SOME FEATURES OF SIGNAL DEMODULATION RESULTING FROM THE PRACTICAL IMPLEMENTATION OF A DIRECT CONVERSION RADIO RECEIVER

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1 Philips J. Res. 41, , 1986 R1l27 SOME FEATURES OF SIGNAL DEMODULATION RESULTING FROM THE PRACTICAL IMPLEMENTATION OF A DIRECT CONVERSION RADIO RECEIVER by R. A. BROWN, R. J. DEWEY and C. J. COLLIER Philips Research Laboratories, RedhilI Surrey RH1 5HA, England Abstract The direct conversion or zero-if radio receiver has been the subject of attention lately as an architecture suitable for VLSI integration and also as a possible basis for a digitally implemented radio. For both of these applications the direct conversion receiver has many advantages over the superheterodyne architecture. To compete successfully with the super het in a multi-mode radio application, the direct conversion receiver must handle all the common analogue modulation schemes: DSB, am, fm and SSB. Any practical receiver will, however, suffer from imperfections in implementation which will cause its performance to depart from ideal. Nevertheless, the direct conversion architecture has been used with great success for SSB reception. This paper considers its extension to the reception of am and fm signals. It is shown that the ac coupling required to block unwanted dc components at the mixer outputs can degrade the subsequent dernodulation of both am and fm but that this can be successfully overcome by adjustment of the receiver local oscillator frequency. PACS numbers: ECO: Introduetion Many applications, for example, pagers and hand portable equipment, require radio receivers which are small, compact and have a low power consumption. Others, such as surveillance receivers and professional and military communications equipment, require receivers which have flexible demodulation and filtering capabilities. The former applications require a receiver which preferably can be integrated onto a single chip thus reducing size, weight and power consumption, while the requirements of the latter can perhaps best be met by implementing as much as possible of the receiver digitally using a programmable digital signal processor (DSP). This approach allows a very flexible receiver, whereby a change in function or mode of operation requires only a change in the software rather than an alteration to the hardware. PhllIps Journalof Research Vol. 41 No

2 R. A. Brown, R. J. Dewey and C. J. Collier The widely used superheterodyne receiver architecture is not ideally suited for integration due to the difficulties of filtering at the non-zero intermediate frequencies (IFs) used. The superhet operates by translating the incoming rf signal to a fixed IF at which most of the amplification and filtering takes place.,the filtering is usually performed by a crystal filter and this component cannot be integrated. Furthermore, if the bandwidth of the passband is required to be varied then additional crystal filters are necessary. An alternative architecture is that of the zero-if or direct conversion receiver in which the rf signal is mixed directly down to baseband by tuning the local oscillator to the same frequency as that of the incoming carrier (fig. I). Digital Demodulator Mixer Low-Pass Filter Fig. 1. Direct conversion radio receiver. A second mixer, fed with a local oscillator signal in phase quadrature to that supplied to the first, is necessary to allow frequencies spaced equally on either side of the carrier to be distinguished. Most of the amplification and filtering is carried out at baseband in this receiver, which makes it suitable for integration since the channel filtering can be implemented with easily fabricated lowpass filters. The ideal digitally implemented receiver is one in which the antenna signal is digitized directly. This is not yet practicable over a sufficiently useful frequency range as AID converters with the necessary sampling speed and resolution are not currently available: Consequently, the frequency and bandwidth of the signal band must be reduced by means of frequency translation and filtering. Both the superhet and direct conversion architectures are suitable and, if subsampling of the IF in the superhet is used, have the same requirements in 220 Philip, Joumol of Research Vot.41 No

