narrow bandwidths can be applied to effectively remove the sidebands. Some other pulse systems having good frequency control may be able to remove the sidebands with filtering at the transmitter.
It is well known that an AM signal contains a carrier plus sidebands (eq. 1). The carrier contains one-half of the peak voltage and the summed contra rotating sidebands add constructively or destructively to double or cancel the peak voltage with 100% modulation. It can be shown by the simple means of removing the carrier from a pulsed signal that the sidebands contribute 50% of the energy.
Similarly, using the special filters with near-zero group delay, reducing or removing the sidebands causes a detected voltage loss of 50%. Those sidebands are not essential to the operation of the system: All of the necessary information for detecting an on/off AM pulse is already present in the carrier alone. Since 1998, this has been proven to be the case with UNB digital modulation (ref. 1). This present article shows near-perfect reception without usable sidebands for AM pulses, although the method does not work for ordinary AM audio, where the sideband energy is essential to the operation of the system.
What are the advantages of transmission and reception without sidebands? With AM pulses, as in radar systems when the sidebands are removed, only the carrier is transmitted, and the bandwidth required is greatly reduced. The signal-to-noise ratio (SNR) is directly proportional to the receiver filter bandwidth required. An improvement of 30 dB or more in the SNR can be obtained by removing the sidebands with a narrowbandwidth, zero-group-delay filter in the case of on/off AM pulse transmission. the approach can also be used to extend the range of UWB signals when applied to UNB communications systems.
To demonstrate how information transmission and reception is possible without sidebands, a basic test system was constructed for experimentation. Figure 1 shows a simple block diagram representing the test pulse generator, in which a 48-MHz carrier was generated with 500-ns pulses and 100% AM. Figure 2 shows the swept response of one stage of a series emitter filter used as the UNB filter in the experiments. The actual 3-dB filter bandwidth is much narrower than this swept-response plot shows, since the spectrum analyzer's resolution-bandwidth (RBW) setting was too broad to accurately show the filter's true response. The filter's actual 3-dB bandwidth is about 1/100,000th of the filter's center frequency (a 3-dB bandwidth of 500 Hz for a 50-MHz center-frequency bandpass filter). Multiple filters can be cascaded to increase the sideband rejection.
The spectrum analyzer was also used to measure the Fourier sinx/x spectrum at the output of the test system. The screen of Fig. 3 shows the sinx/x envelop and the 2π/T sideband frequency spikes prior to any suppression by the zero-group-delay filter. The number and spacing of these spikes depends upon the pulse repetition rate and pulse width. They will null at a frequency equal to the Nyquist bandwidth. In this case, the Nyquist bandwidth from the relationship BT = 1 is 1/500 ns = 2 MHz at baseband and 4 MHz at RF.
When the spectrum analyzer was then used to check the effects of using the narrowband filter (Fig. 4), the sinx/x sideband distribution shows that the sidebands have been reduced by 40 dB by the use of two cascaded stages of zero-groupdelay filtering. For greater suppression, more filter stages can be added. It has been assumed here that once a carrier has been modulated with contra-rotating sidebands, no amplitude change remains in the carrier, and only the carrier needs to be transmitted and received.
The block diagram of Fig. 5 shows the components and circuit elements used in the UNB near-zero-group-delay filter. This filter does not shape or distort the pulse waveform as Nyquist criteria filters do. A rectangular pulse at the input of the filter is a detected rectangular pulse out at input of the receiver. This greatly improves radar resolution and amplitude response. Emitter follower isolation may be used between cascaded stages.
In Fig. 6, the test instrument screen shows the baseband pulse from the test generator at the top and the detected RF pulse at the bottom, after two stages of series-emitter zero-group-delay filtering and using a synchronous detector. Note that the pulse shape is retained and the sidebands were reduced 40 dB. In this experiment, the filter center frequency is 48 MHz, the pulse is 500 ns wide, and the pulse repetition rate (1/Tp) is 100 kHz.
In Fig. 7, the instrument screen shows the same recovered pulse with the RF cycles at the filter input instead of the baseband keying pulse. The screen indicates a resolution of 1 RF cycle in a radar or similar pulse-based system. The range resolution is 3.3 m. This resolution is not possible with a matched Nyquist filter having a bandwidth of B = 1/T. The SNR improvement over a BT = 1 Nyquist filter is approximately 36 dB due to the bandwidth reduction. The leading edge varies 1 RF cycle because the baseband signal and the RF pulse start and stop are not synchronized. The signal in Fig. 7 is the same when detected with or without the two-stage UNB filter, indicating there is no envelop group delay in the filter and that the sidebands are not making any contribution to the detected signal waveform after filtering.
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Any detector circuit can be used with this approach. The spectrum analyzer screen shots of Figure 6 and Figure 7 were made using a Gilbert cell (a model NE602 which is currently available from NXP Semiconductors, www.nxp.com) as a synchronous detector. Synchronous detectors are probably best for weak signals, although square-law diode detectors have also been used successfully.
For all AM methods, the following relationship can be written:
It = Imct) + 0.5K(cosωc+ F)t + 0.5K(cosωc - F)t> (1)
C = the carrier signal; F = the amplitude modulating signal; K = the modulation index (presumed to be 1.0 for pulse modulation); F = the Fourier transform of the modulating signal.
