required bandwidth, unwanted emission, and data power efficiency for residual and suppressed carrier...

34 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATABILITY, VOL. 31, NO. I , FEBRUARY 1995

Required Bandwidth, Unwanted Emission, and Data Power Efficiency for Residual and Suppressed

Carrier Systems-A Comparative Study Tien M. Nguyen, Senior Member, IEEE, Warren L. Martin, Member, IEEE, and Hen-Geul Yeh, Senior Member, IEEE

Abstract- This paper presents a new concept for required bandwidth along with a method for computing this bandwidth and the associated undesired emission for the classes of PCM/PSK/PM, PCM/PM and BPSK signals. The PCM/PSK/PM signals considered here employ either a square wave or sinewave subcarrier with NRZ data format. On the other hand, the PCMlPM and BPSK signals use either a Bi-phase or an NRZ data format. Furthermore, the maximum allowable required bandwidth in the presence of noise and the data power efficiency for these modulation schemes will also be investigated. The term “data power efficiency” as considered in this paper consists of two principal components, namely, the amount of power contained in the data channel, and the Symbol Signal-to-Noise Ratio (SSNR) degradation due to the presence of InterSymbol Interference (ISI) for a specified required bandwidth. This paper evaluates both of these components numerically for the modulation schemes considered and the results are then compared. Furthermore, the impact of baseband filtering on the required bandwidth is also investigated in this paper.

I. INTRODUCTION S the presently allocated frequency bands become more A congested, it is imperative that the most bandwidth-

efficient communication methods be utilized. Additionally, space agencies are under constant pressure to reduce costs. Budget constraints result in simpler spacecraft carrying less communications capability as well as reduced staffing at the earth stations used to capture the data. Therefore, the power- efficiency of each modulation scheme becomes an important discriminator in the evaluation process.

The topic of bandwidth for the space telemetry signals has been investigated in great detail in the recent past [1]-[2]. The space telemetry signals examined in [ll-[2] employed both residual and suppressed carrier modulation techniques, and additionally, these papers only evaluated the Occupied, Bandwidth of the transmitted signal. Based on [ 13 and 141, this’ paper presents a new concept for the required bandwidth along with a method to calculate this bandwidth and the associated unwanted emission for PCM/PSK/PM signals with squarewave

Manuscript received December 13, 1993; revised August 31, 1994. This work was supported by the National Aeronautics and Space Administration. This work was camed out at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91 109 USA. This paper was presented at the International Consultative Committee for Space Data Systems, Subpanel 1 E, RF and Modulation, Munich, Germany.

The authors are with the National Aeronautics and Space Administration, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91 109 USA.

IEEE Log Number 9407405.

and sinewave subcarriers, PCM/PM and BPSK with both NRZ and Bi-phase data formats. The data power efficiency for these modulation techniques will also be evaluated and compared. As mentioned earlier, the term “power data efficiency” considered here includes the effects of InterSymbol Interference (ISI) on the Symbol Error Rate (SER) performance degradation. The IS1 phenomena arises when the transmitter employed some type of spectrum shaping. In addition, the results for the optimum bandwidth in the presence of noise will also be presented and compared with the others.

Traditionally, space agencies have employed subcarriers for both telecommand and telemetry data transmissions. Subcar- riers provided a simple method for separating different types of data as well as ensuring no overlap between the modulated data’s frequency spectra and the RF carrier. Mathematically, the signal can be expressed by

s l ( t ) = hAs in [wc t + md(t)P(t)] (1)

where A’ is the power, wc is the angular carrier center frequency in rads/sec, m is the modulation index in radian, d ( t ) is the NRZ binary valued data sequence with symbol period T, and P(t ) is the subcarrier waveform. Expanding (1) one obtains

s l ( t ) = hA[sin(w,t) cos(mP(t))

+ d ( t ) cos(wct) sin(mP(t))] (2)

The signal expressed in (2) is usually called PCM/PSK/PM signal, and the subcarrier waveforms recommended by the intemational Consultative Committee for Space Data Systems (CCSDS) are the squarewave and sinewave for deep space and near earth missions, respectively [3]. Hence, one has PCM/PSK/PM-Squarewave and PCM/PSK/PM-Sinewave for squarewave and sinewave subcarriers, respectively. Currently, the CCSDS has expressed considerable interest in eliminat- ing the subcarrier to conserve bandwidth. The transmitting signal format without the subcarrier becomes PCM/PM. The mathematical expression for PCM/PM signal is given by

sg( t ) = JZAsin[w,t + md(t)] (3)

Expanding (3) we get:

s Z ( t ) = hA[sin(w,t) cos(m)

+ d(t)cos(w,t) sin(m)] (4)

00 18-9375/95$M.O0 0 1995 IEEE

NGUYEN et ai.: REQUIRED BANDWIDTH, UNWANTED EMISSION, AND DATA POWER EFFICIENCY 35

where the data sequence d ( t ) can be formatted either in the form of NRZ or Bi-phase (or Bi-4). Therefore, one has PCM/PM/NRZ and PCM/PM/Bi-phase for NRZ and Bi-phase data formats, respectively.

The mathematical expression for suppressed carrier modulation, namely BPSK signal, is defined as follow

s3 ( t ) = h ~ d ( t ) sin[w,t] ( 5 )

again, the data sequence d ( t ) can be either NRZ or Bi-phase. Thus, one has BPSK/NRZ and BPSK/Bi-phase for N E and Bi-phase data formats, respectively. In the following sections, the terms required bandwidth as well as unwanted emissions will be defined and a method for calculating these quantities will be presented. Moreover, the optimum bandwidth in the presence of noise and the data power efficiency will also be investigated in detail.

This paper is organized in the following manner. Section I1 defines the term “required bandwidth” and presents a method to calculate this quantity for various modulation schemes mentioned above. Section 111 explains the term “undesired emission” and shows how this quantity can be computed. The data power efficiency is considered in Section IV. The term data power efficiency calculated in this section consists of two components, namely, the power contained in the data channel for the required bandwidths of 2lT and 41T (Where T denotes the symbol period), and the symbol SNR degradation due to the presence of the IS1 caused by filtering in the data channel for various values of required bandwidths. Section V shows how to calculate the maximum required bandwidth in the presence of white Gaussian noise. Section VI investigates the effects of the filtering on the required bandwidth. The discussions and main conclusions are presented in Sections VI1 and VIII, respectively.

11. REQUIRED BANDWIDTH: DEFINITION AND ANALYSIS

A . Introduction and Definition of Required Bandwidth

Several years ago, the Intemational Telecommunications Union (ITU) established criteria for quantifying the bandwidth used by a telecommunications system. Termed “Occupied Bandwidth,” Regulation RR-147, of the ITU’s Radio Regu- lations defined the term as [4]:

“Occupied Bandwidth: the width of a frequency band such that, below the lower and above the upper frequency limits, the mean power emitted are each equal to a specified percentage p/2 of the total mean power of a given emission. Unless otherwise specified by the International Radio Consultative Committee (CCIR) for the appropriate class of emission, the value of p/2 should be taken as OS%.” Under the ITU definition, the Occupied Bandwidth is that

span of frequencies which contains 99% of the emitted power. Hence, the occupied bandwidth is an actual measurement of bandwidth which contains 99% of the power of the signal. Where digital communications are concemed, Occupied Band- widths of unfiltered signals tend to be very large, especially for PCM/PSK/PM signals [l].

