WO1992008307A2 - Optimal demodulator using maximum a posteriori probability estimation - Google Patents
Optimal demodulator using maximum a posteriori probability estimation Download PDFInfo
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- WO1992008307A2 WO1992008307A2 PCT/US1991/007819 US9107819W WO9208307A2 WO 1992008307 A2 WO1992008307 A2 WO 1992008307A2 US 9107819 W US9107819 W US 9107819W WO 9208307 A2 WO9208307 A2 WO 9208307A2
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/18—Phase-modulated carrier systems, i.e. using phase-shift keying
- H04L27/22—Demodulator circuits; Receiver circuits
- H04L27/233—Demodulator circuits; Receiver circuits using non-coherent demodulation
- H04L27/2338—Demodulator circuits; Receiver circuits using non-coherent demodulation using sampling
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/10—Frequency-modulated carrier systems, i.e. using frequency-shift keying
- H04L27/14—Demodulator circuits; Receiver circuits
- H04L27/156—Demodulator circuits; Receiver circuits with demodulation using temporal properties of the received signal, e.g. detecting pulse width
- H04L27/1566—Demodulator circuits; Receiver circuits with demodulation using temporal properties of the received signal, e.g. detecting pulse width using synchronous sampling
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/18—Phase-modulated carrier systems, i.e. using phase-shift keying
- H04L27/22—Demodulator circuits; Receiver circuits
- H04L27/233—Demodulator circuits; Receiver circuits using non-coherent demodulation
- H04L27/2332—Demodulator circuits; Receiver circuits using non-coherent demodulation using a non-coherent carrier
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/0014—Carrier regulation
- H04L2027/0024—Carrier regulation at the receiver end
- H04L2027/0026—Correction of carrier offset
- H04L2027/003—Correction of carrier offset at baseband only
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/0014—Carrier regulation
- H04L2027/0044—Control loops for carrier regulation
- H04L2027/0053—Closed loops
- H04L2027/0055—Closed loops single phase
Definitions
- the present invention relates to communications systems and, more particularly, to phase angle demodulators. Background of the Invention
- the transmitted signal is typically corrupted by noise and, therefore, the receiver must operate with received data that reflects the combination of the transmitted signal and noise.
- the received data equation can be expanded as follows:
- y(t) ⁇ 2eAcos[w o t+ ⁇ (t)] + n(t) (1)
- A is the signal amplitude
- w o is the carrier or reference frequency
- ⁇ (t) is the time-varying phase function
- n(t) is noise.
- phase-locked loop is a circuit that consists of a phase detector which compares a frequency of a voltage-controlled oscillator (VCO) with that of an incoming carrier signal.
- VCO voltage-controlled oscillator
- a phase-error signal output by the phase detector after passing through a linear filter, is fed back to the voltage-controlled oscillator to keep the oscillator generated frequency "locked” in a fixed phase relationship with the input or reference frequency.
- the phase-error signal output of the linear filter is a low frequency (baseband) signal that is proportional to the input frequency and, thus, represents the demodulated information in the FM signal.
- phase-locked loops are suboptimal since the phase-locked loop is a "causal" system.
- a system is causal if the output at any given time depends only on values of the input at the present time and in the past.
- Such a system can also be referred to as “nonanticipative", as the system output does not anticipate future values of the input.
- phase samples based on noisy data can be measured by the extraction of in-phase (I) and quadrature (Q) components from the data which determine a measured phase angle according to the arctangent operation tan -1 (Q/I).
- the optimization of phase demodulation can then be expressed as minimizing the mean- squared error between the phase estimate ⁇ ⁇ ( ⁇ ) and the correct phase value ⁇ ( ⁇ ), with extra information provided by the mean phase ⁇ m ( ⁇ ) of the prior (a priori) phase distribution.
