A much-simplified, yet more general-purpose multi-channel deep-space ranging system correlator design that was used in past JPL spacecraft ranging systems is described. The method applies to detection of both single-component and multiple-component ranging codes, in either sequential (mu) or composite (pi) transmitted forms, and using either pseudonoise or square-wave components. Using this design, the Phobos Probe ranging system correlator computational complexity was reduced by over three orders of magnitude in multiply-and-add circuits and 45,000 bits of accumulator storage

Smith, J. R.

Tausworthe, R. C.

English

NASA Technical Reports Server

TDA Progress Report 42-92
N88-18786
3
October-December 1987
A Simplified, General-Purpose Deep-Space Ranging
Correlator Design
R. C. Tausworthe
Information Systems Division
J. R. Smith
DSN Data Systems Section
This article describes a much-simplified, yet more general-purpose multi-channel
deep-space ranging system correlator design than has been used in past JPL spacecraft
ranging systems. The method applies to detection of both single-component and multiple-
component ranging codes, in either sequential (lz) or composite (r) transmitted forms,
and using either pseudonoise or square-wave components. Using this design, the Phobos
Probe ranging system correlator computational complexity was reduced by over three
orders of magnitude in multiply-and-add circuits and 45,000 bits of accumulator storage.
I. Introduction and Background
JPL Spacecraft ranging systems transmit, from the ground
to the spacecraft, a periodic code x(t) modulated on the
uplink carrier. This signal received by the on-board trans-
ponder, is demodulated and retransmitted via the downlink
to the ground station. The received version of the transmitted
code at the ranging demodulator assembly interface appears
attenuated by a factor _, delayed by the round-trip light-time
r(continuously changing due to the earth and spacecraft rela-
tive velocity), and immersed in noise, n(t). Symbolically,
y(t) = ax(t- r) + n(t) (1)
Present DSN ranging systems [1] use the two-way detected
Doppler signal from the receiver to program the clock oscilla-
tors of the receiver codes, generating replicas of the transmitted-
code component(s) to maintain a constant value of r between
the received signal,y(t), and the local receiver codes.
The optimum [2] estimate in the maximum-likelihood
sense, 7, for the time delay r over agiven observation interval
[0, T], set by ranging accuracy requirements and the incoming
signal-to-noise ratio, 1 is that value maximizing the cross-
correlation integral
fo TIt.. = y(t)c(t -_) dt
(2)
1Typically minutes to hours in duration.
105
https://ntrs.nasa.gov/search.jsp?R=19880009402 2020-03-20T08:22:05+00:00Z
where c(t) denotes a particular code component of the trans-
mitted signal, x(t). Computation of I_. thus requires a ground
receiver channel equivalent to the form shown in Fig. 1.
To determine ?, a set {_/:i = 0 ..... N - 1} of candidate
code-delay values is chosen and used to measure corresponding
"correlation4ag" values {Ig.:i = 0 ..... N - 1}, which are then
inserted into a maximum4ikelihood formula for determining ?.
The ranging codes are binary +l-valued signals having a
symbol-interval time we denote by to . As explained in a com-
panion article [3], the transmitted waveform is either a
Boolean function of several pseudonoise [4] binary sequences
running in parallel (the so-called composite-code approach [ 1] )
or a sequence of binary square waves of increasingly short
periods (the sequential-code approach). For historical reasons,
these were dubbed "r" and "p" methods, respectively.
The first planetary ranging system [5] utilized a combined-
component-code uplink scheme that required 77 receiver
correlations, but only had 2 channels. It was used on Mariner
missions from 1969 through 1973, and was then replaced
by sequential-component-code machines [1 ] because of their
superior ranging acquisition time advantage of some 12 dB
with only 2 correlation channels, at some extra complexity in
receiver code switching and housekeeping logic, and at a
modest 1.75-2.75 dB loss factor from the optimum matched
filter performance.
The acquisition-time advantage of the la system came from
the feasibility of building ranging correlator channels for each
of the needed ri of the/a code (viz., 2). The r scheme would
have required 77 such channels, a need without cost justifica-
tion in that era. The merits of the various transmitter codes
and receiver detection schemes are adequately treated else-
where [1 ], [4], [6], and are not further discussed here.
For determining the phase of incoming symbol transitions,
a "clock" component, or period-2 code, is transmitted in both
r and/a systems. The receiver correlation delays are chosen to
be? o = 0 and_ 1 = to/2, withN = 2.
For a pseudonoise-sequence code [6] of period p bits, the
candidate delay values are ?/= it o/k for i = 0 ..... N - 1, with