3 Some features of signal demodulation terms of AID converter sampling rate and resolution. However, the superhet receiver, because of its non-zero IF, makes more stringent demands upon sample and hold aperture uncertainty time than does the direct-conversion receiver with its lower-frequency signals. The direct conversion receiver would therefore appear to have advantages over the superhet as regards its ability to be integrated and its suitability for use as basis of a digitally implemented radio. A completely general-purpose direct conversion receiver would be required to handle all the common analogue modulation schemes - am, fm and signal sideband (SSB)- as successfully as does the superhet architecture. The use of such a receiver architecture for the reception of single sideband signals using both the phasing method 1) and Weaver's method 2,3) has been well documented. However, the reception of am and fm signals has not been so well documented and so this has been studied 4,6) as part of a program of work on digitally implemented radio transceivers. Any practical receiver will always suffer imperfections which can degrade its performance. This paper considers in detail the effect of ac coupling, required to remove de offsets from the front-end mixers, on the reception, by a direct conversion receiver, of am and fm signals. Although the work reported here deals with digitally implemented demodulators, the results are completely general and equally applicable to analogue implementations. 2. Am and fm demodulation algorithms Conventional am and fm demodulators cannot be used directly with the zero-if receiver since the information is carried in two channels rather than one. Consequently alternative algorithms must be devised. Any modulated signal can, in general, be represented as s(t) = A(t) cos(w c t + tp(t)), (1) where A(t) is the amplitude, tp(t) is the phase, t is time and Wc is the angular carrier frequency. This signal can be written in terms of in-phase and quadrature components. s(t) = I(t) cos Wc t - Q(t) sin Wc t, (2) where l(t) = A(t) cos tp(t) and Q(t) = A(t) sin tp(t).. I(t) and Q(t) are the signals that would be produced by the in-phase (I) and quadrature (Q) channels of the direct conversion receiver. The envelope is given by (3) Phillps Journalof Research Vol. 41 No

4 R. A. Brown, R. J. Dewey and C. J. Collier and the phase by (/J(t) = tan:" (Q(t»). I(t) (4) With an am signal the message waveform is contained in the carrier envelope and so eq. (3) can be used to recover this information. Fig. 2 illustrates this envelope detection algorithm for am demodulation. I CHANNEL Q CHANNEL Fig. 2. Am envelope detector. With fm it is the rate of change of phase which carries the modulation and so the required demodulator output can be obtained by differentiating (/J(t) to give d(/j(t) = ~ [tan -1 (Q(t) )J. dt dt I(t) This is the basis of the fm demodulation (5) algorithm shown in fig. 3 which will I CHANNEL Q CHANNEL Fig. 3. Arctan fm demodulator. 222 Phillps Journalof Research Vol.41 No

5 Some features of signal demodulation be referred to as the arctan algorithm. Upon differentiation it is found that J(t). dq(t) _ Q(t). d/(t) dcp(t) dt dt dt J(t)2 + Q(t)2 (6) This scheme is illustrated in fig. 4 and will be referred to as the differentiate and multiply (DAM) algorithm. Note that the term in the denominator which normalizes any amplitude variations has not been included. DEMODULATED FM Fig. 4. Differentiate and multiply (DAM) fm algorithm. Now approximating the differential terms in the above expression by d/(t) J(t) - J(t - r) and _dq_(_t) = -=Q...:...(t.:. ) _-_Q=--(_t - c_i) dt i dt i' where i is an arbitrary time delay, dcp(t)/dt can be written dcp(t) 1 J(t) Q(t - i) - Q(t) J(t - i) ---=_ dt i (7) This algorithm is shown in fig. 5 and will be called the time delay and multiply (TDM) algorithm. Here again the normalization term has been ignored along.with the l/i scaling {actor. An analysis reveals that this algorithm does not yield a linear approximation to dcp(t)/dt but rather one of the form Ji:'o(t) oe: sin(cp(t) - cp(t - r)), (8) where V o is the demodulator output voltage. Philips Journalof Research Vol. 41 No

6 R. A. Brown, R. J. Dewey and C. J. Collier TIME DELAY TIME DELAY Fig. 5. Time delay and multiply (TDM) fm demodulator. 3. Direct conversion receiver imperfections Any practical receiver will deviate from the ideal in several areas, some of which are: channel matching, local oscillator mis-tuning, circuit de offsets and mixer de offsets. It is the de offset appearing at the output of the two mixers that poses the greatest difficulty for signals which contain a carrier component such as classical am and fm) and it is this problem which is considered here. This offset arises from a combination of imperfect mixer balance and from the mixing down to dc of local oscillator leakage appearing at the rf port. A good double-balanced diode ring mixer may have an isolation between the local oscillator and rf signal ports of 40 db which, for a local oscillator drive level of 10 dbm and a mixer conversion loss of 6 db, will result in a de component of several millivolts. This can be much greater in amplitude than the wanted baseband signal which may only be of the order of microvolts and would cause the post-mixer amplifiers and filters to saturate unless removed. This could be accomplished by adding an equal but opposite de component to the mixer output to effect cancellation but this is difficult as the unwanted de component is not, in general, constant but varies unpredictably. A more practical method is to ac-couple the mixer output, which will remove the unwanted de-component but unfortunately will also remove the wanted 224 Phillps Joumal of Research. Vol. 41 No