The ITU Radio Regulations also contain an alternative definition called Necessary Bandwidth. Regulation RR- 146 defines the Necessary bandwidth as [4]:

“Necessary Bandwidth: for a given class of emission, the width of the frequency band which is just sufficient to ensure the transmission of information at the rate and with the quality required under the specified conditions.”

Here, the problem is one of uncertainty. To a large extent “quality” is a subjective concept. Using Necessary bandwidth definition is difficult without a specific standard. Moreover, no attention is paid to power efficiency which would satisfy the requirements of both space and terrestrial communications systems.

Theoretically, the occupied bandwidth should be equal to the necessary bandwidth to ultilize the spectrum efficiently and to effectively transmit the information. As an example, the necessary bandwidth of analog FM signals using Carson’s rule is about 98% to 99% of the transmitted bandwidth. On the other hand, for some types of digital signals, the 99% filtered bandwidth may be considered more than sufficient to obtain realiable bit error rate performance. [ 131 has derived the necessary bandwidths for several digital modulation schemes, namely, Phase Shift Keying (PSK), Minimum Shift Keying (MSK) and Frequency Shift Keying (FSK). The results presented in [ 131 show that for these digital modulation schemes, the necessary bandwidth, signal power and bit error rate are all interrelated and tradeoffs among these factors are possible.

Given the problems with both the occupied bandwidth and the necessary bandwidth notions, this paper proposes a new measure called the required bandwidth and relates the required bandwidth to the existing measures of bandwidth, e.g., occupied bandwidth and necessary bandwidth. The prin- ciple difference as compared to the occupied bandwidth and necessary bandwidth are that (a) a more realistic value for the percentage of power is selected and (b) a fixed acceptable loss in terms of Symbol Signal-to-Noise Ratio (SSNR) due to filtering is proposed. The proposed definition is:

“Required Bandwidth: For a specific type of modulation, the width of the frequency band such that, below the lower and above the upper frequency limits, the mean power emitted are each equal to 2.5 percent of the total unfiltered, ideally modulated digital data spectrum, using the same modulation scheme.” Note that this definition is not referenced to 99% of the

power in the transmitted spectrum as is for the Occupied Bandwidth. That is because spectrum control is inherent in the concept of required bandwidth. In simple terms, required bandwidth is that bandwidth needed to complete a communication with an acceptable amount of power loss. For example, a 5% decrease in power corresponds to -0.2 dB power loss. Such a reduction in power should be acceptable to most space missions and this will be proved later in the following sections. Yet, the bandwidth required to send identical messages over two channels, one using Occupied Bandwidth definition and other employing the new required bandwidth definition, will be several times less in later channel when compared to the former. As will be demonstrated in the remainder of this paper,

36 IEEE TRANSACIIONS ON ELECTROMAGNETIC COMPATABILITY, VOL. 31, NO. I , FEBRUARY 1995

TABLE I INVESTIGATED MODULATION SCHEMES

I MODULATION TYPE

DESCRIPTION

PCMfPSK/PM Squarewave

PCM/PSK/PM Sinewave

PChWMBi-4

~

NRZ data is PSK modulated on a sinewave subcarrier which I is then Dhase modulated on the RF carrier.

BPSK/Bi-$

PCM/PM/NRZ

BPSWNRZ

NRZ data is PSK modulated on a squarewave subcarrier which is then phase modulated on the RF carrier.

Data is Bi-phase (Manchester) modulated directly on a residual RF carrier.

Data is Bi-phase (Manchester) modulated on an RF carrier fully suppressing it.

NRZ data is phase modulated directly on a residual RF carrier.

NRZ data is phase modulated directly on an RF carrier fully suppressing it.

t MULTIPLIER 91

RECEIVER

RANGING CHANNEL i SHAPING

Fig. 1 . Simplified block diagram of spacecraft radio frequency subsystem.

accepting a small loss in system’s performance, dramatically reduces the actual amount of bandwidth needed to complete the communication.

It is assumed that some spectrum shaping will be employed at an appropriate location in the information transmission system so that only the required bandwidth is transmitted from the spacecraft. Fig. 1 is a simplified block diagram of a spacecraft Radio Frequency Subsystem (RFS). Note that spectrum shaping can be located in the ranging channel, at the input to the modulator, and at the output of the power amplifier. Spectrum shaping is found on most current spacecraft. All of the spectrum shaping devices shown in Fig. 1 may not be required. The actual number and their locations will depend upon the specific RFS design and the linearity of the multiplier and the power amplifier. Obviously, it is desirable to avoid spectrum shaping at the output of the power amplifier because of the RF power loss and increased weight. If the spectrum shaping is done at an earlier point, then the losses resulting from spectrum shaping at the transmitter’s output can be largely avoided.

Coherent tumaround and one-way ranging signals present unique problems in Required bandwidth systems. To achieve the desired measurement accuracy, ranging tones sometimes

have frequency components, and hence required bandwidths, which are larger than those needed for telemetry and telecommand operations. Since many space missions need all of these services, the RFS depicted in Fig. 1 must accommodate the separate spectral requirements imposed by the different services. Clearly, the mechanization of the flight radio system may depend upon a mission’s specific requirements.

Fortunately, the system depicted in Fig. 1 should permit the flexibility to meet the needs of all services. Moreover, even if the Necessary Bandwidth increases during ranging operations, these sessions are usually concluded quickly so that the increased bandwidth requirement is of short duration.

B . Analysis

The required bandwidth for several modulation schemes are calculated in this section. The modulation methods investigated in this paper are discussed in Section I and listed in Table I. Modulation methods listed in Table I are shown in the order of increasing bandwidth efficiency (diminishing required bandwidth). As it will be shown later in Table I1 that in order to compare the required bandwidths for several modulation schemes, power transfer efficiencies of 90% and 95% are used. As noted previously, these correspond to power loss of 0.45 dB and 0.2 dB respectively.

Fig. 2 shows the frequency spectrum of each of the several modulation schemes shown in Table I. Fig. 2(a) shows the frequency spectrum of a system employing a single squarewave subcarrier. Limited space restricted the ability to show the full spectrum. Odd harmonics of the subcamer’s frequency, each with data sidebands, will be present with diminishing amplitude as the order increases. Fig. 2(b) depict the frequency spectrum of a system utilizing a single sinewave subcamer. Unlike the squarewave subcarrier’s frequency spectrum, a sinewave subcarrier will have energy at even harmonics in the form of a Delta function. The Delta function’s amplitude

NGUYEN et ai.: REQUIRED BANDWIDTH, UNWANTED EMISSION, AND DATA POWER EFFICIENCY 31

RESIDUAL RF CARRIER

I , t I , m 1 -21R, -18Rs -15R, -12R, -9R, -6R, -3Rs 1, 3R, 6R, 9R, 12Rs 15RS 18R, 21Rs

RESIDUAL CARRIER, PCM I PSKl PM-SQUAREWAVE

(a)

-21Rs -18RS -15Rs -12Rs -9R, -6Rs - 3 4 1, 3R, 6R, 9R, 12R, 15Rs 18R, 21Rs RESIDUAL CARRIER, PCM I PSK I PM-SINEWAVE

(b)

