IEEE T R A N S A C T I O N S O N C O M M U N I C A T I O N S , VOL. C O M - 2 7 , NO. 12, D E C E M B E R 1979 1849

The Effects of the Amplitude and Delay Slope Components of Frequency Selective Fading on QPSK, Offset QPSK and

8 PSK Systems DOUGLAS H. MORAIS, MEMBER, IEEE. AKE SEWERINSON. MEMBER. IEEE. AND KAMILO FEHER, SENIOR MEMBER, IEEE

Abstract-Amplitude and delay slope are significant components of inband distortion resulting from multipath fading. In this paper, we pre- sent and compare computer simulated results of signal to noise (S/N degradation for probability of error (Pe) of 10-4, due to these distor- tion components on Quadrature Phase Shift Keying (QPSK), Offset Quadrature Phase Shift Keying (Offset QPSK) and 8 Phase Shift Key- ing@ PSK) systems. For all systems the transmitter and receiver fiiter- ing is modeled so as to provide a 50% excess bandwidth raised cosine spectrum at the receiver detector input. The QPSK and Offset QPSK systems are studied with bit rates of 44.7 Mbits/s, the so-called T3 rate, and the 8 PSK system is studied with bit rates of 44.7 Mbitsls and 67 Mbits/s, a 67 Mbit/s 8 PSK system having the same modula- ted frequency spectrum as 44.7 Mbit/s QPSK and Offset QPSK sys- tems.

When the frequency spectrum is, the same for a l l systems, then for a given amplitude slope, results show that QPSK is the least degraded, followed by Offset QPSK, then 8 PSK, and for a given delay slope, Offset QPSK is the least degraded, followed by QPSK, than 8 PSK.

When the bit rate is the same for all systems, then for a given amplitude slope, QPSK is the least degraded. 8 PSK is less degraded than Offset QPSK for values of amplitude slope less than 0.47 dB/MHz, but more degraded for higher values. For equal bit rates and a given delay slope, Offset QPSK is the least degraded, followed by 8 PSK, then QPSK.

By relating degradation results to published information on the oc- currence of amplitude and delay slope distortion components during multipath fading, estimates of S/N degradation for a P, of 10-4 due to these distortion components as a function of frequency selective fade depth are made.

Finally, measured S/N degradations for a P, of 10-4 due to ampli- tude and delay slope on a 44.7 Mbit/s Offset QPSK system with I - tering similar to the computer model are presented and compared to the computer simulation results.

1. INTRODUCTION

F OR a point-to-point digital microwave system subject to significant multipath fading, the susceptibility of the mod-

ulation method to inband amplitude and delay distortions is very important because the multipath fading is accompanied by such distortion^^^^^^. Depending on the modulation method, these distortioos can result in significant P, versus S/N performance degradation, and hence, significant reduction in the 'fade margin from the flat fade value. That is to say, per- formance being degraded when the transmitted signal is sub-

Manuscript received Jaunary 16, 1979. D. H. Morais is with Farinon Canada Ltd., Dorval, P.Q., Canada. A. Sewerinson was with the Department of Electrical Engineering,

University of Ottawa, Ottawa, Ont., Canada. He is now with GTE Lenkurt (Canada) Ltd., Burnaby, B.C., Canada.

K. Feher is with the Department of Electrical Engineering, Uni- versity of Ottawa, Ottawa, Ont., Canada.

jected to the distortions of multipath fading, the system may reach its mute point for center frequency fade values signifi- cantly less than the fade value had the fading been flat. For many microwave systems, the mute point is set for a P, of lop4. Slope amplitude and slope delay are significant compo- nents of multipath fading inband d i s t o r t i ~ n ~ - ~ , ~ ! ~ . This paper examines the effects of these distortions on QPSK, Offset QPSK and 8 PSK radio systems.

Computer simulation results are given that show S/N degra- dation for a P, of lop4 due to various amplitude and delay slopes. For all systems the transmitter and receiver filtering is chosen such as to create a 50% excess bandwidth raised cosine spectrum at the receiver detector input. With no ampli- tude or delay slope added, the system operates free of inter- symbol interference. However, with either of these impair- ments added, intersymbol interference occurs, and increases as the magnitude of the impairment increases.