Equation 1 is the general equation for all AM methods, including methods employing pulse modulation. All components are required for modulation, but not for pulse reception. The carrier is continuous for audio, but pulsed on/off for pulse modulation. Each sideband contributes 0.5K to the signal. When the sidebands are reduced 40 dB, as shown in Fig. 4, it is the equivalent of reducing K to 0.005.
The Fourier spectrum for a pulse using rectangular pulse modulation is:
F(t) = Apeak (t/2Tp) p ) (2/2π)cos2π(t/2Tp ) + (2/3p)cos3π(t/2Tp ) -(2/4π)cos4π(t/2Tp ) + (2/5 π)cos5π(t/2Tp p) ---> (2)
1/Tp = the pulse repetition rate and t = the pulse width.
Equation 2 nulls when nt = 1.0. The DC component can be ignored.
This is the baseband signal equivalent to the modulating signal F in eq. 1. A difference to be noted is that the carrier cosωtis being turned on and off by F(t) This signal results in the sideband frequency spikes seen in Fig. 3. Frequency spikes with alternating positive and negative phases will cancel so that only the difference in level between them adds to the total sideband amplitude. The total contribution of all of the sideband spikes to the total signal power is only 6 dB (eq. 1), with half of the signal energy in the carrier. When a filter with very narrowband negative group delay is used, the components of the Fourier spectrum can be separated and used independently, such as in this experiment where only the carrier is used. For example, some UNB data-transmission methods remove one sideband and use a single sideband frequency.
In Figure 6 and Figure 7, the spectral component level can be seen to rise and fall with change in pulse width, but the voltage peak seen at the narrowband filter, and the detector outputs does not change as the pulse width is varied. This is because F(t) = Apeak(t/2Tp) changes with t/2Tp, but has no effect on carrier voltage levels or detected output level.
Amplitude modulation utilizing pulses is on/off modulation. A signal is present when it is "on" and not present when it is "off." This is equivalent to a tuning fork that is struck to start ringing. If it is critically dampened, the ringing stops when there is no further energy input. Start and stop are near instantaneous in the present case. For an UNB system, filters with negative or near-zero group delay provide the critical damping. The formula Tg = Q/IF applies. If Tg = 0, then Q = 0. If Q = 0, then Tg = rise and fall time = group delay = zero. Therefore, the filter is critically dampened and doesn't continue ringing with stored energy. It must be fed continuously during the pulse period; ringing stops when the pulse ends.
These measurements show that even when the sidebands are significantly reduced, the AM pulse is still recoverable with only a 6 dB loss. The sidebands are therefore not necessary. It should be noted that this is true only for AM pulses. The sideband removal and SNR improvement is applicable to any AM pulse system, such as pulsed radar systems, UWB communications systems, identify-friend-or-foe system (IFF), tactical-air-navigation (TACAN), distance-measuring-equipment (DME), pulse-amplitude-modulated systems, and pulsewidth-modulated systems. All of these systems can make use of the approach provided that they are based on the use of AM pulses.
For this sideband-removal approach to be effective, it is essential that the sideband-removing filters have zero envelope group delay. Filters that match the Nyquist criteria, of BT = 1, exhibit some group delay, which will cause an RC-like rise time and will shape any pulse passing through them. Figure 5 is an example of a near zero group delay filter where the rise time is one intermediate-frequency (IF) cycle and the Nyquist bandwidth B, from BT = 1, is equal to the IF. The method does not in any way violate Nyquist's criteria, or Shannon's Channel Capacity equation, if the proper bandwidth is used in the equations.
As previously mentioned, this sideband-removal approach cannot be used with audio AM. It also can not be applied to systems with frequency-modulation/phase-modulation (FM/PM), but there are methods to transmit audio using the carrier only with excellent results.1 Only when the frequency islands created by the Fourier transform of eq. 2 are present, can the carrier be used separately. But the approach is effective in pulsed systems such as radar systems. The reduced bandwidth and improved SNR made possible by the approach can increase the radar range of a system by factors of 30:1 to 100:1. This improved radar range also makes it possible for a radar system to benefit from improved resolution, to detect much smaller targets over a much greater distance. It should be noted that illuminated moving targets will exhibit a Doppler frequency shift that may cause a returning signal to be outside of the passband of an UNB filter. But the circuits detailed in the literature of refs. 1 and 4 can correct for these effects.
1 H.R. Walker, Ultra Narrow Band Textbook, available for free download from www.vmsk.org, 224 pp.
2. Merrill Sokolnik, Introduction to RADAR Systems, McGraw-Hill, New York, 1962, p. 21.
3. August W. Rehaczek, Principles of High Resolution RADAR, McGraw-Hill, New York, 1969.
4. Donald G. Fink and Donald Christiansen, Electronic Engineers Handbook, McGraw-Hill, New York, 1989. Chap. 25. This reference, especially Chap. 25, is highly recommended for information on Doppler and Resolution using different Nyquist criteria filters.
5. Mischa Schwartz, Information Transmission, Modulation and Noise, McGraw-Hill, New York, 1951.
6. H.R. Walker, "Apparatus and Method for an Ultra Narrow Band Wireless Communications Method," United States Patent No. 7,424,065, September 9, 2008.
7. Google or Bing on "Negative Group Delay."
8. http://www.vmsk.org, File on NGD.
9. H.R. Walker, "Experiments in Pulse Communications with Filtered Sidebands," High-Frequency Electronics, September 2010, pp. 64-68.