I r l l l l l l l l l , l I - 1 . 1 , , 1 , 1 1 , , 1 - 2 1 4 -18RS -15R, 42R, -9R, -6R, 3 R , f, 3R, 6R, 9R, 12R, 15RS 18Rs 21Rs

RESIDUAL CARRIER, DIRECT MODULATION, PCM I PM I BiPHASE

(C)

I ~ ~ I ~ ~ I c B I I t I t t I m I , u I * , I t n I o a I , t I -BIRs -18R, -15Rs - 1 2 4 -9R, -6R, - 3 4 1, 3R, 6R, 9R, 12R, 15R, 18R, 21R,

RESIDUAL CARRIER, DIRECT MODULATION. PCM I PM I NRZ

(d)

I ~ ~ I ~ ~ I o # I t n I I , , l , , I , n l , , J - 2 1 4 -18R, -15R, -12R, -9R, -6R, -3Rs f, 3Rs 6R, 9R, 12R, 15R, 18R, 21Rs

SUPPRESED CARRIER, DIRECT MODULATION BPSK I Bi-PHASE

( e )

2 R, =SYMBOL FREQUENCY = 1

I s I 1 0 a I I 1 I , I I , , l , l ~ . l ~ ~ l ~ ~ l ~ ~ l . ~ l -21Rs -18RS -15RS -12Rs -9Rs -6R, 3 R S fc 3Rs 6Rs 9Rs 12Rs 15RS 18Rs 21R,

SUPRESSED CARRIER, DIRECT MODULATION, BPSK I NRZ

(0 Fig. 2. Spectra of various modulation methods.

will depend upon the RF carrier’s modulation index. It is this energy that is lost during the demodulation process and which accounts for the lower efficiency of sinewave subcarrier systems.

From a spectrum bandwidth perspective, direct modulation with a Bi-4 format is a compromise between direct modulation with an NRZ data format and a conventional subcarrier telemetry system. It places the modulated data sidebands closer to the RF carrier while providing a null in the data’s frequency spectrum at the RF carrier’s frequency. Fig. 2(c) shows the PCM/PM/Bi-4 spectrum which ensures that the carrier will be easily distinguishable from the surrounding data sidebands. The bandwidth advantage of direct modulation schemes is readily apparent in this figure. Direct NRZ differs from Direct Bi-4 modulation in that the double frequency clock component is absent in the former modulation type. Here, the modulated binary data’s frequency spectrum is discernably narrower than the one for Bi-q5 modulation. The RF frequency spectrum for

PCM/PM/NRZ is shown in Fig. 2(d). BPSK/Bi-q5 modulation fully suppresses the RF carrier by modulo-2 adding the data on to a squarewave clock at twice the data symbol’s frequency and modulating the RF carrier with an index of 90 degrees. The BPSK/Bi-q5 spectrum is shown in Fig. 2(e). Like direct residual carrier modulation, BPSK/NRZ differs from BPSK/Bi-q5 in that the double frequency clock component is absent in the former modulation type. The modulated signal’s frequency spectrum for BPSK/NRZ is shown in Fig. 2(f).

Required Bandwidth for PCMIPSKIPM with Squarewave: When P( t) is a unit power squarewave subcarrier of frequency fs,, it has been shown in [l] that the required bandwidth for this case is given by

r ( A l - n ( 2 k - 1)) 8 sin2 (m) [sin(x)/x12dx

+ Cosym) = p% (6 )

38

110

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATABILITY, VOL. 37, NO. 1, FEBRUARY 1995

I I I

' 7 0 -

2 I 2 m-. 8 w

5 0 - -

40

30

a -

n ~ 3 . m = 0.4 rad

- -

.-

L

------.

LEGEND m =MODULATION INDEX

n =Is.$7,

1, = SUBCARRIER FREQUENCY

R, = SYMBOL RATE

0 50 100 150 200

NORMALIZED BANDWIDTH. BW/&

Fig. 3. Band width needed for PCM-PSK-PM-squarewave.

Where M is the normalized required bandwidth (one-sided bandwidth, BWl) with p% power containment-to-symbol rate ratio (Rs) , i.e.,

M = BWi/R, (7)

n = fsc/Rs, (8)

and n is the subcarrier frequency-to-symbol rate ratio, i.e.,

where n is integer and R, = 1/T is the data rate and p% is the percentage of power containment in the signal component. The plot of (6) for various values of n and m is shown in Fig. 3 . This figure shows the power containment as a function of the one-sided bandwidth-to-symbol rate ratio. As an example, for 99% power containment, the one-sided bandwidth is about 328R2, for m = 1.2 rad and n = 9 [1]-[3]. While, form Fig. 3 , the one-sided bandwidth for 90% only requires about 30R,. Therefore, if 90% of the power meets the desired link performance margins, then the required bandwidth will be 30R, which is about 11 times less than the bandwidth required for 99% power containment.

Required Bandwidth for PCMIPSKIPM with Sinewave: When P ( t ) is a sinewave subcarrier, it has been shown in [ 1 I that the required bandwidth for this case is given by

L L

J,2(m> + 2 $(m) + J;(m)uh(L) = p% (9) k even h odd

where uh(L) is defined as

Here f s c and Lfsc are defined as nR, and the required bandwidth with p% power containment, respectively. The normalized required one-sided bandwidth BW2-to-symbol rate ratio is found to be

M2 = BW2/RS = Ln ( 1 1)

Note that S d ( t ) is the Power Spectral Density (PSD) for NRZ data which is defined as

where T is the symbol period. Fig. 4 illustrates a plot of (9) for various values of R. and m. This figure shows that, for n = 9, rn = 1.2 rad, the required one-sided bandwidth for 90% power containment is about 9.35RS. On the other hand, the required bandwidth for 99% power containment is about 27R, which is three times greater than the bandwidth required for 90% power containment.

Required Bandwidth for PCMIPM with Bi-Phase Data For- mat: From (4), the PSD of the PCM/PM with Bi-phase data format can be shown to be:

Using (13) , the required bandwidth can be easily calculated. The relationship between the required bandwidth with p% power containment and the modulation index is found as follow:

M3xf2 2sin2(m) J' [sin4(x)/x2]dx + cos2(m) (14)

-M37rf2

where

BW3 M3 = - Rs

where BW3 is the required one-sided bandwidth for Bi-phase case. This result is the same as the one found in [2]. The plot of (14) is shown in Fig. 5 for various values of m. As an example, for m = 1.2 rad, the required bandwidths for 95% and 99% power containment are 6SR, and 26R,, respectively.

Required Bandwidth for PCMIPM with NRZ Data Format: Again, from (4), the PSD of the PCM/PM with NRZ data format can be shown to be:

Sdf) = cos2(m)S(f - f c )

Using (16), the required bandwidth can be easily evaluated. The relationship between the required bandwidth with p% power containment and the modulation index is found to be:

sin2(m) 1Lf4x p % = ~ / [sin2(x)/x2]dx + cos2(m) (17)

7r

where

fiS

NGUYEN et a/.: REQUIRED BANDWIDTH, UNWANTED EMISSION, AND DATA POWER EFFICIENCY

100

90

80

8 I--

b z s $ 70

w

60

50

40

m =MODULATION INDEX

f,, = SUBCARRIER FREQUENCY

R, = SYMBOL PATE

I I 0 5 10 15 20 25 30 35


Fig. 4. Bandwidth needed for PCM-PSK-PM-sinewave.