N = kp. The integer k may be 1 or 2 or more, depending on
the transmitter encoding and the method used to determine
the received symbol-transition phase, i.e., the code clock
delay.
In any case, in order to compute the N values required,
either N correlator channels are required to calculate the _ in
parallel, or some lesser number may be used serially, but
thereby increasing the acquisition time (equivalently, lowering
the effective signal-to-noise ratio).
II. Conventional Ranging Detectors
Conventional DSN ranging correlators are made up of
analog and digital hardware and software that mirror the direct
calculation of the integral above. Separation into analog and
digital portions derives from the following transformation of
the correlation integral:
= %. y gj=O
(3)
where the integration time T is assumed to be a multiple of the
period, the code delay _. is assumed to be a multiple of the
fractional symbol interval, and the coefficients _. represent the
-+1 code symbol values,
T = Mpt o = Mpkto/k
?i = ito/k
c] = c when i./'/k_l = Lm/kl (mod p)
ck] = cO'to) for] = 0,... ,p- 1
The integral thus represents the sum of integrations of the
incoming signal over fractional code symbol intervals, multi-
plied by the appropriate code symbol values over those inter-
vals. One such sum is required for each channel delay _., and
all multiply's and add's occur in parallel with each other.
The conventional design of a multi-channel range detector
is depicted in Fig. 2. Both the old _-and later ta machines used
this design, with 2 physical correlator channels. Integration
over fractional symbol times is performed by analog hardware,
and only one such integrator is needed. The integration value
is sampled and converted to a digital number, multiplied by
the N delayed code -+1 stream values, and added to the con-
tents of N accumulators, once each fractional symbol time.
Since k consecutive cj_ i values are equal, these sample
values may be preaccumulated before multiplications, if
desired. This, in fact, is done in the current DSN Spacecraft
Ranging System. However, the high-speed logic required for
processing the pre-accumulation and subsequent parallel
multiply-and-add operations contributes significantly to the
ranging assembly cost.
106
The advent of fast, custom-made, Very Large Scale Inte-
gration (VLSI) components has made it possible, albeit still
moderately costly, to build many more correlator channels
using the same form of digital design as shown in Fig. 2, so
that all the needed correlation-delay values can be accumu-
lated digitally in parallel [3].
As a case in point, the ranging uplink design for the Phobos
Probe mission uses a pseudonoise code of period 2047, trans-
mitted at about 1.2 X 10 6 symbols per second. A ranging
correlator design using the conventional approach, using
only k = 2 samples per code symbol, would require nearly
5 X 10 9 multiply-and-add operations per second. In fact, a
preliminary design using the conventional approach was
made; it required a massively parallel pipelined architecture
utilizing the fastest available memory circuits, and still had to
resort to 1-bit quantization of the input signal in order to
simplify the multiplier design, with a corresponding 2 dB
loss in signal-to-noise performance.
The economics and technology requirements of this con-
ventional approach thus place limits on the code period and
performance that can reasonably be expected.
III. The Simplified Digital Correlator
In this section, we note that the correlation integral may be
further transformed to reverse the order of digital accumula-
tion and multiplication in calculating the various needed
measurements. The advantage of this reversal, as we shall see,
is that it reduces the amount of high-speed digital logic and
custom-VLSI chips needed, removes almost all of the ranging
code dependency from the ranging demodulator hardware,
and makes possible the design of a general-purpose ranging
demodulator capable of accumulating thousands of correlation-
lag values.
By making use of the periodicity of the receiver code, the
correlation integral may be further transformed into the
equation
.., k,--E 5-, y'+
j=O m =O '.'O
or merely
dt
(4)
pk -1
_^. = E cl'-iA]
l j=O
(5)
where A i represents the accumulation of integrate-and-dump
values,
A  = m_o y t + dt
= _0
(6)
The revised correlator depicted in Fig. 3 utilizes pk accumula-
tors for the (Ai, / = 0 ..... pk - 1) values. Note that each
integrator sample output is added only into one of the accu-
mulator channels, switched by the accumulator index/, each
to/k seconds. Because of this simplification, only one adder is
required for all the accumulators corresponding to this receiver
code, as shown in Fig. 4. This functionally saves pk - 1 multiply-
and-add logic circuits (4093 of them for the Phobos Probe
mission).
For each integrator sample, the corresponding accumulator
is fetched, added to the sample, and restored into memory.
