Contains reports on two research projects

Gutwein, J. M.

Helgesson, A. L.

DSpace@MIT

XI. MODULATION THEORY AND SYSTEMSProf. E. J. Baghdady J. M. Gutwein R. B. C. MartinsProf. J. B. Wiesner A. L. Helgesson C. MetzadourJ. T. Boatwright, Jr. B. H. Hutchinson, Jr. D. D. WeinerA. ADDITIVE SYSTEMS FOR FM SIGNAL-TO-NOISE-RATIO IMPROVEMENTA theoretical investigation of the statistical difference between FM signals andnarrow-band random noise has been completed. It was found that for most practicalmodulation conditions, the autocorrelation function of noise drops off more rapidly as afunction of the time shift, T, than does that of an FM signal.This statistical difference can be used to increase the signal-to-noise ratio bybuilding circuits that form weighted sums of time-delayed versions of the signal plusnoise. The signal-to-noise-ratio improvement that can be achieved in a particular addi-tive circuit is a function of the i-f bandwidth, the degree of modulation of the signals,and the statistics of the modulating waveform. It is possible to find a time delay thatwill maximize the signal-to-noise-ratio improvement.Additive systems may be used in combination with limiters to achieve greaterimprovement for input signal-to-noise ratios greater than 0. 35. The improvementachieved by limiting takes advantage of the first-order statistical difference betweensignal and noise, and it is therefore independent of the improvement in additivesystems, which use second-order statistical differences.An important disadvantage in additive systems in which time delay is used is that adistortion of the modulation occurs. The distortion depends on the number of additionsperformed by the system and the amount of time delay involved. For simple circuits,the amount of distortion can be computed, but for circuits involving many additions, anexact computation of the distortion is very difficult, and approximate solutions have beenmade. The amount of distortion introduced is a function of the same parameters as thosethat affect the signal-to-noise-ratio improvement. Therefore, any linear, or nonlinear,additive system in which time delays are used trades distortion for improvement insignal-to-noise ratio.The many numerical details supporting these conclusions have been prepared forpresentation in a Ph. D. thesis.A. L. HelgessonB. CAPTURE OF THE WEAKER OF TWO COCHANNEL FM SIGNALS1. Discussion of System and ObjectivesA third form of the dynamic -trapping technique for capturing the weaker of twocochannel, coherent FM signals has been studied experimentally. The system illus-trated in Fig. XI-I is based on the "fixed-trap" concept; but, unlike the trap systems131(XI. MODULATION THEORY AND SYSTEMS)E I E MXWITH FIXED UUNVENiIUNAL AFEQUALIZER MIXER TUNED TRAP AT MIXER FM DEMODULATOR OUTPUTCENTER OF BANDINPUT AMPLIFIERLOCALCONVERTER N OSCILLATORWEAKER- (FREQUENCY,wo)SIGNALSUPPRESSORFig. XI-1. Fixed-trap system that does not require predetection of thestronger signal.investigated previously (1, 2, 3), it does not require prior demodulation of the stronger(undesired) signal. This avoids the necessity of providing for more than one demodu-lator or for critical circuits such as time-variant filters, or a time-variant (modulated)local oscillator.The operation of the system may be described as follows. The output of thei-f amplifier is split into two unilateral independent channels. The upper channel con-tains a delay equalizer whose function is described below. The lower channel containsa weaker-signal suppressor (a cascaded section of narrow-band limiters with, or with-out, feedforward). This device performs the preliminary operation of suppressing theamplitude of the weaker (desired) signal with respect to the stronger (undesired) signal.Assume for the moment that this device is able to achieve complete weaker-signal sup-pression so that in the output of this suppressor we have essentially the stronger signal.This stronger signal is heterodyned with a local oscillator whose frequency, wo, is fixedat the center frequency of the bandpass trap filter in the upper channel. The output ofthis stage of conversion after filtering, econv(t), consists essentially of the strongerFM signal whose spectrum has been linearly translated to a new i-f frequency, el - o"It is important to note what this suppression-conversion operation accomplishes. Itproduces a third FM signal, econv(t), whose instantaneous frequency differs from theinstantaneous frequency of the stronger signal in the output of the delay network by aconstant that equals the fixed center frequency of the trap (or the local-oscillator fre-quency).The signal econv(t) drives two mixing stages. The output of the first stage consistsof two signals. One is a constant-frequency signal whose frequency coincides with thecenter frequency of the trap attenuation band. The other signal has the same centerfrequency but is frequency-modulated by the algebraic sum of the