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Description  |
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TECHNICAL FIELD
The invention relates generally to direct sequence spread spectrum code
division multiplexers, and more particularly toward a method of correcting
timing signal errors which may occur between transmitters and receivers in
such a system.
BACKGROUND ART
In a spread spectrum system, a transmitted signal is spread over a
frequency band that is much wider than the minimum bandwidth required to
transmit particular information. Whereas in other forms of modulation,
such as amplitude modulation or frequency modulation, the transmission
bandwidth is comparable to the bandwidth of the information itself, a
spread spectrum system spreads an information bandwidth of, for example,
only a few kilohertz over a band that is many magahertz wide, by
modulating the information with a wideband encoding signal. Thus, an
important characteristic distinguishing spread spectrum systems from other
types of broadband transmission systems is that in spread spectrum signal
processing, a signal other than the information being sent spreads the
transmitted signal.
Spreading of the transmitted signal in typical spread spectrum systems is
provided by (1) direct sequence modulation, (2) frequency hopping or (3)
pulsed-FM or "chirp" modulation. In direct sequence modulation, a carrier
is modulated by a digital code sequence whose bit rate is much higher than
the information signal bandwidth. Frequency hopping involves shifting the
carrier frequency in discrete increments in a pattern dictated by a code
sequence, and in chirp modulation, the carrier is swept over a wide band
during a given pulse interval. Other, less frequently used, carrier
spreading techniques include time hopping, wherein transmission time,
usually of a low duty cycle and short duration, is governed by a code
sequence and time-frequency hopping wherein a code sequence determines
both the transmitted frequency and the time of transmission.
Applications of spread spectrum systems are various, depending upon
characteristics of the codes being employed for band spreading and other
factors. In direct sequence spread spectrum systems, for example, wherein
the code is a pseudo-random sequence, the composite signal acquires the
characteristics of noise, making the transmission undiscernable to an
eavesdropper who is not capable of decoding the transmission. Additional
applications include navigation and ranging with a resolution depending
upon the particular code rates and sequence lengths used. Reference is
made to the textbook of R. C. Dixon, Spread Spectrum Systems, John Wiley
and Sons, New York, 1976. especially Chapter 9 for application details.
Direct sequence modulation involves modulation of a carrier by a code
sequence of any one of several different formats, such as AM or FM,
although biphase phase-shift keying is the most common. In biphase
phase-shift keying (PSK), a balanced mixer whose inputs are a code
sequence and an RF carrier, controls the carrier to be transmitted with a
first phase shift of X.degree. when the code sequence is a "1" and with a
second phase shift of (180+X).degree. when the code sequence is a "0".
Biphase phase-shift keyed modulation is advantageous over other forms
because the carrier is suppressed in the transmission making the
transmission more difficult to receive by conventional equipment and
preserving more power to be applied to information, as opposed to the
carrier, in the transmission. Characteristics of biphase phase-shift
keying are given in Chapter 4 of the Dixon test, supra.
The type of code used for spreading the bandwidth of the transmission is
preferably a linear code, particularly if message security is not
required, and is a maximal code for best cross correlation
characteristics. Maximal codes are, by definition, the longest codes that
could be generated by a given shift register or other delay element of a
given length. In binary shift register sequence generators, the maximum
length (ML) sequence that is capable of being generated by a shift
register having n stages is 2.sup.n -1 bits. A shift register sequence
generator is formed from a shift register with certain of the shift
register stages fed back to other stages. The output bit stream has a
length depending upon the number of stages of the register and feedback
employed, before the sequence repeats. A shift register having five
stages, for example, is capable of generating a 31 bit binary sequence
(i.e. 2.sup.5 -1), as its maximal length (ML) sequence. Shift register ML
sequence generators having a large number of stages generate ML sequences
that repeat so infrequently that the sequences appear to be random,
acquiring the attributes of noise, and are difficult detect. Direct
sequence systems are thus sometimes called "pseudo-noise" systems.
Properties of maximal sequences are summarized in Section 3.1 of Dixon and
feedback connections for maximal code generators from 3 to 100 stages are
listed in Table 3.6 of the Dixon test. For a 1023 bit code, corresponding
to a shift register having 10 stages with maximal length feedback, there
are 512 "1"s and 511 "0"s; the difference is 1. Whereas the relative
positions of "1"s and "0"s vary among ML code sequences, the number of
"1"s and the number of "0"s in each maximal length sequence are constant
for identical ML length sequences.