The systems are compared for the case where the bit rates are all equal as well as for the case where frequency spectra are all equal. The latter case is of interest in situations where the channel bandwidth is futed and it is important to know the tradeoffs between bit rate and degradation due to slope distortions. The QPSK and Offset QPSK systems are studied with bit rates of 44.7 Mbits/s, the so-called T3 rate, and the 8 PSK system is studied with bit rates of 44.7 Mbit/s and 67 Mbit/s, a 67 Mbit/s 8 PSK system having the same modulated frequency spectrum as 44.7 Mbit/s QPSK and Offset QPSK systems.

It is important to know to what extent P, versus S/N performance is degraded during multipath fading due to ampli- tude and delay slope distortions, since if these degradations are excessive, system reliability will be greatly reduced unless adaptive slope equalizers are employed. Bablerl has published results on the occurrence of amplitude slope distortion during multipath fading and Subramarian et aL3 have published results on the occurrence of delay slope distortion during multipath fading. By relating our results of S/N degradation to these pubiished results, estimated of S/N degradation for a P, of lov4 due to the amplitude and delay slope distortion compo- nents of multipath fading as a function of center frequency fade depth are made.

Finally, measured S/N performance degradations for a P, of loA4 due to amplitude and delay slope on a 44.7 Mbit/s Offset QPSK system with filtering similar to the computer model are presented. These measured results compare favor- ably to the computer simulation results given.

0090-6778/79/1200-1849$00.75 0 1979 IEEE

1850 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-27, NO. 12 , DECEMBER 1979

TRANSMITTER I

I

BINARY TRANSMITTER INPUT -

SOURCE DATA SIGNAL

TRANSMITTER FILTER +

TRANSMISSION IMPAIRMENT

(AMPL OR DELAY) WGN I 1

BINARY GUTPUT 4 -

DETECTOR DATA ERROR

PROB. OF

DETECTOR RECEIVER 1 RECEIVER

A I FILTER

RECEIVER CHANNEL

Figure 1. Block diagram for system simulations

2. COMPUTER SIMULATION DESCRIPTION In the development of a mathematical model to simulate

the modulation methods under study, the real transmitted signal s ( t ) is assumed to be of the form

s ( t ) =&[[x@) -t jy(t)]e'"cf]

= x( t ) cos w,t + y( t ) sin w,t

where w, is the angular carrier frequency and x( t ) + jy(t) is the complex baseband signal.

The information to be transmitted is totally contained in the complex baseband signal and thus, the modulation systems to be studied may be modeled by specifying them in terms of their complex baseband signals. In Ref. 6, pp. 28-37, relation- ships between modulator input data sequences and the re- sulting complex baseband signals are given for a number of modulation methods including those under study here. Our computer program employs the relevant relationships given in Ref. 6. The simulation is carried out entirely in the complex baseband form.

A .block diagram for the systems simulated is shown in Figure 1. The transmitter signal source is composed of shift register 'arrays (two in the case of QPSK and Offset QPSK, three in the case of 8 PSK) which generate long pseudorandom sequences of symbols of a set period. These sequences are then converted into the complex baseband form according to the relationship dictated by the desired modulation. Wherever a filtering operation is called for, fast Fourier transform tech- niques are used. Filtering is performed by transforming the complex baseband signal to the frequency domain, multiplying this frequency domain signal by the complex baseband transfer function of the filter, then transforming the resultant of the multiplication process back to the time domain.

In our model the complex baseband output from the trans- mitter signal source is first filtered by the transmitter filter, then distorted by either a given amplitude or delay slope, and finally filtered in the receiver. For all three systems simulated, the transmitter filter is chosen to be 50% excess bandwidth ideal low pass and the receiver filter to be 50% excess band- width raised cosine, Thus, for each system the transmitter filter limits the transmitted signal within its bandwidth and all filtering to 'create a raised cosine spectrum at the detector input is done in the receiver filter. Note, however, that any combination of transmitter and receiver filtering that results

in the desired raised cosine spectrum would be adequate for our purposes.