modulations of boththe weaker and stronger signals. The second mixing operation restores the originalfrequency modulation to the signals modified by the trap. The output of the second mixerdrives a conventional FM demodulator that will capture the message of the (relatively)augmented weaker signal, with negligible distortion, provided that the amplitude ratioat the input to the system exceeds the trap center-frequency attenuation by132(XI. MODULATION THEORY AND SYSTEMS)a sufficient margin.In practice, we are able to realize only partial presuppression of the weaker signal,so that although e conv(t) is predominantly the stronger signal, it still contains, to asmall degree, the effect of the weaker signal. One of the objectives of this feasibilitystudy was to determine to what degree the weaker-signal suppressors must presuppressthe weaker signal.2. Design FeaturesIn conducting observations and evaluating the fixed-trap system, we determinedthat, in order to achieve the required high degree of correlation between thestronger signals in both channels that feed the first mixer stage, it was nec-essary to include a delay equalizer in the upper channel of the system as shownin Fig. XI-1. This delay equalizer compensates for the time delay of the mes-sage of the stronger signal encountered in the filters of the suppressor-converterchannel. Since the shape of the phase characteristic of the equalizer is approxi-mately the shape of the phase characteristic in the suppressor-converter channelfilters, the equalizer also compensates for the frequency-modulation distortionintroduced into the stronger-signal message by the nonlinearities of the suppressor-converter channel filter phase characteristics.The weaker-signal suppressor consists of a cascaded section of narrow-band lim-iters whose design features included:a. Low limiting threshold (approximately 0. 5 volt);b. Rapid-acting limiters (6BN6 limiters, based on the plate-current saturationmode of operation);c. Limiter characteristic optimized for flatness (minimum fluctuation of outputamplitude);d. Narrow-band filter following each limiter having a flat passband and a well-defined bandwidth equal to the i-f filter bandwidth (200 kc at 3 db pts). (For these partic-ular limiter-filter bandwidths, the maximum input amplitude ratio that can be handledby the limiter so that the limiter will achieve suppression of the weaker signal isa = 0. 863. For amplitude ratios greater than this, the suppression properties of theseparticular limiters are poor.)A rejection amplifier utilizing a bridged-T network in a negative feedbackloop was designed to provide the trap characteristics. This design facilitatedtrap-bandwidth control, trap-null-location control, and trap-attenuation control.This trap filter was placed in cascade with a bandpass filter (BW = 300 kc) toprovide the required fixed-trap depression at the center of the frequency responsecharacteristic of the bandpass filter.133100-- - -90-80 -700 403  0 20 - / FREQUENCY DEVIATION OF EACH SIGNAL 75K_ J SIGNAL A: SIGNAL B0D 400 CYCLE COMPONENT 1000 -CYCLE COMPONENT0 -0,04 0001 0.10 1.0S20AMPL FREUENCY DEVIATIOITUDEN OF EACH SIGNAL NTERFE NCE RA75KSEQUAL CENTER FREQUENCIESS 10 - -9 0 -- I - DISTORTION N0.001 . 1 .10 0 CPSAMPLITUDE INTERFERENCE RATIO, a(a)EQEQUAL CENTER FREQUENCIESTRAP SETTING FIXED100o / DISTORTION ON 1000 CPSS90-S / DISTORTION ON 400 CPS /0 o 100- CPS FUNDAMENTALS 001 400-CPS FU0 DAMENTAL0 1000C) 50-B c 40_AMPL DISTORTION ON I00TERFERENCEPS DISTORTION ON 400PSRATIO, aw a 20- 400-CPS FUNDAMENTAL 1000-CPS FUNAMENTALAMPLITUDE INTERFERENCE RATIO, a(b)EQUAL CENTER FREQUENCIESTRAP SETTING FIXEDz DISTORTION ON 400 CPS DISTORTION ON 1000 CPSO0- 80-1000-CPS FUNDAMENTI 400-CPS FUNDAMENTL \uo 70-I- \ DISTORTION ON 1000 CPS0.0011 DISTORTION ON 400 CPS I0AMPLITUDE INTERFERENCE RATIO, a(c)134EQUAL CENTER FREQUENCIESTRAP SETTING FIXEDDISTORTION ON 400 CPS DISTORTION ON 1000 CPS' /-- - - _ r ..../7o C ---OIO IOAMPLITUDE INTERFERENCE RATIO, a(d)1000EQUAL CENTER FREQUENCIESTRAP SETTING FIXED1000- CPS FUNDAMENTAL 400-CPS FUNDAMENTALDISTORTION ON DISTORTION ON400CPS 1OOOCPS0.10 1.0AMPLITUDE INTERFERENCE RATIO, a(e)Capture curves of system response. (a) Complete weaker-signalpresuppression (predetection of stronger-signal simulated).(b) Weaker-signal suppressor: four narrow-band limiters; delayequalized; frequency deviation of each signal, ±35 kc. (c) Weaker-signal suppressor: four narrow-band limiters; delay equalized;frequency deviation of each signal, ±75 kc. (d) Weaker-signalsuppressor: two narrow-band limiters; delay equalized; fre-quency deviation of each signal, ±75 kc. (e) Weaker-signal sup-pressor: two narrow-band limiters; delay unequalized; frequencydeviation of both signals, ±75 kc.135Fig. XI-2.