0 5 10 15 20 25 30 35

NORMALIZED BANDWIDTH, BW/&

Fig. 5. Bandwidth needed for PCM-PM-Bi-phase.

Here BW4 denotes the required one-sided bandwidth for NRZ case. Illustrated in Fig. 6 is the plot of (17). This figure shows the power containment as a function of the normalized

m=l.Orad

m = I P r a d

m = 1.4 rad

LEGEND

m = MODULATION INDEX

I I I I I I 5 10 15 20 25 30

NORMALIZED BANDWIDTH, BWIR,

Fig. 6. Bandwidth needed for PCM-PM-NU.

bandwidth with the modulation index m as a parameter. For instance, the required bandwidths for 95% and 99% power containment are 1.6R, and 9R,, respectively, for m = 1.2 rad.

Required Bandwidth for BPSK with Bi-Phase Data Format: From (3, the PSD of the BPSK with Bi-phase data format can be shown to be:

Using (19), the required bandwidth can be easily evaluated. The relationship between the required bandwidth with p% power containment is found to be:

p% = 2 / M 5 . i 2 [sin4(z)/zzjdz (20) - h & , ~ / 2

where

BW5 Ms = - R,

here BWs is the required one-sided bandwidth for BPSK/Bi- phase case. The plot of (20) is shown in Fig. 7. As an example, the required one-sided bandwidths for 95% and 99% power containment are 6SR, and 31 R,, respectively.

Required Bandwidth for BPSK with NRZ Data Format: Again, from (3, the PSD of the BPSK with NRZ data format can be shown to have the following form:

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATABILITY, VOL. 37. NO. I , FEBRUARY 1995

TABLE I1 REQUIRED BANDWIDTH FOR THE INVESTIGATED MODULATION SCHEMES

Modulation Type

XM/PSK/PM-Squarewave (n = 9, m = 1.2 rad)

X W S WPM-Sinewave (n = 9, m = 1.2 rad)

F‘CWMh3i-4 (m = 1.2 rad)

90% Power Containment

+30R, (13.1 % allocated to RF

Residual Carrier)

(45.04 %-allocated to RF Residual Carrier)

+9.35R,

- +2.88R, (13.1 % allocated to RF

Residual Carrier)

95% Power Containment

&75R, (13.1 % allocated to RF

Residual Carrier)

+9.56R, (45.04 96 allocated to RF Residual Carrier)

+5. lR, (13.1 % atlocated to RF

Residual Carrier)

pcM/pM/NRz (m = 1.2 rad)

+0.73R, (13.1 %%located to RF

Residual Carrier)

+1.65R, (13.1 %%located to RF

Residual Carrier)

BPSKLli-4 (m = +x/2)

I I I I I I 5 10 15 20 25 30


Fig. 7. Bandwidth needed for BPSK signals.

Using (22), the required bandwidth can be computed easily. The relationship between the required bandwidth with p% power containment is given as

p% = 11 [sin2(x)/x21dx (23) A46 ?F

7r -h&?F

where

where BWG denotes the required one-sided bandwidth for BPSK/NRZ case. Illustrated in Fig. 7 is the plot of (23). This figure shows the power containment as a function of the normalized bandwidth. For example, the required one-sided bandwidths for 95% and 99% power containment are 2R, and 1 1 R,, respectively.

To compare the required bandwidths for the several modulation schemes listed in Table I, power transfer efficiencies of 90% and 95% are used. Additionally, for comparative purposes, the modulation index, m, of 1.2 radians and subcarrier frequency-to-symbol rate ratio, n, of 9 are used in the calculation of the required bandwidth for the residual systems. Table I1 presents the required bandwidths under these specified conditions for the modulation methods listed in Table I.

111. DEFINITION OF UNDESIRED EMISSION

A. Definition of Undesired Emission

is defined as follow: The term “Undesired Emission” used through out this paper

“The undesired emission is the amount of emission such that, below the lower and above the upper frequency limits (the lower and upper frequency limits are defined by the required bandwidth), the total power contained in the undesired emission is equal to a percentage of the total power.” The Radio Regulation, RR-119, has defined the term “Un-

wanted Emission” as the emissions fall outside the necessary

NGUYEN et 01.: REQUIRED BANDWIDTH, UNWANTED EMISSION, AND DATA POWER EFFICIENCY 41

bandwidth and these emissions consist of spurious emissions and out-of- band emissions. The spurious emissions are harmonics, intermodulation products, frequency conversion products, etc. While the out-of-band emission resulted from the modulation process and this emission consists of both continuous spectrum and line spectrum. Based on the definition of the undesired emission, the undesired emission consists of both discrete and continuous spectrum components that fall out side the required bandwidth. Both of these components are produced by the modulation process and the discrete components are usually in the form of the unrecoverable (unrecoverable in the sense that even these components are within the required bandwidth they are still not recoverable by the demodulation process and these are considered as the power wasted due to the modulation process) harmonics. As it will be shown in Fig. 2 and Section II.B.2 that the PCMPSKPM-Sine Wave modulation scheme produces both discrete and continuous spectrum components and that the discrete components are not recoverable.

B . Analysis for the Undesired Emission

By definition, the undesired emission can have both continuous and discrete components. In the followings, the undesired emission caused by each component will be calculated separately for each type of modulation scheme considered above. Notice that from the PSD, we observe that only PCM/PSK/PM/sinewave subcamer have both discrete and continuous components and the rest has only continuous component.

From (6), the undesired emission, denoted as UE1%, for PCMPSKPM with squarewave subcarrier can be evaluated using the following:

8 sin2 (m) 1 UEl% = 1 - - ~

(2k - k 2 l T 3

7r (hI -n(2k-1 ) )

[sin(x)/x12dz - cos2(m)

(25)

From (9), for PCM/PSK/PM with sinewave subcarrier, the undesired emission due to continuous spectrum, denoted by UE2,%, is given by

L

UEZ,% 1 1 - $(m) - J;(?n)ah(L) (26) h odd

and the undesired emission, denoted by UE2d%, due to the discrete component is given by

00

UE2d%= 2 @m) (27) IC even

The undesired emission for PCM/PM/Bi-phase, denoted by UE3%, can be evaluated by using, from (14)

, I I

I I , ',

I I I I I

. I

I

LEGEND

n = F,dR, = 9


1, = SUBCARRIER FREOUENCY

R, = SYMBOLRATE , I ' I

. : m = l . t r a d

J

, 3 ms0.4rad

PCWPSWPM-SINEWAVE

0 50 100 150 200


Fig. 8. Undesired emission for PCM-PSK-PM-signals.