Because the difference between the number of "1"s and the number of "0"s in
any maximal length sequence is unity, autocorrelation of a maximal linear
code, which is a bit by bit comparison of the sequence with a phase
shifted replica of itself, has a value of -1, except at the 0.+-.1 bit
phase shift area, in which correlation varies linearly from -1 to (2.sup.n
-1). A 1023 bit maximal code (2.sup.n -1) therefore has a peak-to-average
autocorrelation value of 1024, a range of 30.1 db.
It is this characteristic which makes direct sequence spread spectrum
transmission useful in code division multiplexing. Receivers set to
different shifts of a common ML code are synchronized only to transmitters
having that shift of the common code. Thus, more than one signal can be
unambiguously transmitted at the same frequency and at the same time. In
an autocorrelation type multiplexed system, there is a common clock or
timing source to which several transmitters and at least one receiver are
synchronized. The transmitters generate a common maximal length sequence
with the code of each transmitter phase shifted by at least one bit
relative to the other codes. The receiver generates a local replica of the
common transmitted maximal length sequence having a code sequence shift
that corresponds to the shift of the particular transmitter to which the
receiver is tuned. The locally generated sequence is autocorrelated with
the incoming signal by a correlation detector adjusted so as to recognize
the level associated with only .+-.1-bit synchronization to despread and
extract information from only the signal generated by the predetermined
transmitter.
Because the autocorrelation characteristic of a maximal length code
sequence has an offset corresponding to the inverse of the code length, or
V/(2.sup.n -1)
where V is the magnitude of voltage corresponding to "1" and n is the
number of shift register stages, overlap occurs in neighboring channels.
Thus, there is imperfect rejection of unwanted incoming signals.
Unambiguous signal discrimination thus requires a guard band between
channels reducing the number of potential transmitters for a given code
length. A long maximal length sequence compensates for the guard band to
increase the number of potential transmitters, but this slows
synchronization and creates power imbalance of the multiplexing
transmitters.
In one type of code division multiplexer a plurality of transmitters
synchronized to a common clock each transmit a data signal spread by a
common bipolar pseudo-random code having a different assigned code
sequence shift. A receiver, synchronized to the clock, discriminates the
signal transmitted by a predetermined transmitter from signals transmitted
by the others by cross-correlating the incoming signal with a trinary
sequence that is developed at the receiver. The receiver develops the
trinary sequence by generating a first pseudo-random code that is a
replica of the common bipolar pseudo-random code transmitted by the
transmitters and having a code sequence shift corresponding to that of the
predetermined transmitter to which the receiver is tuned, and a second
bipolar pseudo-random code that is a replica of the common bipolar
pseudo-random code and has an unassigned code sequence shift.
Correlation consists of multiplication of an incoming signal with the local
reference signal that corresponds to the difference between the first and
second bipolar pseudo-random code sequences. Integration of the product
averages out random noise to enhance the signal-to-noise ratio. When the
information transmitted is binary, two different waveforms are generated:
one for a "zero" and another for a "one" at the receiver. When the
transmitted signal is biphase, the transmitted waveforms for a "one" and a
"zero" differ from each other by a 180.degree. phase shift. When the
predetermined transmitter and the receiver are synchronized with each
other, the multiplier output is at a maximum at a positive polarity for a
"one" and a negative polarity for a "zero". The multiplier output is
integrated for the duration of 1-bit period. If the initial integrator
output is "zero" then the polarity of the integrator output at the end of
a bit period corresponds to the transmitted binary information.
The degree of correlation between the predetermined transmitter and the
receiver is determined by comparing the outputs of several correlation
detectors having reference signals that are displaced in time with each
other. Each detector develops two output signals, an in-phase signal that
is at a maximum and a quadrature-phase signal that is at a minimum when
the receiver and predetermined transmitter are aligned. The receiver is
fine tuned to the predetermined transmitter by adjusting the receiver
timing until the quadrature-phase signal is minimized.
During fine tuning of the receiver, a decision is made on each incoming
sequence bit whether to advance or retard receiver timing by an equal
fraction of a code chip. The receiver timing is advanced by the code chip
fraction if the in-phase and quadrature-phase correlation signals are of
opposite polarity. If the in-phase and quadrature-phase correlation
signals are of the same polarity, the receiver timing is retarded.