(XI. MODULATION THEORY AND SYSTEMS)3. Results of TestsFigure XI-2 shows some capture characteristics of the receiver performance.Figure XI-3 illustrates some of the demodulated weaker-signal message waveformspertinent to the tests and curves presented in Fig. XI-2. A summary of the deductionsmade from these capture characteristics will now be given.a. Figure XI-2a shows characteristics obtained by simulating complete weaker-signal suppression. The system for this test was connected by applying the strongersignal (from a laboratory FM generator) directly to the converter. This stronger signalwas also added (at the equalizer input) to a second signal from another FM generator tocreate the interference situation. This is the manner in which Sheftman conducted mostof his tests of the fixed-trap circuit (2).In our test, it was desirable to determine whether or not the response of redesignedfixed-trap circuit was as good as, or better than, the response of Sheftman's circuits.Among other features, the inclusion of a delay equalizer in the system resulted inimproved capture of the weaker signal. Capture of the weaker signal was achieved foran input amplitude ratio of a = 0. 02, with less than 10 per cent distortion for all con-ditions of modulation of the weaker and stronger signals. Although there was consider-able improvement, the same trends of response that Sheftman experienced were alsoexperienced with this system. Apparently the delay equalizer did not provide adequatecompensation, and so the response still varied with the modulation conditions of bothsignals.b. The rest of the capture curves (Fig. XI-2b, 2c, 2d, and 2e) show the response ofthe system connected as shown in Fig. XI-1. The first test was run to determine thevariation of response with varying conditions of modulation of the weaker and strongersignals for a fixed degree of weaker-signal suppression (four narrow-band limiters). Incomparing Fig. XI-2b with Fig. XI-2c, we note that the weaker-signal capture perform-ance of the system that has limiters to presuppress the weaker signal varied in accord-ance with the frequency modulation of both cochannel FM signals. The worst captureperformance (Fig. XI-2b) occurred when both signals were centered in the i-f band andthe frequency deviated only ±35 kc, or one-fourth of a limiter bandwidth. For thesedeviations, the amplitude of the detected weaker-signal fundamental component was only70 per cent of the full modulation with 45 per cent attendant distortion.The best capture performance occurred when both signals were fully deviated ±75 kc,or one-half of a limiter bandwidth. Figure XI-2c shows the characteristic for these con-ditions. For these deviations, the amplitude of the detected weaker-signal fundamentalcomponent was 90 per cent of the full modulation with only 17 per cent attendant distor-tion.The reason for the poorer response when the frequency deviation was decreased with136(a)a= 0. 8Fundamental = 99%Distortion = 6%(b)a = 0. 1Fundamental = 98%Distortion = 7%(c)a= 0. 05FundamentalDistortion= 91%= 17%Weaker-Signal Modulation75-kc deviation1000-cps modulating frequencyStronger-Signal Modulation75-kc deviation400-cps modulating frequency(d)a= 0.8Fundamental = 99%Distortion = 8%(e)a = 0. 1FundamentalDistortion= 92%= 15%a = 0. 05Fundamental = 59%Distortion = 57%Weaker-Signal Modulation75-kc deviation400-cps modulating frequencyStronger-Signal Modulation75-kc deviation1000-cps modulating frequencyDemodulated weaker-signal waveforms. Weaker-signal suppressor:two narrow-band limiters; delay unequalized, 5 Fsec.137Fig. XI-3.(XI. MODULATION THEORY AND SYSTEMS)respect to the limiter bandwidth was that for smaller deviations, the suppression prop-erties of the limiters were impaired. As a result of this impaired suppression of theweaker signal, the fixed-trap circuit was unable to adequately suppress the strongersignal with respect to the weaker signal, and poor capture performance resulted.c. A third test (4) was conducted in which four limiters were used, while fullydeviated signals were applied to the system. The trap attenuation was optimized at eachsetting of a. Quite surprisingly, optimizing the trap at each setting of a did not improvethe capture of the weaker signal in the capture region where a >> 5 (5 is the finite traptransmission at center frequency). The only effect of optimizing the trap was to shiftthe capture transition region to a lower a ratio.d. In comparing Fig. XI-2c with Fig. XI-2d, we note that the capture performanceof the system was not significantly affected by a reduction in the degree of weaker-signalsuppression for situations with the delay equalized. When the number of weaker-signalsuppressor limiters was reduced from four to two, the capture of the weaker signaldropped from 90 per cent to 80 per cent with a slight rise in distortion from 17 per centto 20 per cent. It is evident from all of these capture characteristics that the capturetransition region centered near a = 1 is quite sharp. In this region the suppressionproperties of the limiters are known to be very poor, but still we achieved weaker-signalcapture. These results