From (17), the undesired emission for PCM/PM/NRZ, denoted by UE4%, can be evaluated by using, from (14)

sin2(m) UE4% = 1 - - 1 [sin2(x)/x2]dx-cos2(m) (29)

T -n147r

Similarly, from (20), the undesired emission for BPSK/Bi- phase, denoted by UE5%, is given by

From (23), the undesired emission for BPSK/NRZ, denoted by UE6%, is given by

The undesired emission for each modulation type is calculated and the numerical results are plotted in Figs. 8-10. The key results presented in Figs. 8-10 are summarized in Table 111. This table shows the results for one-sided bandwidth of 2R, and 4R, for both BPSK and PCM/PM signal with m = 1.3 rad for PCM/PM, and one-sided bandwidth of 20R, for PCM/PSK/PM signals with m = 1.3 rad and n = 3.9 . Again, the values of m and n used in these computations are for comparative purpose only.

42

70

M)

50

8 e- $ 40

t 2 8

30

B

20

10

0

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATABILITY, VOL. 37, NO. 1. FEBRUARY 1995

I I I I I I I I , , , ., I

I I , LEGEND


, I , , , , I

. I

I I . I

I I I ,PCWPNi-PHASE

I I , ,

.J m = 0.4 rad

0 5 10 15 20 25 30 35

NORMALIZED BANDWIDTH, B W / q

Fig. 9. Undesired emission for FCM-PM signals.

IV. DATA POWER EFFICIENCY

A . Power Contained in the Data Channel

The power contained in the data channel for a specified bandwidth can be calculated from the results presented in Section 11. From (6), (9), (14), (17), (20) and (23), the power contained in the data channel can be calculated. Notice that for BPSK signals, the power contained in the data channel are calculated using the same as (20) and (23) for BPSK/Bi-phase and BPSKBRZ, respectively.

For PCM/PSK/PM/Squarewave subcarrier, the data power containment, denoted as P1%, is given by

8 sin2 (m) 1 p l % = l - - ~

7r3 ( 2 k - 1 ) 2 k>l

[sin(z)/zl2dz (32)

For PCMPSKPWSinewave subcarrier, the data power containment, denoted as P2%, is given by

L

P2% = J;(m)ah(L) (33) h even

For PCMPMBi-phase, the data power containment, denoted as P3%, is given by

I I I

0 5 10 15 20 25 30 35

NORMALIZED BANDWIDTH. BW/R,

Fig. 10. Undesired emission for BPSK signals.

For PCM/PM/NRZ, the data power containment, denoted as P4%, is given by

The power containment in the data channel for each modulation type is evaluated and the numerical results are presented in Figs. 11 and 12. The key results are also tabulated in Table 111, for the sake of comparison. This table shows the calculations of the data power efficiency for one-sided bandwidth of 2R, and 4R, for both BPSK and PCM/PM signal with m = 1.3 rad for PCM/PM, and one-sided bandwidth of 20R, for PCM/PSK/PM signals with m = 1.3 rad and n = 3 and 9.

B. Symbol SNR Degradation Due to IS1 As mentioned earlier, the data power efficiency consists

of two components, namely, data power containment and SSNR degradation due to ISI. The issue conceming data power containment has been investigated in the preceding section, Section 1V.A. This section deals with SSNR degradation due to ISI.

When the RF filter bandwidth is of the order of the main spectrum hump of the modulated carrier, the information- bearing pulses are spread out in time. Each pulse is overlaid with the tails of previous pulses and the precursors of the subsequent ones, and this so-called Intersymbol Interference (ISI) behaves like an additional random noise [71-[12]. This additional random noise can cause potential degradation to the receiver. In addition, excessive filtering of the pulse can also

NGUYEN et a!.: REQUIRED BANDWIDTH, UNWANTED EMISSION, AND DATA POWER EFFICIENCY

~

43

PCWPSWPM-SQUAREWAVE

I: LEGEND

n f d R , = 9 J

' O t 60-

ap +- zl 5 0 - t 2 8 a 40 -

30 -

20-

10 -

O I 0

J = 1.3 rad

& PCMIPSWPM-SINEWAVE

PC WPSWPM-SQUAREWAVE J'0'4rad ........................ ... .. \I... PCWPSWPM-SINEWAVE

60 I 50

$

8

-I I

_I 10

I I I I O L 50 100 150 200 0


PCMIPMMRZ

PCMIPMBi-PHASE

I I I I I I I 5 10 15 20 25 30 35


Fig. 1 1. Data power containment for PCM-PSK-PM. Fig. 12. Data power containment for BPSK and PCM-PM.

cause a loss of symbol energy during the symbol time. The effects of symbol energy's loss for specified bandwidths are already examined in Section 1V.A for the required bandwidth of 2R, and 4R,. This section investigates the effects of IS1 and the combined effects of IS1 and imperfect carrier tracking on the symbol SNR degradation.

The effects of the IS1 on the performance degradation of the PCMPM receivers have been investigated in [7], where the SSNR degradation is evaluated for both PCM/PM/NRZ and PCM/PM/Eii-phase receivers for an ideal low-pass filter. Using results presented in [7]-[12], one can extend these to include PCM/PSK/PM and BPSK signal formats. To extend these results, it is necessary to give a brief summary on these key results. It has been shown in [7] that, for BT > 1 (where B denotes the required bandwidth), the average probability of error is given by:

(36)

where Pe(Be) is the conditional probability of error and P(0,) is the probability density function (pdf) of the carrier tracking phase error 8,. If the number of pulses, P , before and after the present pulse being detected is between 1 and 2, Le., 1 5 M 5 2, then direct computation of the conditional error probability Pe(Or) is feasible through the following; [7], [ 121

(37)

where g ( t ) is defined as

d t ) = P( t ) * h(t) (40)

where * denotes the convolution.

energy is defined as For both PCM/PM/NRZ and PCM/PM/Bi-phase, the symbol

T E, = A2 siu2(mT) 1 Ig(t)12dt (41)

Note that P ( t ) denotes the pulse shape of the data and h( t ) denotes the impulse response of the equivalent low-pass filter of the RF bandpass filter with the required bandwidth B.

44

Continuous Component

5 % (Bw = 2RJ

2.5 % (Bw = 4RJ

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATABILITY, VOL. 31, NO. I , FEBRUARY 1995

Discrete Component

0 %

TABLE 111 DATA POWER EFFICIENCY AND UNWANTED EMISSION FORVARIOUS MODULATION TECHNIQUESUNDER INVESTIGATION

Modulation Type

BPSWNRZ

Data Power Efficiency Without Filtering

95 % (BW = 2RJ

91.5 % (BW = 4R3

BPSWBi-Phase

PcM/pM/NRz (m =1.3 rad)

P W S K P M -

When the loop signal-to-noise ratio is high, the Tikhonov pdf can be approximated by

P(t9,) M exp(-6~/2a2)/[2~a2]-1’2, -cc < 8, < cc (42)

For perfect NRZ data stream and high-data-rate case (i. e.,BL/R, << 0.1, where BL and R, denote the one-sided carrier loop bandwidth and the symbol rate, respectively), the variance of the carrier tracking phase error is found to be

c2 = (l/po) + ( B L / R , ) tan2(7rw) (43)

and, for perfect Bi-4 data format, o2 becomes

where po is the carrier loop SNR (under ideal operating conditions) which is found to be

