Performance of a 30 GHz frequency division multiple access (FDMA) uplink to a processing satellite is modelled for the case where the onboard demultiplexer is implemented optically. Included in the performance model are the effects of adjacent channel interference, intersymbol interference, and spurious signals associated with the optical implementation. Demultiplexer parameters are optimized to provide the minimum bit error probability at a given bandwidth efficiency when filtered QPSK modulation is employed

Fargnoli, J.

Riddle, L.

English

NASA Technical Reports Server

N92-14222
OPTIMIZATION OF AN OPTICALLY rMPLEMENTED ON-BOARD FDMA DEMULTIPLEXER
J. Fargnoli and L. Riddle
Westlnghouse Electric Corp.
l_altlmore, Maryland
SUMMARY
l>erlormdnce of a 30 GHz FDMA uplink to a processlng satelllte Is
modelled for the case where the on-board demultiplexer is implemented
optically. Included in the perforance model are the effects o[ ad}a-
cent channel interference, intersymbol interference, and spurious s_gnals
associated wlth the optical implementation. Demultiplexer parameters are
optimized to provide the mlnimum bit error probabll ity at a given
bandwidth effLctency when filtered QPSK modulation is employed.
INTRODUCTION
Satellite communication using frequency division multiple access
(FDMA) on the uplinks and time division multiple access (TDMA) on the
downlinks has attracted much interest [1,2]. FDMA on the uplink permits
the use of ground transmitters that do not require amplifzers having
excessively high power. Also, FDMA does not require complicated network
timing. TDMA on the down!ink takes advantage of recent developments in
satellite on-board processing and switching capabilities to provide high
data rate downlinks to VSAT-type ground receivers. In addition, the
heavily-used C-band and Ku-band frequencies will be supplemented by
higher frequency Ka-band transmission (30 GHz uplink / 20 GHz downlink).
This permits the use of smaller ground terminal antennas, but at a cost
of higher rain attenuation.
On-board processing is needed to efficiently service multiple users
while at the same time minimizing earth station complexity. Figure i is
a simplified overview of a SATCOM system that services FDMA uplink users.
Th_ processing satellite first receives the wideband uplink at 30 GHz and
downco_verts it to a suitable IF. A demultiplexer then separates the
composite IF signal into assigned channels. All channels are then de-
modulated by "bulk" demodulators, with the baseband signals being routed
to the downlink processor for retransmission to the receiving earth sta-
tions via a high-rate TDMA 20 GHz downlink. This type of processing
circumvents many of the difficulties associated with bent-pipe repeaters.
First, uplink signal distortion and interference are not retransmitted on
the downlink. Second, downlink power can be allocated in accordance with
user needs, independent of uplink transmissions. This allows the uplink
users to employ different data rates as well as different modulation and
coding schemes. In addition, all downlink users will then have a common
frequency standard and symbol clock on the satellite, which is useful for
'network synchronization.
179
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These considerations led to a requirement for on-board multi-
channel demodulators (MCD) that can separate and process the individual
transmissions with minimal degradation in bit error probability.
Implementation of an MCD is critical because future systems will be
highly bandwidth-efficient, which implies very close spacing of the
carriers in the composite FDMA uplink.
On-board FDMA demultiplexers can be implemented in a variety of
ways. One way is to do a wideband A/D conversion on the uplink signal
received at the satellite, followed by digital processing that performs
the channel filtering and demodulation operations [3]. However, on-board
demultiplexing can also be performed using integrated optics [4,5]. An
acousto-optical spectrum analyzer performs both down-conversion and
channel filtering, with potential savings in hardware size and weight.
This paper shows how an acousto-optical demultipl_xer can be
modelled in system performance analyses. Bit error performance is deter-
mined in the presence of adjacent channel interference, intersymbol
interference, and spurious signals generated by the optical processing.
ON-BOARD DEMULTIPLEXER
An acousto-optical spectrum analyzer (Fig. 2) employing heterodyne
detection can function as a channelized receiver. The spectrum analyzer
converts the composite FDMA uplink into acoustic waves in a Bragg cell.
These acoustic waves modulate a laser beam, and diffract the beam at
angles proportional to the uplink RF signal frequencies. Reference beams