7 Some features of signal demodulation. de-component produced by the down-converted carrier of the incoming signal. This has been found to affect the subsequent recovery of the modulating signal with both am and fm demodulation. 4. Approximate analysis The effect of ac-coupling is not readily amenable to a simple analysis and so extensive use has been made of computer simulation. However, some indication of the likely effect can be obtained in the following way. The purpose of ac-coupling is to remove the large unwanted de component from the output of the front-end mixers. In doing this, though, the wanted dc component in the signal itself is also removed. The ac-coupling can therefore be modelled to some extent by assuming it to be equivalent to adding an equal but opposite de component to the signal. The I and Q channel signals can then be written as and I'(t) = I(t) + D Q'(t) = Q(t) + E, where D and E are the added de components. The TDM and DAM fm demodulation algorithm (eqs 5 and 6) can be applied quite simply to produce the following outputs: Vo(t) = A2 sin(tp(t) - tp(t - r) + D(Q(t) - Q(t - r) + E(I(t - r) - I(t» for the TDM algorithm and for the DAM demodulator Vo(t) = dtp(t) (A2 + D. I(t) + E Q(t». dt In both cases a proportion of the original I and Q channel baseband signals appear at the demodulator outputs in addition to the correct demodulated signal. Since the baseband I and Q signals consist of the down-converted and folded sidebands of the received fm signal, then, if the receiver is exactly ontune, these sideband will appear at the demodulator output as frequency components occurring at multiples of the modulating signal frequency and cannot be distinguished from those due to harmonic distortion. Thus the ac coupling should produce an apparent increase in harmonic distortion. The arctan fm demodulator (eq. (4» and the envelope detector for am (fig. 2) are not so readily analysed. Results, obtained both from computer simulation and from experimental measurements using a digital signal processor for the Phlllps Journalof Research Vol. 41 No

8 R. A. Brown, R. J. Dewey and C. J. Collier receiver, are presented to illustrate in more detail the effects of ac coupling on direct conversion am and fm demodulator performance. Experimental measurements were carried out on only two of the three fm demodulation algorithms - the DAM and TDM - since these are more easily implemented on the digital signal processor than the arctan algorithm. The digital signal processor (DSP) used was a TMS 320 which has a 16 bit word length and a hardware multiplier capable of forming a 32 bit product. In order to digitize the I and Q channel signals from a direct conversion front-end, 14 bit AID converters were used, operating at a 40 khz sample rate. The differentiation required by the DAM algorithm was performed using a 4 section finite impulse response (FIR) differentiating filter while the square root required by the am envelope detector was carried out using a successive approximation technique to an accuracy of 7 bits. 5. Results In this section results of simulation and experimental studies are presented. An audio modulation consisting of a single tone is applied to a carrier using either am or fm as appropriate. The effect of receiver ac coupling on the demodulated output is considered in detail. Fig.6 illustrates the output spectrum resulting from a computer simulation of the am envelope detector with no unwanted dc component present and dc coupling throughout. It can be seen that the 1.8 khz modulating tone - chosen because it lies in the centre of the voice band - is some 60 db above the noise arising from the 7 bit accuracy of the square root routine. The corresponding time waveform is shown in fig. 7. Fmod == 1.8kHz Depth of modulation == 80"; Fsample = 40kHz -10 ~ -20 (IJ ~ -30 o 2 40 :J ~ -50 «w -60 > j -70 ~ FREQUENCY(kHz) Fig. 6. Spectrum of de-coupled envelope detector (successive approx. sq. root). 226 Philips Journalof Research Vol.41 No