~ ~

Remark

Recommend Filtering

Recommend Filtering

Recommend Filtering

and I/C is the interference-to-carrier ratio which is given by

For Si-4 data format, one gets

(45 ) 1 . yBi-$(t + kZ) = -[s1{27rB(t + T(k + 1/2))}

K

NGUYEN el a/.: REQUIRED BANDWIDTH, UNWANTED EMISSION, AND DATA POWER EFFICIENCY 45

+ s i { 2 ~ B ( t + T(k - 1/2))} - 2 s i ( 2 ~ B ( t + kT)]

where fco is the 3-dB bandwidth which is related to the single-sided noise bandwidth B of the arm filter: (48)

where B is the one-sided bandwidth of the low-pass filter

si(z) = [sin(u)/u]du (49)

fco = (2Bn/7r) s i n ( ~ l 2 n ) (61)

For ideal arm filter, i.e. rectangular frequency response, the where it can be set equal to the required bandwidth, and

squaring loss SL becomes

(62) K32 sL = K3 + [BT/(ES/No)]

LX For PCMPSKPM with n > 3, the variance of the carrier

tracking phase error becomes where

2 = ( l / P o ) (50)

For PCMPSKPM-squarewave, the carrier loop SNR is identical to PCMPM (see (45)). However, for PCMPSKPM- sinewave, the carrier loop SNR becomes

where E, is given by T

Es = 2A2J?(mT) 1 Ig(t)12dt (52)

For BPSK, the loop SNR, p, of a Costas is given by [6]

A2 p = -

N0BL sL (53)

sin2 ( T B T ) TBT

and Si(x) is defined in (49).

channel is well-known to be given by: In the absence of ISI, the average BER, PEo, for an uncoded

PEo = ; e r f c ( d m o ) (64)

where (E,/No)o is the required symbol SNR to achieve a desired SER, PEo, for unlimited bandwidth case.

In the presence of bandlimiting channel, the average SER, PE1, for an uncoded channel can be calculated from (36). Let (E,/No)l be the required symbol SNR to achieve a desired SER, PE1, for bandlimiting case. Thus, if we fix the SER, i.e.,

PEo = PE1 = S E b (a desired value)

then the SSNR degradation in dB for this specified SERo is defined as:

where SL is the squaring loss which is given by the simple relation [6]

(54) SL = K: KiKz + KLK A(dB) = (Es/No)o - (Es/No)i (65)

where

(57)

where Sd(f ) denotes the power spectral density of the data modulation d( t ) , H ( j 2 ~ f ) is the transfer function of the low-pass arm filter. Again, the parameter B in (47) is the single-sided noise bandwidth of the low-pass arm filter of the Costas loop, i.e.,

(59)

The value of (Es/No)o can be computed by using (64). To compute (E,/No)l for PCM/PM/NRZ, we substitute (37) and (42) into (36) with the carrier tracking jitter ( F ~ ) given by (43) and performing numerical integration on the digital computer. Having (Es/No)o and (Es/N0)l, one can calculate the SSNR degradation in dB using (65). The calculated SSNR degradation in dB for various modulation types presented in Table I1 are shown in Tables IV and V. Table IV shows the results for m = 1.3 rad, ( ~ B L / R , ) = 0.001 at SER = Note that the carrier loop SNR ( P O ) is fixed in the calculation of the SSNR degradation for all cases.

The SSNR degradation due to IS1 alone can be computed form (36) by letting the loop SNR approaches infinity. Using the same input parameters as in Table IV, the results of the calculations are shown in Table V. Comparing the results presented in Tables IV and V, it is clear that, for BT > 5, the SSNR degradations are about the same for both cases, Le., perfect and imperfect carrier tracking.

Note that B can have the same value as the required bandwidth.

For NRZ and Bi-phase data modulation, the power spectral densities are identical to (12) and (19), respectively. Further- more, for n-pole Butterworth filter, the transfer function of the arm filter is

I W 2 T f ) I 2 = [1 + (f/fco)2n]-1

V. MAXIMUM ALLOWABLE REQUIRED BANDWIDTH IN THE PRESENCE OF NOISE

Since it is interested to know at what required bandwidth the noise power within this bandwidth, for a specified SSNR (Es /No) , would have the same power as the transmitted signal, and that one may consider this bandwidth as the "maximum allowable required bandwidth". This is because when the (60)

I

Modulation Type

PCMA’SKIPM-Squarewave (m = 1.3 rad, 2BL/R, = 0.001)

PCM/PSK/PM-Sinewave (m = 1.3 rad, 2 B L 4 = 0.001)

PcM/PM/NFu (m = 1.3 rad, 2BL/R, = 0.001)

PCMPMBi-Phase (m = 1.3 rad, 2BLni, = 0.001)

46

symbol SNR Degradation (dB)

B T = 1 B T = 2 B T = 5

0.85 0.17 0.01

0.85 0.17 0.01

0.85 0.17 QO 1

10.1 0.18 0.09

IEEE TRANSAnIONS ON ELECTROMAGNETIC COMPATABILITY, VOL. 31, NO. I , FEBRUARY 1995

BPSK/NRZ (2BL/R, = 0.001)

TABLE IV SYMBOL SNR DEGRADATION IN DB DUE TO IS1 AND IMPERFECT CARRIER TRACKING FOR VARIOUS MODULATION SCHEMES AT S E R = lo-’

0.70 0.14 0.0 1

BPSWBi-Phase (2BL/R, = 0.001) , 10.1 0.18 0.09

required bandwidth exceeds that of the maximum allowable

of the total transmitted signal power and hence degrades the system performance. Therefore, the term “maximum allowable

the required bandwidth and it is given by required bandwidth, then the noise power will exceed that BW

required bandwidth” considered in this section is defined as the maximum allowable bandwidth that is required to achieve the same amount of the total power contained in the transmitted signal as well as in the noise for a specified Es/No. Note that the total transmitted power is A2 (see (1)) and Es is the symbol energy which is equal to A2T for fully suppressed carrier (e.g.. BPSK). Therefore, for BPSK signal operates at a specific SSNR, the maximum allowable bandwidth is defined as the bandwidth BWAf that makes the ratio Ps/(2NoBW,) equal unity. Where Ps is the transmitted signal power within

Where S ( f ) is PSD of the transmitted signal. Observe that Ps/(NoBWnr) is the transmitted signal-to-noise power (in the required bandwidth) ratio, which is not the same as the SSNR.

This section focuses on the calculation of the maximum allowable required bandwidth in the presence of the white Gaussian noise for BPSK signals only. Extension of the method presented here to other modulation types is straight- forward. Let Pt be the total transmitted signal power (which is A2 and P,be the transmitted signal power within the required bandwidth BW. The signal power-to- the total transmitted

NGUYEN el a/.: REQUIRED BANDWIDTH, UNWANTED EMISSION, AND DATA POWER EFF'ICIENCY 47

IWJ

90

BO

70

z. 60

1 50

u re 5 40

5

2

30

20

10

0 0 5 10 15 20


Fig. 13. BPSK-NRZ in the presence of noise

power can be defined as follows

S ( f )d f (67)

where BW is the required bandwidth and S ( f ) is the normalized PSD of the transmitted signal. As an example, for BPSK/Bi-phase and BPSK/NRZ, the PSD's are given by (19) and (22), respectively. Similarly, the noise power-to-the total transmitted power (in the required bandwidth ratio) is given by

where NO is one-sided spectral density of the noise. Note that (68) can be rewritten in terms of the normalized bandwidth M , Le., M = BW/R,, and the Symbol Signal-to-Noise Ratio (SSNR), SSNR = E,/No = PtT/No = A2T/No, as follows

Dividing (67) by (69) one obtains

where the maximum allowable required bandwidth is selected in such a way that the ratio in (70) is unity. The plots of (67), (69), and (70) are shown in Figs. 13-16. Figs. 13 and 14 show the results for BPSK/NRZ, and Figs. 15 and 16 are for BPSKBi-phase. These figures plot the percentage of power containment as a function of the normalized bandwidth

I

E f10=15dB

I

E g o = 5 dB

/

0 5 10 15 20


Fig. 14. BPSK-NE in the presence of noise

with SSNR as parameter. These figures show that for SSNR = 10 dB, the optimum bandwidths for both BPSK/NRZ and BPSK/Bi-phase are about 5 R,. Furthermore, maximum P,/P, occurs at BW = R, for BPSK/NRZ, and at BW = 2R, for BPSKBi-phase.