- This approach implies that the receiver must solve a nonlinear integral equation as follows:
- ⁇ ⁇ ( ⁇ ) - ⁇ m ( ⁇ ) is the difference between the phase estimate ⁇ ⁇ ( ⁇ ), at a time ⁇ , t o ⁇ t, and the prior mean phase ⁇ m (issue) at time TL
- N 0 /2 is the noise power spectral density
- ⁇ is time
- R ⁇ ( ⁇ - ⁇ ) is the phase covariance function defined as the expected value E ⁇ [ ⁇ (r)- ⁇ m ( ⁇ )] [ ⁇ ( ⁇ ) - ⁇ m ( ⁇ )] ⁇ .
- phase-locked loop (PLL) for phase estimation, as for example shown in Figure 1, follows from the similarity of the loop equation, equation (3) below, to the estimate in equation (2).
- the loop equation which is implemented as a phase-locked loop, is described by the following equation:
- Equations (2) and (3) are similar if ⁇ m (t) is either 0 or is added to the estimate obtained from the loop equation. Although the equations are superficially similar, they differ in that whereas the phase-locked loop uses information in the interval [ - ⁇ , ⁇ ] , the optimum demodulator uses all of the information in the observation integral [t 0 ,t] to determine the phase estimate at time ⁇ .
- fading signal amplitude fluctuations
- time-dependent noise power are phenomena that are prevalent in mobile receivers such as aircraft and automobiles.
- the Tufts and Francis block process uses a sequence of samples from a time interval defined by a block. An estimated phase sample at the beginning of the interval can thus be influenced by data samples at the end of the interval, emulating the desired noncausal process.
- the demodulated phase samples are available after the complete block has been processed. This implies that there is a delay of up to one block length between a data sample and the corresponding phase estimate. Nonetheless, such a delay can be so small as to be unnoticeable in a two-way communication system, and is irrelevant to one-way systems such as consumer radios, televisions receivers and facsimile machines.
- the error of a time invariant signal can be reduced by averaging noisy samples over the duration of the block.
- the averaging process is replaced by filtering, where the filter is based on the expected correlation between signal samples.
- the same correlation information can be used to predict a given sample from past data, and a MAP estimator often forms a weighted sum of a prediction based on past data and filtered, demodulated samples from the current data block.
- the phase estimation process uses a weighted sum of a phase sample ⁇ m predicted from past data and a processed version of the measured phase samples ⁇ from the current data block.
- the operation that must be applied to current phase samples is difficult to implement because the desired MAP phase estimate ⁇ ⁇ from the current data block is a filtered version of a nonlinear (sine function) version of the same desired phase estimate, as well as desired estimates at other sampling times within the data block.
- the iterative MAP estimation method is inefficient for practical, real-time receivers which employ standard, sequential instruction execution, or von Neumann, computers.
- Hopfield U.S. Patent No. 4,660,166
- Hopfield U.S. Patent No. 4,719,591
- Hopfield, et al. U.S. Patent No. 4,719,591
- a Hopfield network (also called a crossbar network) comprises a set of amplifiers, typically including operational amplifiers, that are interconnected by feedback lines.
- the output of each operational amplifier is nonlinearly filtered so that the output voltage of each amplifier lies in the unit interval [0,1]. Network stability is assured because the maximum voltage at each output is thereby limited.
- the network amplifiers are fed by a set of bias currents, ⁇ b ⁇ , which are generated external to the network and are generally associated with external data.
- ⁇ b ⁇ bias currents
- a set of variable gain amplifiers are interposed in the feedback lines.
- the gain on each amplifier is adjusted by a set of feedback weights, (T).
- T feedback weights
- phase angle demodulation is fundamental to many communication systems and FM radio receivers.
- high quality FM receivers use phase-locked loops for demodulation, but these systems are theoretically suboptimal.
- the optimal demodulator must solve a non-linear integral equation. As is well known, such an integral solution is difficult to achieve in real-time. If a simple analog or digital circuit could be found to more closely approximate the desired optimal demodulator, such a circuit would improve demodulation performance thereby replacing the traditional phase-locked loop found in high performance radio, television and communication systems.
- the present invention which includes a system and method for optimal maximum a posteriori (MAP) angle demodulation.
- the system described herein uses a set of amplifiers interconnected via feedback (referred to herein as a Hopfield or crossbar network) to quickly solve the angle demodulation equation, and thus obtain optimal phase estimates.