9 Some features of signal demodulation Fmod = 1.8kHz Depth of modulation = 80% Fsample = 40kHz 0.6 ~ ~ 0.5 ::J f- 1\ ~ 04 ~ \ z; 0.3 ~ ü Vi ~_J ::J o ::> w o 0.1 I I \,I V 0.0 L o L 25 L Fig. 7. Time waveform of de coupled envelope detector (successive approx. sq. root), vertical scale is in arbitrary units. When ac-coupling was introduced into the simulation it was found that the demodulator output spectrum worsened considerably. Fig. 8 plots the resulting power spectrum. In this case (and most of the others discussed here) the ac-coupling was carried out using a first order RC time constant corresponding to a 3 db cut-off frequency of 50 Hz. It can be observed that the frequency component at twice the original modulating frequency is dominant, being some 20 db larger than the fundamental. This is readily apparent from consideration of the corresponding time waveform shown in fig. 9, where the signal has an appearance rather like that which would result from full-wave ree- Fmod = 1.8kHz Depth of modulation = 80% Fsample = 40kHz AC cut-off = 50Hz -10 ~ -20 CD w o ~ -40 :J ~ -50 <r w -60 > j -70 ~ FREQUENCY (khz) Fig. 8. Spectrum of ac-coupled (50 Hz) envelope detector (successive approx. sq. root). Philip. Journalof Research Vol. 41 No

10 R. A. Brown, R. J. Dewey and C. J. Collier Fmod = 1.8kHz Depth of modulation = 80% Fsample = 40kHz AC cut-off = 50Hz w Cl 0.25 ::::l... ::J I ::E 0.20 «-' «z 0.15 (!) Vi Cl ~ -' ::::l 0.10 Cl ::E w Cl L SAMPLE NUMBER Fig. 9. Time waveform of ac-coupled (50 Hz) envelope detector (successive approx. sq. root), vertical scale is in the same arbitrary units as in fig. 7. tification. When voice modulation is applied, the demodulated speech is unintelligible. This distortion is due to the loss of the carrier component in the received signal which is down-converted to de and not passed by the ac coupling network. This loss could be avoided if the carrier were down-converted, not to de, but to an ac component sufficiently high in frequency to pass through the ac-coupling network. This can be achieved by deliberately mis-tuning the local oscillator in the receiver so that it is no longer a true zero-if receiver but operates instead with a small (compared to the signal bandwidth) non-zero IF. An analysis of the envelope detector reveals that its performance is not affected, in the case of de-coupling, by a local oscillator offset and so this technique should result in an improvement in performance when ac is coupled. This has been found to be so, as can be noted from the graph of fig. 10. Here the levels. of the second and third harmonic components, relative to the wanted fundamental tone, are plotted as a function of local oscillator offset. Both experimentally measured and simulated results are shown. It can be seen that, although the second harmonic is initially much longer than the fundamental, it decreases rapidly, reducing to 40 db below the fundamental for an offset of several hundred Herz. This level is sufficient for good-quality speech communication. Good agreement is obtained between experiment and simulation. The fm demodulation algorithms were affected similarly by the ac-coupling. The simulations revealed that, even for the ideal case of perfect error free I and Q channel signals, both the DAM and TDM demodulators produced odd 228 Phlllps Journalof Research Vol. 41 No

11 Some features of signal demodulation Fmod = 1.8kHz Depth of modulation = 80% Fsample = 40kHz AC cut-off = 50Hz "id' 10.:!lz o ~ -to o lïi -20 is I.&J -30 > ~ J ~ ' -70 L-, -'---' L...LLL.J_--'----'--'---'-l..J...l...L ~ ~ ~ OFFSET FREQUENCY (Hz) -60 Experimenta~ Simulation Fig. 10. Effect of local oscillator offset on ac-coupled envelope detector (successive approx. sq. root). order harmonic distortion. The DAM demodulator is theoretically distortionfree but the distortion produced here is due to the imperfect realization of the differentiating filters. The largest component was found to be the third harmonic, which, for the 2 khz deviation typicalof narrow-band fm, was about 50 db below the fundamental. This level of performance is more than adequate for good-quality voice communication. When ac-coupling was introduced, the distortion increased considerably as with the am demodulator. Fig. 11 shows the effect of the local oscillator offset on the TDM fm demodulator. Again both experimental and simulation results are plotted with good agreement Fmod = 1.8kHz Fdev = 2kHz Fsample = 40kHz AC cut-off = 50Hz 'éii'.:!l- -io...j z ~ -20 UJ ::::; Cl z 2-40 ~ UJ -50 > j -60 UJ a: z >= a: -80 ~VI 10' a :_~---- p..c 2nd DC 3rd ~ 10' OFFSET FREQUENCY (Hz) Experimental Simulation 10' Fig. 11. Effect of local oscillator offset on ac- and de-coupled TDM demodulator. Phlllps Journalof Research Vol. 41 No