VI. EFFECTS OF THE FILTERING ON THE REQUIRED BANDWIDTH

This section assesses the impacts of filtering on the required bandwidth and relates with the required bandwidth for unfil- tering case. Since this subject is very broad, this section only considers baseband filtering and assesses the impact of baseband filtering on the required bandwidth for PCM/PM/NRZ modulation scheme only. The baseband filter used in the following analysis will be the first-order Butterworth low pass filter with the transfer function H&+) is given by

where fo denotes the 3 dB cutt-off frequency of the filter in Hz. From (17), one can show that the relationship between the

required bandwidth with p% power containment and the filter cut-off frequency has the following form

sin2(m) ~4~

p% = ___ 1 [sin' (x) /z2] HT (x) dz +cos2 (m) (7 2) .rrN - A f 4 a

where M4 is defined as in (18), and N (the normalization factor) and H ( x ) are given by, respectively

(73) N = ?r 1 " J _ _ [ s i n ' ( z ) / x ~ ~ ~ ( z ) d r

48

60

50

40

$ +- 5

30 t

$. B

g u IT

20

10

0

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATABILITY, VOL. 37, NO. I , FEBRUARY 1995

TABLE VI EFFECTS OF BASEBAND FILTERING ON REQUIRED BANDWIDTH FOR PCM/PM/NRZ AND B P S W "

90 % Power Containment 95 % Power Containment

BPSK/NRZ (m = d 2 rad)

I k 0.55Rs I k 0.65Rs 11 k lRs 11 - + 0.67Rs I - + 1.28Rs 1 k 2Rs

P, =SIGNAL POWER IN 2 BW

P, = NOISE POWER IN 2 BW

P, = TOTAL TRANSMITT!ED POWER

E g o = SYMBOL ENERGY-TO-NOISE SPECTRAL DENSITY RATIO

0 5 10 15 20

NORMALIZED BANDWIDTH, B W / q

Fig. 15. BPSK-Bi-phase in the presence of noise

(74)

where FN is defined as

(75)

Note that the required bandwidth for the BPSK/NRZ with first-oder Butterworth filter can be obtained by setting m = 900 in (72). Numerical results obtained from (72) are summarized in Table VI for m = 1.2 rad and ~ / 2 rad.

Table VI clearly shows that the effects of baseband filtering on the required bandwidth at 90% power containment is in- significant. However, at 95% power containment, the required bandwidth for unfiltered PCM/PM/NRZ signal is almost three

fo FN = - R,

0 5 10 15 20


Fig. 16. BPSK-Bi-phase in the presence of noise.

times that of the filtered signal, and that for BPSK/NRZ signal it is more than three times that of the filtered one.

VII. DISCUSSIONS

It is clearly shown in Figs. 3 and 4 that as the desired signal power containment increases above 90%, the required bandwidth for PCM/PSK/PM-squarewave increases much faster than that of PCM/PSK/PM-sinewave. As mentioned earlier, for 99% power containment, the one-sided bandwidths for PCM/PSK/PM-squarewave and PCM/PSK/PM-sinewave are about 328R, and 27R,, respectively, for m = 1.2 rad and n = 9. Hence, for PCM/PSK/PM-squarewave signal with high data rate, it is suggested that the required bandwidth should be calculated before the frequency assignment.

NGUYEN el a/.: REQUIRED BANDWIDTH, UNWANTED EMISSION, AND DATA POWER EFFICIENCY 49

Fig. 5 and 6 shows that for signal power containment below 95%, the required bandwidth for PCMPMBi-phase is approximately twice that of PCM/PM/NRZ. But when the signal power containment exceeds 95%, the required bandwidth for PCMPMBi-phase grows exponentially as compare to PCM/PM/NRZ. The same is true for BPSK/Bi- phase and BPSKNRZ. This is demonstrated in Fig. 7. Based on the numerical results shown in Figs. 3-7, BPSK/NRZ and PCM/PM/NRZ signals require the least bandwidth and PCMPSKPM-squarewave requires the most bandwidth.

Figs. 13-16 illustrate the effects of the noise on the optimum required bandwidth for BPSK/NRZ and BPSK/Bi+. The numerical results show that the optimum required bandwidth in the presence of noise for BPSK, regardless of the data format, is about 4Rs (two-sided bandwidth),

It is also shown in Table 111 that for a fixed one-sided bandwidth of 2R,, BPSK/NRZ and PCM/PM/NRZ have the most power in the data channel as compare to the other modulation schemes. Concerning the unwanted spurious emission, the use of squarewave subcarrier and Bi-phase data format produce more out-of-band power than the sinewave subcarrier and NRZ data format.

Tables IV and V exemplify the effects of IS1 on the symbol SNR degradations when the required bandwidths are at R, (BT = l), 2R,(BT = 2) and 5R,(BT = 5). The results show that PCMPM/NRZ provides relatively good performance as compared with the others. For instance, for BT = 2, the symbol SNR degradations (caused by IS1 and imperfect carrier tracking) associated with PCMPSKPM-Square, PCMPSKPM-Sine, PCM/PM/NRZ, PCMPMBi-phase, BPSK/NRZ and BPSKBi-phase are about 0.15, 0.18, 0.21, 0.34, 0.17 and 0.29 dB, respectively.

The effects of baseband filtering on the required bandwidth were investigated for PCM/PM/NRZ and BPSK/NRZ and the results are summarized in Table VI. These results show that moderate filtering (3 dB cut-off frequency is set at the symbol rate) can offer some reduction in the required bandwidth (reduced by a factor of 3 or more for BPSK/NRZ and PCM/PM/NRZ). However, these theoretical results do not fully reflect the reality. In practice, filtering is applied both at baseband and at RF levels.

VIII. CONCLUSION A new definition for bandwidth has been proposed in this

paper. Because spectrum shaping is intrinsic in the concept of the proposed required bandwidth, the definition should specify the percentage of power containment (acceptable loss). A suggested level of 95% (0.2 dB) is recommended for the required bandwidth.