In the receiver portion of the simulation, the programming to determine the P, is modulation-dependent. For QPSK and Offset QPSK, the received complex baseband signal is demodu- lated according to the given modulation to give the original sequences modified by the effects of intersymbol interference. In the detector, the average signal power at the input is com- puted, and for each symbol, the peak amplitude relative to its decision threshold is computed. For a specified power of Gaussian noise at the detector input, the individual symbol P, is calculated according to theory'. The average of 'these calculated Pe's over the total transmitted symbol sequence is calculated to give the estimate of P, for the given simulated system. This average P, is associated with the ratio of the average signal power to the specified rms noise at the detector input. For 8 PSK modulation the phasor plane is divided into eight equal sectors, each of which represents a region for correct detection of a complex symbol. The probability of a received complex symbol being in error is simply the proba- bility that the received signal plus noise vector, the signal vector being modified due to intersymbol interference, lies outside the given region. In the simulation, the P, of each complex symbol at the detector input is calculated according to theory6 for a specified power of Gaussian noise, and an average P, obtained by averaging the individual symbol P, over the entire pseudorandom sequence. As in the cases of QPSK and Offset QPSK, this'average P, is associated with the ratio of the average signal power to the specified rms noise at the detector input.

3. PERFORMANCE DEGRADATION DUE TO AMPLITUDE AND DELAY SLOPE

Computer simulation results of S/N degradation for a P, of 10F4 due to amplitude slope on 44.7 Mbit/s QPSK, Offset QPSK and 8 PSK systems, as well as on a 67 Mbit/s 8 PSK system are shown in Figure 2.

When the frequency spectrum is the same for all systems (i.e., 8 PSK at 67 Mbits/s and the 4-phase systems at 44.7 Mbits/s) then, for a given amplitude slope, the amplitude dis- tortion to the filtered spectrum at the detector input of each system is identical. Under this condition our results show that for a given amplitude slope, QPSK is the least degraded, fol- lowed by Offset QPSK, then 8 PSK.

MORAIS e t a l . : FADING AND QPSK, OFFSET QPSK, AND 8 PSK SYSTEMS 1851

0 0.1 0.4 0.5

4 AMPLITUDE SLOPE IdBIMHzI *

Figure 2. Simulated degradation of S/N due to amplitude slope

When the bit rate is the same for all, i.e., 44.7 Mbits/s, the width of the main lobe and side'lobes of the 8 PSK spectrum is only two-thirds that of QPSK and Offset QPSK. Thus, the width of the required raised cosine filtering to the 8 PSK system is only two-thirds of that required to the others. This narrower 8 PSK fdtering means that for a given amplitude slope the amplitude distortion to the filtered spectrum at the detector input of the 8 PSK system is only two-thirds that of the equivalent distortion to the 4-phase systems. As a result, the relative degradations of the systems due to amplitude slope are different as compared to the equal spectrum case. QPSK is the least degraded as before. However, the degradations of 8 PSK and Offset QPSK, compared to each other, depend on the slope amplitude. 8 PSK is less degraded than Offset QPSK for values of slope amplitude less than 0.47 dB/MHz, but more degraded for higher values.

Computer simulation results of S/N degradation for a P, of loF4 due to delay elope are shown in Figure 3. Results are given for the same bit rates as used in the amplitude slope degradation results of Figure 2 .

When the frequency spectrum is the same for all systems and hence delay distortion to the filtered spectrum at the detector input the same for all systems, then, for a given delay slope, Offset QPSK is least degraded, followed by QPSK, then 8 PSK. We note that the order of relative degradation is dif- ferent as compared to the case of degradation due to ampli- tude slope.

When the bit rate is the same for all systems, the relative degradation is different compared to the equal spectra case. Offset QPSK is the least degraded as before. However, the narrower 8 PSK spectrum leads to the 8 PSK system being marginally less degraded than the QPSK system.

The difference in degradation due to both amplitude and delay slope between QPSK and Offset QPSK indicates cross- talk between the in-phase and quadrature channel. Should there be no crosstalk, then degradation to the in-phase chan- nel, say, would be due solely .to intersymbol interference

0 0.2 0.4 0.6 0.8

< DELAY SLOPE IntlMHd *

Figure 3. Simulated degredation of S/N due to delay slope

resulting from the effect of the slope distortion on the in- phase component of the transmitted signal. This degradation would be independent of the timing of the quadrature chan- nel. Degradation to the quadrature channel would be similarly controlled. As a result degradation to the combined channels would be independent of relative channel timing and thus, there would be no difference in degradation between QPSK and Offset QPSK. From the relative degradations of QPSK and Offset QPSK we conclude that amplitude slope results in greater crosstalk to Offset QPSK than to QPSK and that delay slope results in greater. crosstalk to QPSK than to Offset QPSK. As 8 PSK can be viewed as a'multilevel two-dimen- sional system with channels operating in quadrature', then we further conclude that the degradation to 8 PSK is also in part due to crosstalk between the in-phase and quadrature channel.