are also provided to achieve heterodyne operation, resulting in larger
dynamic range. The diffracted light impinges on an array of photodetec-
tors, which function as square-law detectors, and the individual photo-
currents are routed to QPSK demodulators. Thus, the acousto-optical
spectrum analyzer serves as both a channelizer and downconverter, so that
180 ORIGINAL PAGE IS
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Flg, 2 Acousto-optlcal Heterodyne Spectrum Analyzer
the composite uplink signal is demultiplexed into separate channels, each
at a common IF.
To estimate system performance from a demultiplexer of this type,
it is first necessary to determine its transfer function. In a classical
linear system, a sinusoidal input to the system results in a sinusoidal
output at the same frequency, whose amplitude and phase depend on the
frequency. But for the heterodyne system considered here, a sinusoidal
input results in not only a sinusoidal output at that frequency, but also
sinusoids at f + _nF, where F is the channel spacing. These spurious
sinusoids are generated intern_l to the demultiplexer by the reference
frequency comb. In contrast, the frequencies provided by other transmit-
ters external to the demultiplexer make up the ACI, which is characteris-
tic of all FDMA systems.
DEMULTIPLEXER TRANSFER FUNCTION
As indicated in Fig. 2, two channels constitute the acousto-optical
spectrum analyzer: the "signal" channel and the "reference" channel.
When the beam has a Gaussian cross section, the light into the signal
channel Braqq cell can be expressed as
OF PO0_ " _::-v
where IL is the light frequency, x denotes distance from the center of
the Bragg cell, and c_ is a constant determined by the laser beamwidth.
This light is modulated by an acoustic wave produced by the input
sinusoid of frequency fs , which can be expressed as
e,2.1s(t_ _} ('2)
where v is the acoustic velocity in the Bragg cell. Therefore, the modu-
lated light out of the cell is the product of (i) and (2), and the signal
channel light distribution in the k-plane is the spatial Fourier trans-
form:
f'_,(k) : e '2"</L÷/_lt /__ e -_ ';'{_+_}_dz (3)
where ds is the length of the Bragg cell. Similarly, the light distribu-
tion resulting from the multi-diffracted beam in the reference channel is
/ 4_2 2 ] _.nF
oo !a -_R_ -,2q_+k}*dx
rR(k}: _ +,_.{1_+J,,÷..8, _ +
n : --cio
{4)
One of the reference beams is directed toward the signal channel light
distribution (3) in the k-plane. However, because the other reference
beams also overlap the signal beam to some extent, spurious output
signals occur. If a high bandwidth efficiency is required, then the
beams must overlap more, which implies a higher level of spurious
signals.
The total light intensity in the k-plane is
IFs + FRI_ = IFsl _ + IFal 2 + 2RefsF_ {5)
By suitably filtering the photodetector output, the only important
contribution to the output will be the cross product G(k) = Re _F_. The
photocurrent is proportional to the integral of the intensity over the
photosensitive area:
k0 --
! : J_-_ G(k)dk {6)
where ko is the location of the photocell in the k-plane and K is the
width of the photocell. Now let fo be the nominal channel carrier
frequency, and let f = _ -fm represent the input frequency relative to
this nominal frequency. Assume that the k-plane location k¢ corresponds
to the frequency _ , so that k_ = -_ /v. Then the photocell output,
translated in frequency to baseband, reduces to
I = _ HR(f,_,f)¢os2,_(f-.F),
n -_--oo
(7}
182
where
/l_( J, 'I / I ,- .... ,- "_ ,,,s--(/_ +-/'_) --
v s v
' I<,,_ -!Jr n 1",/) dzdV
r x 4 _
The functlon H_(f,0) is the transfer function which will be denoted H_f),
and which can be calculated by numerical integration after the system.pa-
rameters have been selected. The terms for which n=0 give the amplitudes
of the spurious slnusolds.
Figure 4 is the computed transfer function for a particular set of
MCD parameters. The parameters were selected to give the minimum bit
error probability in the presence of ACI and ISI when the earth station
transmissions are filtered with fifth-order Butterworth filters having
time-bandwidth products of 0.5. A bandwidth efficiency of 1.6 bps/Hz has
been assumed. We now describe the method used to compute the ACI and
ISI, and then the bit error probability itself.
I'_ SIGNAL BCJ_ fROM
FRO@I IrR£OUENCY CO@tll _--
0
.0
(a) SpuriOuS Stqn41 O|sr.t'Lbution from Reference COlUJD
0
0
!-*
":0
;:.
,(hi ACZ 01strl_tLam (roe ][nterferim;I Tr4nsmLt_e:s
Fig. 3 Znr.arference rftects
183 OF POOR QUALITY
10
08
8T = 0.4
8ragg Cell Length: ds = dR = 2.46 cm (Te 02)
_1 Beamwidlh: 2.21 cm
e 2
Photocell Size: 1;2 of Channel Spacing
0.6
H R (X)
0.4
0.2
- 4 5 6 X = 2Tf
• • • • • Channel
Centers
Flq. 4 HCO Transfer _-unct Ion
ADJACENT CHANNEL INTERFERENCE