- One preferred embodiment of the present invention is an angle demodulator comprising a network having a plurality of amplifiers each amplifier having a plurality of inputs, a bias, b, and an output wherein a set of feedback lines are connected between a selected set of amplifier outputs and a selected set of amplifier inputs, and block processing means for iteratively setting each amplifier bias as a function of the difference between a predicted mean phase estimate ⁇ m and a measured phase ⁇ at a time where 1 ⁇ j ⁇ K for a K-sample data block and is a sampling period of a signal time sample y
- the system requires that specific operational amplifier bias currents and feedback weights be determined by input data, and that the sigmoid nonlinearity at each of the amplifier outputs have a specific functional form.
- Each desired phase sample ⁇ ⁇ can be obtained by adding the corresponding measured phase sample ⁇ to the difference value ( ⁇ indicating the final state of convergence) determined by the Hopfield network.
- the disclosed system and method generalize the previous MAP results for angle demodulation by incorporating time dependent (non-stationary) signal and hoise power, as well as an estimate of this power. Since the present invention more heavily weights samples with high signal-to-noise ratio (SNR), theoretically, it will significantly out-perform other demodulation techniques including the phase-locked loop.
- SNR signal-to-noise ratio
- the phase-locked loop can still be used in application receivers as a pre-processor for estimating some of the signal parameters that are used in the optimum demodulator, namely, time-varying amplitude and noise power.
- Other parameters including the predicted mean phase, can be predicted from past data with the help of an operation that uses past estimates to update information about the demodulated signal.
- This updated information in the form of estimated signal covariance values, can also be used directly in the optimal demodulator.
- the receiver can thus "learn" to better demodulate a given type of signal, e.g., voice, music, a specific kind of acoustic or electromagnetic emission, or a sequence of phase shifts, as it performs a demodulation task.
- the learning process of the present invention is applicable to phase, frequency and amplitude demodulation.
- the MAP phase demodulator can be used as a detector-classifier of random (stochastic time series) data.
- different phase modulation processes are represented by different phase covariance functions implemented in a parallel set of demodulators.
- a model of the received signal is synthesized from each demodulator output, and the corresponding signal models are correlated with the original input data.
- the correlator with the largest output indicates the best match between the synthesized signal and the actual data.
- the largest correlator output is compared with a predetermined threshold in order to detect the signal, and the signal is classified in accordance with the largest correlator output if the threshold is exceeded.
- This receiver configuration is an example of an estimator- correlator configuration for detection/classification of random signals.
- the disclosed system differs from standard estimator-correlators in that the covariance of the phase function is specified, rather than the covariance of the data samples themselves.
- Figure 1 is a block diagram of a conventional phase-locked loop.
- Figures 2a, 2b are representations of large overlap and fifty percent overlap means of making phase estimates with K- sample data blocks using the principles of the present invention.
- FIG. 3 is a block diagram of one presently preferred embodiment of a maximum a posteriori (MAP) angle demodulator of the present invention, using a Hopfield network.
- MAP maximum a posteriori
- FIG. 4 is a block diagram of the Hopfield network shown in Figure 3.
- FIG 5 is a block diagram of two amplifiers with feedback connections as used in the Hopfield network shown in Figure 4.
- Figure 6 is a block diagram of one preferred memoryless nonlinear filter circuit, shown in Figure 5, used to generate a nonlinear sigmoid function.
- Figure 7 is a block diagram of one presently preferred embodiment of an amplitude demodulator and noise power estimator having a phased-locked loop for providing amplitude and noise power parameters to the angle demodlator shown in Figure 3.
- Figure 8 is a block diagram of one presently preferred embodiment of a signal detector-classifier that incorporates the angle demodulator of the present invention.
- FIG 1 is a block diagram of a phase-locked loop 100 which is known in the prior art.
- the input to the phase locked loop 100 is received signal data y(t) as defined in equation (1).
- the received signal in many applications is an FM signal, such as that generated by a radio station, that is received via an antenna.
- the received signal data is correlated with the generated carrier signal at a phase-detector 102.