During perfect correlation between the receiver and predetermined
transmitter, however, the fine tuning mechanism of the receiver tends to
drive the receiver timing from the optimum reception point, causing the
receiver to continually search for correct synchronization, since there is
no deadband. Further, because there is a delay inherent in the feedback
loop of the receiver, the correction decision is made using information
more than one data bit old, causing the receiver to tend to overshoot as
it attempts to lock in the optimum synchronization point.
As another problem, a direct sequence spread spectrum receiver does not
readily distinguish between a signal and noise, particularly since the
incoming signal is a data modulated carrier that is spread by a
pseudo-noise sequence. The receiver will thus tend to attempt to lock onto
noise in the absence of a signal.
DISCLOSURE OF INVENTION
It is accordingly one object of the invention to improve synchronization in
a direct sequence spread spectrum receiver.
A further object is to improve receiver synchronization in a direct
sequence spread spectrum receiver in which the data sampling rate can be
higher than the timing signal frequency.
These and other objects are satisfied by the method of the present
invention which improves the synchronization between a transmitter and a
receiver used in a direct sequence spread spectrum code division multiplex
system, and in particular where a plurality of transmitters and at least
one receiver are synchronized to a common timing signal source. Each
transmitter transmits a data signal spread by a pseudo-random code which
is a different assigned shift of a common code sequence. The receiver is
synchronized to one of the transmitters transmitting a data signal spread
by the pseudo-random code having a predetermined assigned code sequence
and to the timing signal source by the steps of sampling the data signal
at a rate equal to the frequency of the timing signal source or an
integral multiple thereof, combining one or more consecutive data samples
together to generate a data sample point corresponding to a particular
timing point of the timing signal source, detecting which one of the data
sample points has a maximum value, and locking the receiver to the timing
point of the timing signal source corresponding to which one of the data
sample points is detected as having a maximum value.
An advantage of the above method is that it eliminates the need for
redundant data channels sampling each point of possible synchronization
ambiguity. Further, the above method allows data sampling to take place at
a rate faster than the frequency of the timing signal source. By combining
together consecutive data samples to generate a data point, data sampling
may take place at a rate greater than the net data rate, which is in
effect the number of data sample points or bits (generated from the
combination of one or more consecutive data samples) per second. This
arrangement allows the data samples to be combined digitally (for example
in a microprocessor) and allows the data rate to be independent of the
actual hardware timing.
Still other objects and advantages of the present invention will become
readily apparent to those skilled in this art from the following detailed
description, wherein there is shown and described only the preferred
embodiment of the invention, simply by way of illustration of the best
modes contemplated of carrying out the invention. As will be realized, the
invention is capable of other and different embodiments, and that several
details are capable of modification in various, obvious respects, all
without departing from the invention. Accordingly, the drawings and
description are to be regarded as illustrative in nature, and not as
restrictive.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a simplified block diagram showing a DSSS code division multiplex
receiver;
FIG. 2 is a representation of a bipolar pseudo-random pulse sequence;
FIG. 3 is a diagram showing an autocorrelation pattern for a bipolar
pseudo-random pulse sequence of the type shown in FIG. 2;
FIG. 4 is a superposition of several autocorrelation patterns corresponding
to neighboring transmitters in a code division multiplex system;
FIG. 5 is a diagram corresponding to FIG. 4, with signals of neighboring
transmitters separated by guard bands;
FIGS. 6(a)-6(d) are wave forms showing trinary code generation;
FIG. 7 is a simplified block diagram showing a receiver operated in
accordance with the principles of the invention;
FIG. 8 is a diagram showing an idealized cross-correlation pattern between
a locally developed trinary code sequence and an incoming binary code
sequence in accordance with the invention;
FIGS. 9(a)-9(c) are diagrams showing correlation patterns developed by
multiple channel correlation detectors in accordance with various
embodiments of the invention;
FIG. 10 illustrates an actual correlation pattern obtained in the receiver
of the present invention when operated in the presence of various
degrading factors;
FIG. 11 illustrates an analog embodiment of multiple correlation detectors
for determining the degree of correlation in accordance with the
invention;
FIG. 12 is a circuit simplification of the analog embodiment of FIG. 11
using binary reference signals;
FIG. 13 is a further circuit simplification of the analog circuit of FIG.