12 R. A. Brown, R. J. Dewey and C. J. Collier being obtained. As with the envelope detector for am, increasing the local oscillator offset reduces the distortion components and in the limit they tend towards these values that would be achieved with de coupling. The offset required to reduce the distortion to an acceptable level for satisfactory voice communication is several hundred Herz for an ac cut-off frequency of 50 Hz but this can be reduced by lowering the cut-off point further, Fig. 12 illustrates Fmod = 1.8kHz Fdev = 2kHz Fsample = 40kHz AC cut-off = 1Hz 'id'.:g J ~ -20 w ::; z 2-40 g w -50 > j -60 w ct: AC - 2nd AC3rd --_ ~ -~~~~~~~----~~~~~----~ --- DC 3rd --- DC 2nd ~ -BO L- ~~~~WiL ~~~_w~ ~ ~ ~ ~ Cl OFFSET FREQUENCY (Hz) Fig. 12. Experimental effects of local oscillator offset on ac- and de-coupled DAM fm demodulator. the improvement obtained experimentally using the DAM algorithm and a cut-off frequency of 1 Hz. It should be noted that the experimental results of figs 5 and 6 for de-coupling were only obtainable using a specially built direct conversion receiver and under closely controlled laboratory conditions and that de-coupling would not be possible with a more practical receiver under typical operating conditions. 6. Conclusions It has been shown, both by simulation and experiment, that the ac-coupling necessary to block the de offsets present at the front-end mixers of the direct conversion receiver degrades the performance of both am and fm demodulators. This is due to the loss of the carrier in the received signal which is downconverted to de and rejected by the ac-coupling network. It was, however, shown that off-tuning the local oscillator in order to down-convert the carrier to a frequency which would pass through the de block, resulted in greatly improved demodulator performance. The frequency offset required was several times the 3 db cut-off frequency of the first order de block and this was suffi- 230 Phlllps Journalof Research Vol.41 No

13 Some features of signal demodulation cient to enable the direct conversion receiver to demodulate both am and fm successfully. While the local oscillator offset is successful in reducing the distortion caused by the ac-coupling it can produce side effects. For instance, channel. mismatch and de-offsets can cause a tone, related to the offset frequency, to appear at the demodulator output. This tone appears as an annoying background whistle and.can be particularly obtrusive during pauses in the speech. However, this effect is easily overcome. The direct conversion receiver has been proven to be a successful architecture for the reception of SSB signals and would appear to be equally viable for the reception of double sideband am and fm to yield a receiver which can offer considerable advantages over the more common superheterodyne receiver. 7. Acknowledgement The authors acknowledge the assistance of Paul Bucknell in programming TMS algorithms and of Richard Salmon and John Naylor in performing experimental measurements. REFERENCES 1) D. E. Norgaard, Proc. IRE 44, 1735 (1956). 2) D. K. Weaver, Proc. IRE 44, 1703 (1956). 3) W. A. Painter, Proc.IERE Conference on Radio Receivers and Associated Systems, Leeds, England (1981). 4) R. A. Brown, R. J. Dewey and C. 1. Collier, Proc.IERE 3rd International Conference on Land Mobile Radio, Cambridge, England (1985). 6) R. A. Brown, R. J. Dewey and C. J. Collier, to be published in Proc.IERE 2nd International Conference on Radio Receivers and Associated Systems, Bangor, Wales (1986). Phillps Journalof Research Vol. 41 No

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