4. PERFORMANCE DEGRADATION RESULTING FROM SELECTIVE FADING

Bablerl has shown the dependence of amplitude slope on fade depth for a 42 km, 6 GHz system in Georgia. From his Figure 8, it is shown that 30 dB and 35 dB mid-channel fades are accompanied by amplitude slopes in excess of 0.2 dB/MHz and 0.35 dB/MHz, respectively, for 50% of the time. Subramarian et aL3 have shown the dependence of delay slope on fade depth for the same 42 km, 6 GHz system in Georgia observed by Babler. Their Figure 11 shows that 30 dB and 35 dB mid-channel fades are accompanied by average delay slopes of 0.3 ns/MHz and 0.6 ns/MHz, respectively.

1852 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-27, NO. 12, DECEMBER 1979

TABLE I

DUE TO AMPLITUDE SLOPE ACCOMPANYING THE FADE RELATIONSHIP BETWEEN FADE DEPTH ANDSINDEGRADATION

SiN degradation (dB) for BER = lW4 ,due to a”. amplitude slope accompanying fade.

QPSK. Offset QPSK. 8 PSK. 8 PSK, 67 Mbitris

35 dB 3.6 2.9 9 6

. TABLE11 RELATIONSHIP BETWEEN FADE DEPTH AND SIN DEGRADATION

DUE TO DELAY SLOPE ACCOMPANYING THE FADE

SIN d “radatlon (dB1 for BER =lo- 4 ,due to .:$! delay slope accompanying fade.

67 Mbitsls

35 dB 0.9 - 0.2 0 85

I F

. A- PATTERN

GENERATOR

TRANSMISSION

T3144.736 Mblrl 70 MHz 70 MHz 1 AGC

70 g!% T

PHASE NOISE ?i; ’ r ’ L

,-L

70MHr

SHIFTER

70MHr

GENERATOR

lllllillllllllllllilllollli -* . ?

ERROR 1

DETECTOR - ’ MODEM

T3

1 OMHz

PW R METER

Figure 4. Experimental system

.It is of interest to correlate the above results extracted from Babler and Subramarian. et al. with the results presented in Figures 2 and 3, and thus generate relationships between fade depths and system degradatia For example, a 35 dB fade is accompanied on the average 1 y an.,amplitude slope of 0.35 dB/MHz which, from Figure 2, results in an S/N degradation to a QPSK system of 1.7 dB. In a similar fashion, other such relationships have, heen determined and are presented in Tables I and 11. Table I gives the relationship between fade depth and S/N degradations due to the amplitude slope accompanying the fade, and Table I1 gives similar reladonships but for degra- dations due to delay slope. While these relationships are appli- cable only to the theoretical systems studied operating at 6 GHz over a specific path,,it is hoped that they at least provide an order of magnitude of the performance .degradations that can be expected of real systems operating at similar frequen- cies over similar paths elsewhere.

In studying the re.sults given in Tables I and 11, we note that for any given system and fade depth, the degradation due to amplitude slope is larger than that due to delay slope. This finding is in agreement with similar studies by Hartmann and Alleng; Thus, should it be felt necessary to improve system reliability by the addition of an adaptive slope equalizer, then the logical choice for all the systems would be an AMPLITUDE slope equalizer. We also note that the degradation results are strongly dependent on bit rate. The 67 Mbit/s, 8 PSK system is in all cases significantly more degraded than any of the 44.7 Mbit/s.systems.