In order to achieve the same data power containment, the use of residual carrier modulation technique will require more bandwidth than the suppressed carrier modulation technique. In particular, BPSK/NRZ provides the best compromise between data power efficiency and unwanted emission as compared to BPSKBi-phase, PCM/PM/NRZ, PCMPMBi-phase, PCMPSKPM-squarewave and PCMPSKPM-sinewave. However, PCM/PM/NRZ also provides compatible perfor-

mance, in terms of high power containment and low level of unwanted emission, as compared to BPSK/NRZ. It is clearly shown in this paper that the use of subcarrier requires much larger bandwidth than that of the systems without using subcarrier. Because frequency spectrum is a scarce resource, it is recommended that the use of subcarrier should not be employed at high data rate, and that PCM/PM/NRZ modulation scheme should be used in place of PCM/PSK/PM.

Further work regarding the effects of filtering on the required and maximum allowable bandwidths is recommended for future study.

ACKNOWLEDGMENT The authors are indebted to F. Bomkamp for his comments

and suggestions in the calculation of the optimum bandwidth presented in Section V and Dr. S. M. Hinedi and the reviewers for their careful review of this paper and Dr. D. Cohen for his invaluable suggestions.

REFERENCES

[ I ] T. M. Nguyen, “Closed form expressions for computing the occupied bandwidth of PCMPSKPM signals,”l991 IEEE Inr. Symp. Electro- magn. Compat. Proc., Cherry Hill, NJ pp. 41-15,

[2] J. F. Pelayo, “PCM/PSK/PM and PCM-SPLPM signals-occupied bandwidth and BER,” XRT Section, European Space Agency (ESA), Eu- ropean Space Res. and Technol. Center (ESTEC), Noordwijk, The Netherlands, Oct. 1992.

[3] Consultative Committee for Space Data Systems (CCSDS), Recom- mendations for Space Data System Standards, Radio Frequency and Modulation Systems, Part 1, Earth Stations and Spacecraft, CCSDS 401 .O-B, Blue Book, CCSDS Secretariat, Communications and Data System Division, (Code OS), NASA, Washington DC.

[4] Intemational Telecommunications Union Radio Regulations, RR- 147, Geneva, Switzerland.

151 M. M. Shihabi, T. M. Nguyen and S. M. Hinedi, “A comparison of telemetry signals in the presence and abseence of a subcarrier,” IEEE 7kans. Electromagn. Compar., vol. 36, no. 1, Feb. 1994, pp. 6C73.

[6] J. Yuen, Deep Space Telecommunications Systems Erigineering. New York: Plenum Press, 1983, ch. 3.

[7] T. M. Nguyen, H.-G. Yeh,“Behavior of PCM/PM /NRZ receivers in non-ideal channels, - The seperate effects of imperfect data streams and bandlimiting channels on performance,” IEEE GlohEcom ‘94, pp.1380- 1384, Sun Francisco,CA.

[8] R. Lugannani, “Intersymbol interference and probability of error in digital systems,” IEEE Trans. Inform. Theory, vol. IT-15, no. 6, Nov. 1969, pp682-688.

[9] 1. Kom, “Probability of error in binary communication systems with causal band-limiting filters-Part I: non-return-to-zero signal,” IEEE Trans. Commun., vol. COM-21, no. 8, Aug. 1973, pp. 878-890.

[ I O ] - “Probability of error in binary communication systems with causal band-limiting filters-Part 11: Split-phase signal,” IEEE Trans. Commun., vol. COM-21, no. 8, Aug. 1973, pp. 891-898.

[ 1 I] - “Bounds to probability of error in binary communication systems with intersymbol interference and dependent or independent symbols,” IEEE Trans. Commun., vol. COM-22, no. 2. Feb. 1974, pp.251-254.

[ 121 C. W. Helstrom, “Calculating error probabilities for intersymbol and cochannel interference,” IEEE Trans. Commun., vol. COM-34. no. 5, May 1986, pp. 430-435.

1131 D. J. Cohen, “Necessary bandwidth and spectral properties of digital modulation,” NTIA Report 84-168, Feb. 1985, U.S. Dep. of Commerce, National Telecommunications and Information Administration.

1141 W. L. Martin and Tien M. Nguyen, “The joint CCSDS-SFCG modulation study-A comparison of modulation schemes,” Consultative Committee for space data systems (CCSDS), report of the proceedings of the RF and modulation, CCSDS B20.Cy-I, YellowBook, pp. 191-213, February 1994.

50 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATABILITY, VOL. 31, NO. I , FEBRUARY 1995

Tien Manh Nguyen (S’78-M’83-SM’93) was born in Sai Gon, Viet Nam in 1957. He received the A.A., B.S.E., and M.S.E. degrees (specializing in electromagnetic field theory) from Fullerton College and California State University, Fullerton, CA in 1978, 1979, and 1980 respectively. He received the M.S.E.E. degree (specializing in communication theory and systems) in 1982 from the University of California, San Diego. Mr. Nguyen received the Ph. D. degree in electrical engineering from Columbia Pacific University, CA in 1986, and the M.A. degree

in mathmatics from the Claremont Graduate School, (CGS) Claremont, CA, in 1993. Currently, he is completing his Ph.D. dissertation in engineering mathematics at CGS. Mr. Nguyen has been a Certified Manufacturing Technologist and certified EMC Engineer since 1984 and 1990, respectively. Presently, he is a member of the technical staff of the Communications Systems Research Section, Jet Propulsion Laboratory (JPL), Pasadena, CA. His current interests include integral transforms, statistical decisions, digital communications systems, parameter estimation, and digital signal processing. He was a Vice-Chairman of IEEEEMCmC6, was Session Chairman of the 1986 IEEEEMC International Symposium, and is a member of the New York Academy of Sciences, American Association for Advancement of Science, Phi Kappa Phi, American Mathmatical Society, Society of Manufacturing Engineers, and a senior member of AIAA.

Warren Leicester Martin (M ’94) was born in Los Angeles CA in 1935. He received his B. S. and M. S. degrees in Engineenng from the University of Califomia at Los Angeles (UCLA) in 1958 and in 1964 respectively. Thereafter, he earned his B.S. in Law 1973 and J.D in Law in 1976. Since that he has been active member of the California State Bar.

Since 1962, he has been employed by the Jet Propulsion Laboratory. During the first fourteen years, he worked in the Communications Research

Section and was a Co-Investigator on Celestial Mechanics and Relativity Teams for: the Lunar Orbiter, the Mariner, and in 1980, he was manager for the Telecommunications and Operations Directorate’s Advanced Missions Program. In that capacity his office assists new users of NASA’s Deep Space Network in their Mission and Spacecraft design phases to ensure compatibility with that Network.

Mr. Martin has served as Chairman of the Radio Frequency and Modulation Subpanel of the Consultative Committee for Space Data Systems (CCSDS). The CCSDS is an international consortium of 29 space agencies who meet periodicallly to establish technical system standards to ensure interoperability among members space data systems. Mr. Martin is also the designated CCSDS representative to the Space Frequency Coordination Group.

Hen-Geul Yeh was born in Taiwan, China in 1957. He received the B.S. degree from the National Chen-Kung University, Taiwan, China in 1978. He received the M.S. and Ph.D. degrees from the Uni- versity of California, Irvine, CA in 1979 and 1982 respectively. Currently he is a professor at the Elec- trical Engineering Department of California State University, Long Beach, CA. He is a Faculty Part- time worker at the Jet Propulsion Laboratory. His research interests are communication systems, adap- tive signal processing, and VLSI signal processing.

required bandwidth, unwanted emission, and data power efficiency for residual and suppressed carrier...

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