11, using digital logic to reduce the number of analog multiplexers;
FIGS. 14(a) and 14(b) illustrate two methods of implementing the circuit of
FIG. 13;
FIG. 15 is a digital implementation of one channel of the circuit shown in
FIG. 11;
FIG. 16 is an N-channel generalization of the circuit implementation in
FIG. 15;
FIG. 17 shows another digital implementation of a single channel correlator
of a type shown in FIG. 11;
FIG. 18 is an N-channel generalization of the circuit shown in FIG. 17;
FIG. 19 illustrates an in-phase and quadrature-phase correlation pattern,
together with the locations of sub-receiver channels for correlation
detection;
FIGS. 20(a) and 20(b) are flow charts showing two alternative methods for
performing fine tuning of the receiver;
FIG. 21 illustrates a microprocessor based circuit for performing fine
tuning of the receiver and signal presence detection;
FIGS. 22(a) and 22(b) are flow charts respectively showing methods for
correcting receiver timing and for performing signal presence detection;
FIG. 23 is a flow chart showing one technique for performing coarse tuning
of the receiver;
FIGS. 24(a)-24(e) are timing diagrams showing the relationship of timing
pulses between a transmitter and a receiver;
FIG. 25 illustrates a circuit for locking a transmitter and receiver to the
same timing pulses; and
FIG. 26 illustrates a microprocessor based circuit for performing data
recovery in the receiver.
BEST MODE FOR PRACTICING THE INVENTION
General
In spread spectrum communications, spreading of signal bandwidth beyond the
bandwidth normally required for data being transmitted is accomplished by
first phase shift keyed (PSK) modulating a carrier waveform by data to be
transmitted, and then modulating the resultant signal by a reference
pseudo-random code of length L running at a repetition rate which is
normally at least twice the data rate. Forms of modulation other than PSK
can be applied to modulate the carrier as well as to spread the composite
signal, although PSK is preferred for reasons set forth earlier.
To demodulate the signal transmission, the received signal is heterodyned
or multiplied by the same reference code as the one used to spread the
composite transmission, and assuming that the transmitted and locally
generated receiver codes are synchronous, the carrier inversions caused by
the code PSK modulation at the transmitter are removed and the original
base-band modulated carrier is restored in the receiver.
FIG. 1 illustrates the fundamental elements of a basic spread spectrum
receiver incorporating one aspect of the invention. Receiver 100 receives
a direct sequence spread spectrum (DSSS) signal transmitted by a
particular transmitter among a plurality of such transmitters, and
processes the received signal to discriminate the signal transmitted by
the particular transmitter from among the signals transmitted by all the
transmitters. Bearing in mind that the received signal is essentially
modulated twice, that is, the carrier is modulated with data and then the
composite is modulated by a pseudo-random code sequence to spread the
composite over a bandwidth that is comparable to the bandwidth of the
pseudo-random sequence, receiver 100 provides two stages of demodulation
of the received signal to extract the transmission data. The received DSSS
signal is first heterodyned or multiplied by the code of the particular
transmitter whose signal is being discriminated from among the others.
Thus, assuming that the codes generated at the transmitter and receiver
are synchronous, the carrier inversions caused by the code PSK modulation
at the transmitter are removed at multiplier 102, and the original
base-band modulated carrier is restored. The narrow-band restored carrier
is applied to a band pass filter (not shown) designed to pass only the
base-band modulated carrier. Base-band data are then extracted by
heterodyning or multiplying the restored carrier by a locally generated
carrier at multiplier 104. The output of multiplier 104 is applied to a
conventional correlation filter 106, such as an integrate and dump
circuit, followed by a sample and hold circuit which develops signals
corresponding to the transmitted data.
The receiver 100 is controlled by a standard microprocessor 108,
synchronized to a system clock 110, to which the transmitters are also
synchronized. Because noise and undesired transmissions are treated in the
same process of multiplication in multiplier 102 by the locally generated
reference code that compresses the received direct sequence signal into
the original carrier bandwidth, any incoming signal not synchronous with
the locally generated reference code is spread into a bandwidth equal to
the sum of the bandwidth of the incoming signal and the bandwidth of the
reference code. Since this unsynchronized input signal is mapped into a
bandwidth that is at least as wide as the reference code, a base pass
filter can reject a significant amount of the power of an undesired
signal. This is the significance of a DSSS system: synchronous input
signals at the reference code modulated bandwidth are transformed to the
base-band modulated bandwidth, whereas non-synchronous input signals
remain spread over the code-modulated bandwidth.