Design of any bandwidth-efficient FDMA system involves a fundamen-
tal trade-off. If the system bandwidth is narrow, we achieve good ACI
performance at the cost of high ISI. Widening the bandwidth reduces the
ISI but increases the ACI. The design procedure is generally to select
filter types and bandwidths that give the best bit error performance in
the presence of both ACI and ISI. We first consider the ACI.
Each ground transmitter is assumed to include bandpass0filtering to
reduce the amount of ACI entering the satellite receiver. As a first
approximation for performance analysis, the demultiplexer can be treated
conventionally as a bank of bandpass filters, each followed by a demodu-
lator. The model is later generalized to take into account the spurious
signals that are characteristic of the demultiplexer implementation.
It is straightforward to compute the ACI under the assumption that
the interference can be treated as noise that adds to the thermal noise
at the receiver input. This assumption is valid when there is a large
number of interfering users because according to the central limit
theorem, this implies that the interference has nearly Gaussian statis-
tics. We also assume for simplicity that all transmissions arrive at the
satellite with equal power.
184
The unfiltereo
interfering signal is
spectral density of the n-th QPSK-modulated
[sin2_T(/ nF)] _ (10)
All ground transmitters have identical filters, and the n-th filter
transfer function is denoted by Hx(f-nF ) . Thus the filtered transmission
from the n-th interferer has a spectral density given by S(f-nF)IH_(f-nF)} z
Suppose the transfer function of the on-board demultiplexer is H_(f),
which was evaluated in the previous section. Then the sgectral density
of the interference into the demodulator is
.5(/- ,_F)]}IT(/- ,2F)HR(I)I2 Ii)
Assume that the symbol detector is a filter matched to the
undistorted symbol (i.e. an integrate-and-dump detector). Its transfer
function is Hm[(f)=sin(2_Tf)/ 2nTf. Then the total ACl power out of the
matched filter relative to the undistorted signal power is
FI = _ S(/- nr)If_T(/- nF}IIR(/)HMF(f)[_df
n_O oo
(12)
This is added to the thermal noise to estimate the error probability.
INTERSYMBOL INTERFERENCE
Unlike the ACI, the ISI cannot be accurately approximated as addi-
tive Gaussian noise. Ynstead, we determine explicitly the effect of the
transmitter and receiver filtering on the amplitude of the signal out of
the integrate-and-dump detector.
Expressing any one of the unfiltered QPSK signals before transmis-
sion as s(t) = m(t)cos(2 f t + ), the complex modulation is
(13)
where a and b are binary data on the I- and Q- channels respectively,
which are assumed to be offset I/2-symbol. The modulation spectrum of
the filtered and demultiplexed signal at the input to its demodulator is
_(f) = M(f)HT(f)Hm(f), where M(f) is the spectrum of the undistorted QPSK
modulation. The Fourier transform of this is the distorted modulation,
which we will call _(t), and the output of the I-channel integrate-and-
dump detector in the demodulator is
__ {sin 2xT f'_ 2 e'2"(2"r+'W dI1 /Z+_ ,h(t)dt=T_a_, HT(f)gR(f)\ _ ) (14)
185
. _ ," ,:= tS
C_F k:*,:_ _'_ , ,
where _ is the samp±_ng time relative to the symbol transition. The Q-
channel output is similar. Because the filters introduce qroup delay,
the sampling time is generally nonzero. We can split the composite
transfer function H_(f)H[(f) into its real and imaginary parts denoted
by _(f) and _(f) respectively. Because _ is an even function of f and
is odd, the signal amplitude out of the I-channel of the detector becomes
(t5)
after changing the integration variable. This shows that the detector
output includes contributions from not only the desired (n:0) symbol, but
from all symbols, which is what is meant by intersymbol interference.
The bit error probability can be estimated from either the I-channel or
Q-channel output.
By differentiation, we find that the value of for which the
average value of S is a maximum is the solution of
Once the optimum _ is found we can compute the contribution to S from rne
n:0 symbol and from all important interfering symbols. It has been found
that the n : 1,2, 3, and -I interfering symbols are the important ones in
our application.
The bit error probability is then computed by averaging the error
probability, conditioned on a particular sequence of these interfering
symbols, over all 16 possible sequences of these symbols. The noise in
this computation consists of the ACI, which was calculated in the pre-
vious section, plus the thermal noise at the input to the satellite
receiver. If No is the thermal noise density at the input, the thermal
noise power at the output of the integrate-and-dump detector is
FNo [Ha(f)HMr(f)12d.t "
oo
(17)
which is added to the ACI in the error probability computation.