- the carrier signal generated by the phase-locked loop 100 is a periodic function that results from system feedback.
- the signal that is output by the phase detector 102 is fed into a linear filter 104 having an impulse response defined by the phase covariance matrix, R ⁇ (t).
- the output of the linear filter 104 is the phase-error signal e(t) as defined in equation (3).
- the carrier signal which is one of the inputs to the phase-detector 102, is generated by a feedback path which originates from the output of the linear filter 104.
- the phase-error signal is fed into a device that measures the rate of change of the phase-error, as indicated at a derivative block, or differentiator 106.
- the output of the derivative block 108 controls a voltage-controlled oscillator 110 which generates the carrier signal.
- phase-error signal which results from the phase- locked loop 100 is fed to an inverting input of a summing amplifier 110.
- the other input of the summing amplifier 110 is received from an outside source (not shown) as a predicted mean signal phase ⁇ m (t).
- Equation (5) is an iterative process for block MAP phase estimation, given amplitude
- ⁇ m can be computed via regression (linear prediction) from prior phase estimates, again using R ⁇ ( ⁇ ).
- SNR signal-to-noise ratio
- the size K of each received signal data block should ideally be such that is at least as large as the duration of R ⁇ ( ⁇ ), so that correlated phase samples on both sides of a given sample contribute to the estimated phase of the sample by way of the phase covariances R ⁇ ( ⁇ ).
- estimated phase samples near the left (early) edge of a block will be influenced primarily by later data samples, rather than by both earlier and later samples, as desired.
- FIGS. 2a are one representation of how data samples would be processed in a phase angle demodulator according to the present invention.
- a compromise between non-overlapping and overlapping configuration e.g., that shown in Figure 2a, is to use blocks with fifty percent overlap, and to only save phase estimates from the middle half of each block.
- Figure 3 illustrates one preferred embodiment of a maximum a posteriori (MAP) angle demodulator 200.
- the angle demodulator 200 relies upon the fundamental result of the present invention: the iterative equation for block MAP phase estimation can be realized by a Hopfield network (mathematically represented below in equation (15)).
- the Hopfield network is provided with inputs (the feedback weights T jk and bias currents b(k) defined, respectively, in equations (17) and (18) below) that represent a time-series , 1 ⁇ k ⁇ K of functions of sampled phase sampled amplitude
- the feedback weights T jk and bias currents b(k) defined, respectively, in equations (17) and (18) below
- the received signal data y(t) is fed into two parallel paths, beginning at a pair of multipliers 202a,b so as to decompose the received signal into its in-phase (I) and quadrature (Q) components (hereinafter collectively referred to as quadrature components).
- the multiplier 202a multiplies the cosine of the product of carrier frequency and time t, cos(w o t), by the received signal data to obtain the in-phase component thereof.
- the multiplier 202b multiplies the received signal data by -sin(w o t) to obtain the quadrature component of the received data.
- the quadrature components are then independently integrated by a pair of integrators 204a,b.
- the outputs of the integrators 204a,b are sampled by a pair of sampling circuits 206a,b, respectively.
- the sampling circuits 206a,b sample the integrator outputs at a predetermined interval
- the sampled quadrature components are fed by the sampling circuits 206a,b into an arctangent circuit 208 which performs the function arctan(Q/I).
- the output of the arctangent circuit 208 is a time series of phase samples ⁇ of the received signal, which include additive noise.
- the arctangent function could be implemented with a lookup table memory wherein the value Q/I would address prestored values corresponding to the result of the arctangent function.
- phase samples ⁇ are fed into the inverting input of a summing amplifier 210.
- the other input of the summing amplifier 210 is fed by the output of a phase predictor 212.
- the phase predictor 212 receives estimates of the past phase angle estimates and generates a predicted mean phase ⁇ m based thereon.
- the output of the summing amplifier 210 is a sequence of errors that contribute to the bias currents of a Hopfield, or crossbar, network 214.
- the structure and function of the Hopfield network 214 is more fully discussed below with reference to Figures 4 and 5.