5. MEASURED RESULTS

A 44.7 Mbit/s,Offset QPSK system .was used to evarlgg performance degradation 8ue to inband distortions. The ; e x -

perimental system is shown in Figure 4. The, transmit and receive modem u&b was a Farinon DM-45 digital modem used in the Farinon DM8-2A-45C, 8 GHz digital radio. The trans- mitter filter and the bandlimiting filter following the noise generator were, both wider than the 50% raised cosine receiver baseband filter and did not contribute to the overall pulse shaping. A sample of the 70 MHz carrier oscillator in the mod- ulator was taken and used in the demodulator to .create a coherent system. This eliminated carrier recovery errors and left intersymbol interference as the characteristic degraded by the inband distortions. Signal and noise powers were measured at the raised cosine baseband filter output located in the receive modem. Measured and simulated degradation, results can thus be compared since the hardware system and the computer model were constructed similarly and equivalent parameters were measured.

The measured S/N degradations for a P, of are shown in Figure 5. The computer simulations show only a s m a l l amount of degradation due to delay slope distortion. The measured results are 0.4 dB worse than the computed values at the highest slope measured (0.8 ns/MHz). For amplitude slope distortions the measured results deviate 1.3 dB from the simulated results at the maximum slope measured (0.29 dB/ MHz). Thus, it is seen that the measured results compare

MORAIS et 41.: FADING AND QPSK, OFFSET QPSK, AND 8 PSK SYSTEMS 1853

I I

0.1 0.2 0.3

* AMPLITUDE SLOPE IdBIMHzI D

0.4

I I I I O 0.2 0.4 0.6

I

< DELAY SLOPE IndMHil D

0.8

Figure 5. Measured SIN degradation due to amplitude slope and delay slope

favorably to the computer simulation results. The main reasons for the deviations between measured and computed results are believed to be imperfections in the actual receiver raised cosine response and that the transmission impairments were not perfectly linear but had some higher order compo- nents.

6. CONCLUSION

Computer simulation results of SIN degradation for P, of 10-4 due to amplitude and delay slope distortions on QPSK, Offset QPSK and 8 PSK systems have been presented. In addi- tion, measured results due to these distortions on an Offset QPSK system have been given which compare favorably wi” the simulation results. By relating the computed degradations to published results on the occurrence of amplitude and delay s l o ~ p distortion components during multipath fading, esti- mates of degradation due to these distortion components as B function of frequency selective fade deR have been made.

REFERENCES , > + l F

I G. M. Babler, “Selectivity Faded Non-Diversity and Space Divers/ty Narrowband Microwave Radio Channels,” B . S . T . J . . Vol. 52. No. 2; Feb. 1973, pp. 239-261.

2. G. M. Babler, “Measurements of Delay Distortion During,Selective Fading.” IEEE International Conference on Communications. June

3 M. Subramarian, K . C. O’Brien and P. J . Pulgris, “Phase Dispension Characteristics during Fade in Microwave Line-of-Sight Radio Channel.” B . S . T . J . . Vol. 52, No. I O , December 1973. pp. 1877-1902.

4 C. Anderson. S . Barber and R. Patel, “The Effects of Selective Fading on Digital Radio,” IEEE International Conference on Communications. June 1978, pp. 33.5.1-33.5.6.

5 P. O’Kelly, “Multipath Fading Simulation for Evaluation of a Digital Microwave Channel.” IEEE Conference on Communications. June

6 H. C. Chan, D. P. Taylorand S . S . Haykin, “Comparative Evaluation of Digital Modulation Techniques: Simulation Study.’’ CRL Internal Report Series. No. CRL-18. Part 111, McMaster University.

7 W. R. Bennett and J. R. Davey. Data TransmiSsion (New York, N.Y.: McGraw-Hill Book Co.) 1965.

8 M. Ramadan. “Availability Prediction of 8 PSK Digital Microwave Systems during Multipath Propagation.” IEEE Conference on Com- munications. June 1979. pp. 32.4.1-32.4.8.

9 P. R. Hartmann andE. W. Allen, “An AdaptiveEqualizerforCorrection of Multipath Distortion in a 90 Mb/s 8 PSK System.’’ IEEE Conference on Communications. June 1979. pp. 5.6.1-5.6.4:

10 K . Feher. “Digital Modulation Techniques in an Interference Environment.” Vol. 9 of the EMC Encyclopedia (Germantown, MD: Don White Consultants, Inc.) 1977.

1974, pp. 12A-I-12A-4.’

1975, pp. 21-1-21-4.

* Douglas H. Morais (M’79), for a photograph and biography, see this issue, p. 1849.

*

Kamilo Feher (M:68-SM’77), for a photograph and biography, see this issue, p. 1750.