Synchronization processing makes use of a property inherent in the
particular code that is employed at the transmitter. The autocorrelation
of a maximal length (ML) sequence, that is, multiplication of the sequence
by a time shifted replica of itself, is at a peak when synchronization is
achieved and has an absolute value that drops to -P.sup.2 /L, where P is
the magnitude of the code sequence and L is the code length, as
synchronization becomes lost (i.e., the time difference between the code
and its replica approaches a code chip or greater). The sign of the
autocorrelation pattern is dependent upon the data bit being used to
modulate the transmitter. It is thus possible to recover the transmitted
data at the receiver by monitoring the sign of the autocorrelation output
when the receiver and transmitter are properly synchronized.
Referring to FIG. 2, a pseudo random code sequence of a type to which
receiver 100 is tuned is bipolar, that is, it is assumed to switch
polarities of a constant voltage power supply. In the invention, bipolar,
rather than unipolar, sequences are used to improve power transmission
efficiency, since the carrier is suppressed in bipolar transmission.
Bipolar transmission also avoids high concentrations of energy in any
frequency band to help avoid interference between transmissions by
different transmitters in the system. Each bipolar sequence has a
magnitude P and a chip duration T.sub.c. The length of the ML sequence
depends upon the number of different transmitters whose signals are to be
code-division multiplexed within the system. Each transmitter is assigned
the same transmission code having a different specified chip of the common
ML sequence. The maximum number of transmitters that are capable of being
multiplexed within this system thus corresponds to the length of the ML
sequence.
The number of transmitters that may be multiplexed without interference
within a code-division multiplex system of this type is equal,
theoretically, to the bit length of the sequence. For an ML code having a
length of 63 bits, for example, the transmission channel is theoretically
capable of multiplexing 63 different transmitters. This assumes that
synchronization is deemed to be achieved between the receiver and a
preselected transmitter when the autocorrelation between the code received
from the transmitter and the locally generated code, both synchronized to
a common timing source, is at a peak. In practice, however, the number of
transmitters that can be code division multiplexed in the system is much
lower than the theoretical maximum, because there is overlap between
neighboring correlation curves due to the -P.sup.2 /L term in the
autocorrelation of the ML sequence. This can be better appreciated with
reference to FIG. 3 which shows a correlation curve for a single
transmission and FIG. 4 which shows a number of correlation curves for
neighboring transmissions, that is, for transmissions that are time offset
from each other by a single code chip.
In FIG. 3, the correlation curve has a magnitude -P.sup.2 /L when the
transmitted and locally generated code sequences are time offset from each
other by greater than a code chip T.sub.c, where P is the absolute
magnitude of the sequence and L is the sequence length in bits. When the
transmitted and locally generated codes are near synchronization, that is,
are within a time offset of one code chip of each other, the correlation
increases in magnitude to a peak of P.sup.2 at perfect synchronization.
Thus, synchronization between the receiver and a single transmitter can be
detected by monitoring the correlation output and deeming synchronization
to exist when the correlation signal is above a predetermined positive
value.
Referring now, however, to FIG. 4, assume that there are three transmitted
code sequences k, k-1 and k-1, time shifted from each other by a single
code chip. Each correlation has a positive peak value of P.sup.2 and a
negative peak value of -P.sup.2 /L, as in FIG. 3. The correlation curves
of neighboring code sequences overlap, within the regions shown by
cross-hatching in FIG. 4. In those regions, neighboring code sequences
have common correlations, making it impossible to distinguish between
transmissions. As a practical matter, to avoid interference between
transmissions, it is necessary to insert a guard band between sequences,
as shown in FIG. 5. This is provided by assigning transmissions to
sequence shifts corresponding only to alternate code chip delays, rather
than to every code chip delay as in FIG. 4. The result is that, at best,
only one-half the number of transmissions, compared to the theoretical
maximum number, can be multiplexed. In practice, even fewer than one-half
the theoretical maximum transmitters are capable of being multiplexed in a
code division multiplex system using bipolar sequences because a guard
band that is greater than that provided using only alternate code shift
delays is required to avoid synchronization ambiguities.