- the sample amplitude is fed into a multiplier 222 which multiplies the amplitude by scaling factors comprising an estimate of time-varying inverse noise power samples separated by seconds ) and an estimate of the time- varying signal amplitude
- a multiplier 222 which multiplies the amplitude by scaling factors comprising an estimate of time-varying inverse noise power samples separated by seconds ) and an estimate of the time- varying signal amplitude
- angle demodulator 200 may also be configured without the time-varying inputs. However, such scaling factors are desirable for certain applications including mobile receivers as previously discussed.
- each scaled sample amplitude output by the multiplier 222 is fed into a shift register 224.
- the shift register 224 thus saves a sequence of scaled amplitude values in the chronological order:
- the parallel outputs of the shift register 224 are used to feed the scaled amplitude samples into a set of multipliers 226 which multiply the stored scaled amplitude values by the phase covariance matrices R ⁇ [(k-j)
- These matrices can be updated over time so that the system "learns" or adapts to a particular type of transmission, e.g., an FM radio station broadcasting Bizet's Carmen.
- One preferred mechanism to determine the covariance parameters is discussed below with respect to equations ( 28 ) and (29 ) .
- Figure 3 also shows that the outputs of the multipliers 226 are the feedback weights T jk that are fed into the Hopfield network 214. Since the process of obtaining a MAP phase estimate is iterative, the Hopfield network must be allowed to converge after each sample is input into the angle demodulator 200, based upon the surrounding K-sample block which affects the biases b(k) and the feedback weights
- FIG. 4 illustrates a general configuration of a Hopfield, or crossbar, network such as indicated at 214 in Figure 3.
- the generalized network comprises a set of N amplifiers, represented in Figure 4 by the four amplifiers 240a,b,c,d.
- the amplifiers of the Hopfield network 214 are implemented by operational amplifiers having an output voltage determined by a nonlinear function of the input voltage.
- the operational amplifiers may contain nonlinear filtering circuitry, or, as described herein, additional nonlinear filtering circuitry (not shown) may be fed by the outputs of the operational amplifiers 240.
- the combination of operational amplifier and nonlinear filter will hereinafter be referred to collectively as an amplifier.
- the amplifiers 240 are interconnected by a set of feedback lines 242a,b,c,d.
- the amplifier 240a receives auto-feedback, or feedback from itself, via the line 242a.
- cross-feedback is received from the amplifier 240b via the feedback line 242b, and so on for the remaining feedback lines 242c,d connected to the amplifier 240a.
- the four feedback lines 242a,b,c,d are thus shown as feeding the amplifier 240a.
- the network is configured such that the number of feedback lines is equal to the number of amplifiers N in the network.
- variable gain amplifiers 244a,b,c,d are interposed in the feedback lines 242a feeding amplifier 240a. Although not shown, similar amplifiers would be interposed in the feedback lines feeding the remaining N-1 amplifiers.
- the variable gain amplifiers 244 have their gains controlled by a set of feedback weight lines 246a,b,c,d.
- the feedback weight lines 246 carry voltages to the variable gain amplifiers 244 that are defined as T jk .
- the weights T jk are a function of sampled amplitudes generated by the angle demodulator 200 ( Figure 3). In an embodiment where signal amplitude is constant, the weights T jk could be constant.
- the amplifiers 240 thus act to sum the weighted feedback signals which are fed into the amplifiers 240 by the feedback lines 242.
- the stable state of the network is governed by varying currents across a set of bias lines 248.
- the bias currents, or signals, transmitted across the bias lines 248 are, in turn, a function of the sampled angle ⁇ and a summation of feedback weights T jk .
- the outputs of the amplifiers 240 (representing the output of the Hopfield network) may be sampled across the lines 250a,b,c,d.
- the bandwidth of the demodulated phase function ⁇ (t) can be between 50 kHz and 500 kHz if each sample is at the center of its own block.
- the corresponding bandwidth of the phase function ⁇ (t) is between 1.6 MHz and 16 MHz.
- the required Hopfield implementation is obtained by comparing the MAP iteration equation (5) with the discrete- time update equation of a Hopfield network.