RESULTS
Having derived the demultiplexer transfer function, and having
calculated the ACI and ISI, it is ,straightforward to write down an
expression for the total power out of the device:
P= _, _ /-_ooS(J- nF)IHT(]- nF)HR(f, mF)HMF(f)I2df
186
The first sum is over the number of interfering earth stations, while the
second is over the number of spurious signals produced by the reference
beams. The m=n=O term is the desired output; the m=0, n_0 terms are the
ACI; the m#O, n=O terms are the spurious outputs when there is only one
uplink signal; and the m_0, n_0 terms are additional spurious outputs
arising from interaction of the interfering channels with the n_0 refer-
ence beams. Of this latter category, the m=n terms dominate, so they are
included in the performance calculation. The m_n interaction terms are
illustrated in Fig. 2.
Figure _ shows the bit error probability when the MCD transfer
function is that shown in Fig. 4- Fifth-order Butterworth filters are
used in the earth station transmitters, and integrate-and-dump symbol
detection is assumed. The effects of ACI, spurious signals, and ISI are
all included in the calculation. Also shown for comparison is a case
where the optical MCD is replaced by a bank of bandpass fifth-order
Butterworth filters whose bandwidths are optimized to give the smallest
bit error probability in the presence of the same interference. Figure
6 shows that the performance of an optical MCDI compares favorably with
that of an MCD implemented electronically.
Figure 7 shows the sensitivity of system performance to timing
errors in the symbol detection circuitry. This is evaluated by varying
the sampling time about its optimum value when computing the error pro-
bability. It is evident that when the timing error is less than approxi-
mately ten percent of the symbol duration, its contribution to bit error
degradation is insignificant companed to the ACI, spurious signals, and
ISI.
AWGN
r .............. .
I • I
I 8Pf De_oo
I Oemo@
I I
t
: i
I
: i
..... fl
-t'" H °--}F,;
i
: c
MCO Moae,
................. J
f'Lq. 5 Ana|¥tJca] Mode| tot PecFormance £valuaClon
187
10 -2
10 3
10 .4
10 -_
10 -e
10 -7
\
ACOUS;T©
OPTI('AI MC[)
2
.... ±____ 2 _ t i .... I_ __ I _____J_
2 4 6 8 10 12 14 16 18 20
E B/N (dB)
Degradation at PE = 5X40-7
(dB)
6
5
4-
3-
2-
1-
I 1 t l t I
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
Clock Error (Units of T)
Fig. 6 Bit Error Probabi1ity Fig. 7 5ensttlvlty to Syrnbo]. Synchronization Error
DISCUSSION AND CONCLUSION
The goal of this effort was to evaluate the performance of an
optically implemented on-board demultiplexer that can service inex-
pensive, low-power earth stations. For such earth stations, no attempt
has been made to improve bandwidth efficiency by using advanced modu-
lation and coding schemes. In addition, we have assumed that no effort
has been made to minimize ISI by careful design of the earth station
transmitter filters. We have shown that an optically implemented MCD,
which promises size and weight advantages over other implementations of
on-board processors, can perform as well as other implementations so far
as bit error probability is concerned.
However, to'achieve comparable performance with the optical MCD,
whose transfer function must be carefully controlled, it was found
necessary to reduce the ground transmitter filter bandwidths. As seen in
Fig. 6, this worsens performance &t low signal-to-noise ratios because of
the increased ISI that results. The optical MCD transfer function (Fig.
41 has amplitude and phase characteristics different from most classical
filter responses. Also, spurious responses from the reference beams
exist. Therefore, the ACI/ISI trade-off for an optical implementation
differs significantly from that for an electronic one.
188
REFERENCES
[I] Ananasso, F. and Saggese, E., "A survey on the Technology of multi-
carrier Demodulators for FDMA/TDMA User-oriented Satellite Systems",
IEEE International Conference on Communications, Chicago, 1985, pp.
6.6.] - 6.1.7.
[2] Ananasso, F. and De] Re, E., "Clock and Carrier Synchronization in
FDMA/TDMA User-oriented Satellite Systems", IEEE International Confer-
ence on Communications, Seattle, 1987, pp. 41.7.] - 41.7.5.
[3] Kappes, J. and Sayegh, S., "Programmable Demultiplexer/Demodulator
Processor", IEEE Military Communication Conference, Monterey, 1990, pp.
7.3.1 - 7.3.5.
[4] Goutzoulis, A. and Abramovitz, I. "Digital Electronics Meets Its
Match", IEEE Spectrum, Aug. 1988, pp. 21-25.
[5] Ananasso, F. and Bennion, I., "Optical Technologies for Signal
Processing in Satellite Repeaters", IEEE Communications Magazine, Feb.
1990, pp. 55-64.
189



Optimization of an optically implemented on-board FDMA demultiplexer

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