In accordance with one aspect of the invention, the number of transmitters
that are capable of being multiplexed is increased to one less than the
theoretical limit by cross-correlating the input signal with a trinary
code developed by obtaining the difference between the code sequence
assigned to the particular transmitter to which the receiver is tuned and
a code sequence that is unassigned. In other words, two bipolar code
sequences are developed at the receiver. One of the codes is the replica
of the common code sequence transmitted by all the transmitters and has a
sequence shift that corresponds to the sequence shift of a predetermined
one of the transmitters. The second code is a replica of the common
bipolar sequence and has a code sequence shift that is not assigned to any
of the transmitters. One of the locally generated codes is subtracted from
the other, and the resultant, which is a trinary code sequence, is
correlated with the incoming signals. The sequence shift of the trinary
code sequence is brought to within one code chip of the sequence generated
by the preselected transmitter, using a static synchronization technique
to be described below. Perfect synchronization between the receiver and
preselected transmitter is obtained using dynamic synchronization, also to
be described in detail below, obtained generally by successively shifting
the timing of the receiver by a fraction of a code chip and monitoring the
output of the correlator. When the correlation output is at a peak, the
receiver and preselected transmitter are considered to be synchronized to
each other. Assuming now that the receiver and transmitter are also
synchronized to corresponding clock pulses (i.e., the transmitter is not
synchronized to one clock pulse and the receiver synchronized to another),
the polarity of the correlation output is monitored to extract the
transmitted data.
Development of the trinary pulse sequence to be cross-correlated with the
transmitted sequences is better understood with reference to FIGS.
6(a)-6(d). In FIG. 6(a), a transmitted bipolar sequence s(t) having an
absolute magnitude P and chip period T.sub.c is shown. This sequence is a
simplification of an actual sequence which, in practice, would be
substantially longer, e.g., 63 bits. Within the receiver is developed a
first reference pulse sequence r(t) shown in FIG. 6(b). The sequence r(t)
is identical to the sequence s(t) transmitted by the predetermined
transmitter shown in FIG. 6(a), because the transmitter and receiver
sequences have the same delay and are presumed synchronized to each other.
The receiver generates a second reference pulse sequence e(t), shown in
FIG. 6(c), which is the same sequence as the one transmitted by the
preselected transmitter as well as by all the other transmitters but has a
sequence delay that is not assigned to any of the transmitters.
The difference [r(t)-e(t)] between the two locally generated reference
pulse sequences is obtained, to provide the trinary pulse sequence shown
in FIG. 6(d). The trinary sequence has a value [+2, 0, -2], depending upon
the relative binary values of the two reference pulse sequences r(t) and
e(t).
It is to be understood that the sequence length in the example shown in
FIG. 6 is 7 bits, although in practice, much longer sequences would be
applied to accommodate a relatively large number of transmitters to be
code division multiplexed.
Referring to FIG. 7, development of the trinary reference sequence to be
cross-correlated with incoming bipolar pulse sequences for signal
demultiplexing is provided in a receiver 200. The receiver 200 receives
the transmitted pulse sequences s(t) and applies the incoming sequences to
the inputs of a first correlation multiplier 202 and a second correlation
multiplier 204. The first correlation multiplier 202 multiplies the
incoming sequences s(t) by the locally generated reference pulse sequence
r(t) having a sequence shift corresponding to the sequence shift of the
preselected transmitter. The multiplier 204 multiplies the incoming
sequences s(t) by the pulse sequence e(t) having an unassigned pulse
sequence shift. The resultant multiplication products are applied to a
difference circuit 206, and the difference is integrated and sampled in a
standard correlation filter 208 to develop an output signal y.sub.out.
It is pointed out that in FIG. 7, the input sequences s(t) are first
multiplied respectively by the two reference pulse sequences r(t) and
e(t), and then the product difference is obtained in difference circuit
206. This is equivalent to obtaining the difference between the two
reference pulse sequences r(t) and e(t) and then multiplying the
difference by the incoming sequences s(t).
The resultant cross-correlation is shown in FIG. 8. Note that each
correlation curve has a value 0 when the preselected transmission and
locally generated reference sequence r(t)-e(t) are displaced from each
other by more than one code chip. This contrasts with the
cross-correlation curve of FIG. 3, wherein there is a negative residual
correlation having a magnitude P.sup.2 /L. The magnitude of the
correlation curve increases linearly to a peak value of P(L+1)/L when the
preselected transmitted and locally generated reference pulse sequences
are synchronized.
The advantage of this correlation strategy is appreciated by comparing FIG.