- the Hopfield network is generalized such that each operational amplifier in the network is allowed to feedback to itself, as well as to all the other amplifiers as shown in Figure 4. Auto-feedback does not upset the stability of the network; stability is assured by the sigmoid nonlinearities at the outputs of the operational amplifiers, which limit the maximum output voltage of each amplifier to unity, e.g., input and output voltages between 0V and IV.
- the output of each operational amplifier is nonlinearly distorted by the amplifier so as to lie in the interval (0,1) and is fed back to every other element as shown in Figure 4.
- ⁇ k is a resistor-capacitor (RC) time constant that can be set equal to unity for convenience
- T kj are elements of a feedback connectivity matrix
- v(j,t) is an output voltage from the j th amplifier
- b(k) is a constant bias current
- Equation (7) The discrete-time update equation of a Hopfield network is obtained from equations (6) and (7) by letting w(k,i) denote the input voltage to the sigmoid nonlinearity at the output of the k th operational amplifier at time i ⁇ , where ⁇ is the sampling interval.
- the feedback weight from the j th operational amplifier output v(j,i) to the input of the k th operational amplifier is T kj .
- the bias current of the k th operational amplifier is b(k) and the RC time constant ⁇ i of the i th operational amplifier is assumed to be unity.
- K b (k) e m - ( 1/2 ) ⁇ T kj
- Figure 5 illustrates two elements, j and k, of a preferred embodiment of the Hopfield network 214 ( Figure 3) included in the present invention.
- the operational amplifiers 260a,b are respectively connected to the external bias signals b j , b k and feedback weight signals T jk , T kj via the variable gain amplifiers 262a,b.
- the variable gain amplifiers 262 receive their input current from feedback lines (only cross-feedback lines are shown).
- the operational amplifiers 260a,b are linear devices comprising, respectively, summing amplifiers 264a,b.
- the summing amplifiers 264 sum all of the weighted feedback signals including the bias currents b j , b k .
- the output of each summing amplifier 264 is fed into multipliers 266a,b where the summed signal is multiplied by the time constant ⁇ k .
- the resultant signal is output from the operational amplifier 260 and fed back to the summing amplifiers 264 through derivative devices 268a,b.
- the derivative operation and associated time constant are a consequence of feedback of the linear amplifier output through a resistor arid capacitor connected in parallel.
- the output of each amplifier 260 is also fed to a nonlinear filter 270 to implement a nonlinear function such as the sigmoid nonlinearity defined in equation (15).
- one preferred embodiment of the nonlinear filter 270 for implementing equation (15) includes a hard limiter 272 to clip or limit the input signal e to take on values between - ⁇ /2 and ⁇ /2.
- the limited input signal is thereafter fed to a sinewave generator 274 such as, for example, the AD639 distributed by Analog Devices.
- the output of the generator 274 is the trigonometric function sin(e).
- the sinewave is fed into an amplifier 276 wherein the gain is set to one- half.
- the resultant signal is received by a summing amplifier 278 that adds in a constant or dc signal of one- half, e.g., .5v.
- Figure 7 shows a phase-locked loop approximation to the optimum amplitude demodulator and noise power estimator at time
- the estimates thus provided are the inputs to the multiplier 222 of the angle demodulator 200 shown in Figure 3.
- a voltage-controlled oscillator 280 receiving a control signal from the phase-locked loop 100, provides a carrier signal to a multiplier 282.
- the multiplier 282 outputs the carrier signal multiplied by the received data y(t).
- the resultant value is input into a summing amplifier 284.
- the summing amplifier 284 also is fed a constant amplitude A o .
- the result of the summing amplifier 284 is fed into a linear filter 286 to output the difference between the estimated amplitude A ⁇ (t) and the constant amplitude A o .
- the difference A ⁇ (t)-A o and the constant amplitude A o are then fed into a summing amplifier 288 to arrive at the estimated amplitude A ⁇ (t).
- the output of the summing amplifier is then sampled at the system sampling period by a sampling circuit 289 to produce an estimated amplitude & A (
- ⁇ ⁇ n 2 E[y -s ] 2
- the phase-locked loop approximation to the estimated noise power is achieved in Figure 7. beginning from the path feeding the estimated amplitude A ⁇ into a multiplier 290.