indicate that there is not necessarily any great need for havinga high degree of weaker-signal suppression to realize intelligible response.e. Figure XI-2e is a capture plot obtained by using two narrow-band limiters withfully deviated signals. In this test the delay between the two channels feeding the firstmixer was unbalanced approximately 5 Lsec. The effect of an unbalance in the delayequalization resulted in an expected reduction in the range of a over which the weakersignal was satisfactorily captured.The reduction in the range of a over which capture was achieved was more notice-able when the modulating frequency of the interfering signal was the higher audio-frequency component because, then, the fixed time delay represented a greater phaseshift. But even with this reduction in capture range, satisfactory capture of the weakersignal was still achieved with less than 10 per cent distortion over a range of a extendingfrom a = 0. 1 to a = 0. 9.f. The effect of an unbalance in the delay equalization resulted in an unexpectedimprovement in the capture of the weaker signal for the same conditions of weaker-signal suppression (compare Fig. XI-2d with Fig. XI-2e). For all situations investi-gated (5), whenever the delay was unbalanced, the capture of the weaker signal was inexcess of 95 per cent, with attendant distortion below 10 per cent.The reason for this improved response when there is a small delay differential (evenfor situations in which we have only partial weaker-signal suppression, that is, withtwo limiters) is that there is a reduction in the correlation between the weaker signal138(XI. MODULATION THEORY AND SYSTEMS)in the output of the delay equalizer channel and the residual weaker signal in the outputof the suppressor-converter channel. The reduction in this correlation prevents removalof the weaker-signal modulation; this would occur when the delay is balanced for partialweaker-signal presuppression. As a result, the weaker signal does not suffer as severean attenuation by the trap as it would if the correlation were preserved (delay balanced).This same argument could also be applied in reference to the stronger signal, and itwould seem that the system would work poorly, if at all. However, from Sheftman's (3)tests (complete weaker-signal presuppression), in which the delay was unbalanced con-siderably, we note that the fixed-trap system is still operative. The only deterring effectthat the delay unbalance had was to reduce the range of a over which capture of theweaker signal was achieved. For our test conditions, in which only partial presuppres-sion of the weaker signal is realized, apparently, there would be a compromise delaydifferential that would result in optimum capture performance over a wide range of a.However, the value of this delay unbalance was not determined in these tests.g. The capture-transition region centered at a = 1 is affected only slightly by theinclusion of more weaker-signal suppressors. However, the suppression ability of thelimiters does have some effect in this region of the characteristics. With poorer limi-ters or with a feedforward circuit that was effective only up to a = 0. 75, a broadeningof this capture transition was noted. A significant improvement (narrowing) of thistransition region was again noted when the delay was unbalanced (5 [psec).In conclusion, the results of tests of the system (Fig. XI-1) indicated that satis-factory, intelligible response can be achieved for almost all conditions of modulationof both signals just by using two narrow-band limiters as weaker-signal suppressorsin conjunction with a small delay differential between each channel. Capture of thefundamental component exceeded 90 per cent of full modulation, with a total distortionlevel below 10 per cent (after 3 kc of lowpass filtering). This capture performance wasachieved for interference ratios in the range 0. 1 < a < 0. 9.J. M. GutweinReferences1. E. J. Baghdady, New developments in FM reception and their application to therealization of a system of "power-division multiplexing," IRE Transactions on Commu-nications Systems (PGCS) pp. 147-161, September 1959.2. F. I. Sheftman, A Fixed-Trap System for Capturing the Weaker of Two CochannelFM Signals, S. M. Thesis, Department of Electrical Engineering, M. I. T. , September1958.3. G. J. Rubissow, Dynamic Trap for Capture of Weaker Signal in FM Interference,S. M. Thesis, Department of Electrical Engineering, M. I. T. , January 1958.(References continued on following page)139(XI. MODULATION THEORY AND SYSTEMS)4. J. M. Gutwein, The Capture of the Weaker of Two Co-channel Frequency-Modulated Signals, S. M. Thesis, Department of Electrical Engineering, M. I. T. ,June 1960; see p. 170.5. Ibid., see Chapter 8.140

Modulation Theory and Systems

http://dspace.mit.edu/bitstream/1721.1/53433/1/RLE_QPR_058_XI.pdf

Modulation Theory and Systems

Abstract

Similar works

Full text

Available Versions

DSpace@MIT