Each accumulator is only accessed once each pt o time interval.
Using this technique, the redesigned Phobos Probe ranging
correlator requires only 2.4 × 106 additions per second. As a
result, conventional Random Access Memory circuitry can be
used to hold the values.
Moreover, the accumulators are in jeopardy of overflow
only lip as much as in the conventional design. Consequently,
each accumulator can be shorter by log2(p ) bits than those of
the conventional design. This represents an additional logic
savings of pk log2(p) bits, or about 45,000 bits (5600 bytes)
in the Phobos Probe ranging correlator storage.
The address generator is merely a counter clocked at the
code fractional symbol rate and reset at the beginning of each
period of the receiver code. This is the only code-dependent
signal entering the digital portion of the design. Except for the
number of lag-value accumulators, the digital portion of the
correlator assembly is completely independent of the receiver
code cbmponents. No receiver coder hardware is necessary.
Conventional deep-space ranging correlators required hard-
ware code generators for each of the different receiver code
components.
Code multiplications are not made until after the complete
accumulation of A/ values has been read into the computer
of the ranging assembly. Then the same A i set serves to calcu-
late all of the _. for i = 0 ..... N - 1. The vector I containing
the 1_. is related to the vector A of accumulator values A i by
the equation
I = CA (7)
107
where C is the N × kp matrix of binary code values, ci, j = ej_ i.
Since the receiver codes are stored solely in the computer
memory as C, since the vector I is computed separately from
the accumulation process, and since this computation only
needs to take place infrequently, there is a greater degree of
flexibility and generality in the simpler design than existed in
the previous ranging assemblies.
IV. Conclusion
This article has presented a design simplification for the
digital hardware design of a deep-space binary-code ranging
system. The simplification is significant in that it
(1) Makes use of easily obtainable RAM storage, one
memory location for each correlation lag to be accu-
mulated, accessed serially, rather than special VLSI
devices or high-speed-logic circuits accessed in parallel;
(2) Reduces the high-speed digital logic requirements to a
single sample accumulator and adder, regardless of the
number of correlation lags computed, representing a
savings of pk - I multiply-and-add circuits;
(3) Reduces the number of bits required by each accumu-
lator by log2(p ) bits each, for a savings ofpk log2(p )
bits for the entire correlator;
(4) Makes the analog and digital portions of the system
independent of both the transmitter and receiver
codes, except for timing signals;
(5) Removes the need for receiver coders (simple period
counters will do); and
(6) Stores the receiver code component(s) as a vector
in the ranging computer, where the accumulated
correlation-lag values are computed by a single simple
matrix multiplication, infrequently calculated.
Using this approach, the new Phobos Probe mission ranging
system design uses no special components, is smaller, is easier
to design and maintain, and does not need to 1-bit quant'ize
the input signal. The details and particulars of the correlator
design will be the subject of a subsequent article.
References
[1 ] J. H. Yuen (ed.),Deep Space Telecommunications Systems Engineering, JPL Publica-
tion 82-76, Jet Propulsion Laboratory, Pasadena, California, pp. 123-178, 1972.
[2] W. B. Davenport and W. L. Root, An Introduction to the Theory of Random
Signals andNoise, New York: McGraw-Hill, 1958.
[3] R.C. Tausworthe, "Tau Ranging Revisited," TDA Progress Report 42-91, vol.
July-September 1987, Jet Propulsion Laboratory, Pasadena, California, pp. 318-
323, November 15, 1987.
[4] R.C. Tausworthe, "Optimum Ranging Codes," Trans. of the 1EEE PTG-SET,
vol. 10, no. 1, pp. 19-30, March 1964.
[5] R. C. Tausworthe, "Ranging the 1967 Mariner to Venus," inProc, oflEEENational
Convention, New York, pp. 294-295, March 1967.
[6] S. W. Golomb, et al., Digital Communications with Space Applications, Englewood
Cliffs, New Jersey: Prentice-Hall, Inc., 1964.
108
y(t)
Fig. 1. Ranging correlator channel functional design
y(t)_
SAMPLE
CLOCK
INTERFACE
I
_ ACCUMULATOR _ I_.0
I
c(t - 30) • I
I
I
ACCUMULATOR I_.N _
I
Ic(t - _"N _ 1) II
I DIGITAL I
I I
I TO MAXIMUM
LIKELIHOOD
ALGORITHM
1
COMPUTER
Fig. 2. Conventional multi-channel ranging correlator design
y(t) dt
1
SAMPLE
CLOCK
CODE
SYNCH
INTERFACE
I
swtc., ACOU.UL.TORI _ I ACCUMULATOR
i IAOORESSGENERATORI
I
I
I DIGITAL
I
I
Cpk - 1 - i
i=O .... ,N-1
COMPUTER
Fig. 3. Revised multi-channel ranging correiator design
SAMPLE [ ESULT
_ ADDEND _
ACCUMULATOR
MEMORY (RAM)
1
ADDRESS
GENERATOR
Fig. 4. Ranging correlator digital processor
109


A simplified, general-purpose deep-space ranging correlator design

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