9a showing the correlations of a number of neighboring transmissions in
accordance with the invention and FIG. 4. In particular, FIG. 9a shows
codes with a separation of 2 code chips. However, it will be appreciated
that the FIG. 9a transmissions can be displaced from each other by a
single code shift and that there is no overlap between the correlations of
adjacent transmissions, whereas in FIG. 4, overlap occurs in the
cross-hatched portions. The invention thus enables the number of
transmissions capable of being multiplexed to be equal to one less than
the length of the pulse sequence in bits, a result that is not possible
using prior art systems. Even if a guard band is placed between
transmissions in the strategy shown in FIG. 9a, the number of
transmissions that can be reliably multiplexed is substantially greater
than the number that can be reliably multiplexed using the correlation
strategy shown in FIG. 4.
Assume that the code-division multiplexed PSK signal Y(t) incoming at the
receiver is expressed as follows:
##EQU1##
where for J incoming transmissions: 0.ltoreq.t.ltoreq.T, where T is a code
chip period;
P.sub.j is the power within each incoming bipolar pulse sequence;
d.sub.j is the polarity or sign of each corresponding incoming sequence;
X.sub.j (t) is the transmitted data;
W.sub.c is the frequency of the carrier in radians;
0 is the carrier phase; and
N(t) is noise.
The output V.sub.A (T) of the conventional receiver, using a single
reference code sequence, is defined by the following:
##EQU2##
where: P.sub.r is the power of the desired incoming sequence;
d.sub.r is the data sign of the desired sequence;
L is the pulse sequence length in bits;
P.sub.j is the power of each of the undesired sequences;
d.sub.j is the corresponding data sign of the undesired sequence; and
N.sub.A is noise.
The output V.sub.B (T) of the receiver operating in accordance with the
principles of the invention is defined as follows:
V.sub.B (T)=P.sub.r d.sub.r (1+1/L)+N.sub.B (3)
Because the correlation method of the invention involves a subtraction of a
code sequence having an unassigned code sequence shift, all undesired
transmission components (identified by the subscript "r") in the output
V.sub.B (T) are perfectly rejected, whereas in the prior art receiver, the
output V.sub.A (T) involves contributions of the undesired transmissions
(having the subscript "j") as well as the desired transmissions (subscript
"r").
Multiplexer trinary signal correlation induces an additional three decibels
of degradation in data signal-to-noise demodulation with respect to white
noise appearing at the receiver input, compared to conventional
correlation using only the particular transmission binary pulse sequence.
Thus,
##EQU3##
The multiplexing strategy discussed above results in perfect unwanted
access rejection capability using ML codes of any length in a
code-division multiplex system. In the past, only ML codes of sufficiently
long length were potentially usable with the number of allowable
multiplexers being much less than the code length. Even there, power
imbalances of the multiplexing transmitters occurred.
Additionally, the ideal cross correlation pattern in FIG. 9a lends itself
to multiplexing schemes using more than the theoretical limit of code,
each time-offset by less than a code chip, and assuming a more complex
receiver configuration. For example, it has been discovered that the
number of transmitters which could be multiplexed can be increased to
2.times.(L-2) channels by adding a code between each of the code sequences
shown in FIG. 4, with only a slight trade off in overall receiver
signal-to-noise performance. As shown in FIG. 9b an additional code can be
inserted between each of the codes shown in FIG. 4. The codes are detected
at a plurality of taps provided at the receiver. The outputs of the
various receiver taps shown in FIG. 9b are as follows:
TABLE I
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1. extra code
2. 1/2 extra code
3. null
4. 1/2 code 1
5. code 1 + 1/2 code 1'
6. 1/2 code 1 + code 1' + 1/2 code 2
7. 1/2 code 1' + code 2 + 1/2 code 2'
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The sequence of equations may then be solved for each channel:
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channel 1 = 2 .times. tap 4
channel 1' = 2 .times. (tap 5 - channel 1)
tap 4)l 2 = 2 .times. (tap 7 - channel 1'
channel 2' = 2 .times. (tap 7 - channel 2 - tap 5)
"
"
channel L' = 2 .times. tap (2L + 3)
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In practice, the above arrangement would be somewhat difficult to implement
due to both noise and synchronization problems. An alternative
implementation would require that a null of the carriers occurred at the
point where the correlation envelope is equal to 1/2 the maximum. In such
an arrangement, the equations for the outputs of the taps become:
TABLE II
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1. extra code
2. null
3. null
4. null
5. code 1
6. code 1'
7. code 2
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This arrangement allows for full data recovery without interference.
However, it may still be somewhat susceptible to noise.
In order to overcome the above problems, there is shown in FIG. 9c an
arrangement in which two or more code sequences are grouped together and
separated | | |