- the estimated amplitude is multiplied by the carrier signal generated by the voltage-controlled oscillator 280.
- the carrier signal is thus also fed into the multiplier 290, and the resultant value is summed at a summing amplifier 292 with the received signal data y(t).
- the result of the summing amplifier 292 is fed into a squaring circuit 294 which feeds its results into an integrator 296.
- the output of the integrator 296 is divided by the sampling period at a block 298 thus providing the noise power estimate ⁇ ⁇ n 2 at time
- each estimated phase sample is computed from its own block of surrounding data samples ( Figure 2a)
- a linear prediction of ⁇ ) based on past estimated phase values is a weighted sum of the past values as defined below: ⁇ ⁇ m - ⁇ ⁇ [(k-j) (23)
- the matrix C ⁇ can be obtained from the phase covariance matrix R ⁇ , since
- ⁇ ⁇ m [ ⁇ ⁇ m ( , ⁇ ⁇ m [(k+1) ,..., ⁇ ⁇ m [(k-1+K/2)]] ⁇ ,
- ⁇ ⁇ [ ⁇ ⁇ (k-K/2), ⁇ ⁇ (k+1-K/2),..., ⁇ ⁇ (k-1)] ⁇ ,
- phase covariance matrix An updated estimate of the phase covariance matrix can thus be used to compute ⁇ m and to change the feedback weights T kj in equation (17) from one data block to the next.
- a suboptimum but simpler phase demodulator is obtained by assuming that ⁇ n 2 and A are constant over a block, and by using a fixed covariance matrix as in Tufts and Francis. If a fixed phase covariance matrix is used, the matrix inverse C ⁇ -1 can be precomputed and implemented as a weighted sum of data samples for predicting ⁇ m from past ⁇ ⁇ estimates as in equation (24).
- FIG 8 shows a block diagram of a signal classifier that incorporates the angle demodulator of the present invention.
- the received signal data y(t) is input to a set of estimators 320a,b,c.
- Each estimator demodulates the signal data y(t) to find the phase function ⁇ (t) using phase covariance information (using the angle demodulator 200 shown in Figure 3, for example) and then synthesizes a version of the input signal based on the estimated phase function.
- the synthesized signals output by the estimators 320 are correlated with the received data at a set of multipliers 322a,b,c.
- a set of delays 323a,b,c are interposed between the incoming signal y(t) and the correlators 322 to properly synchronize the correlation process.
- the resulting correlation signals output from the multipliers 322 are integrated by a set of integrators 324 and thereafter sampled by a set of sampling circuits 326.
- the classifications based on the bank of estimator- detectors have output signals that are compared to find the largest at a compare circuit 328.
- the compare circuit also determines whether the largest correlation is greater than a predetermined threshold. If the largest correlation is greater than the predetermined threshold, then the signal address associated therewith is generated by the compare circuit 328.
- the use of the phase covariance as a model of a given process implies a nonlinear estimation. This is in contrast to the usual form of estimator-correlator which employs a linear estimator based on covariance functions of "raw" data samples.
- a Hopfield network with appropriate sigmoid nonlinearity is well matched to solving the nonlinear integral equation associated with optimum phase demodulation.
- the present invention represents a new and important use of the Hopfield network exploiting all aspects of the network, including nonlinear effects. It is believed that the present invention is a significant improvement over existing phase-locked loop circuitry which exists in many radio, television and other like receivers.
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JP3518497A JPH06502519A (en) | 1990-11-01 | 1991-10-23 | Optimal demodulator with maximum a posteriori probability estimation |
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US07/607,582 US5303269A (en) | 1990-11-01 | 1990-11-01 | Optically maximum A posteriori demodulator |
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PCT/US1991/007819 WO1992008307A2 (en) | 1990-11-01 | 1991-10-23 | Optimal demodulator using maximum a posteriori probability estimation |
Country Status (5)
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US (3) | US5303269A (en) |
EP (1) | EP0555348A1 (en) |
JP (1) | JPH06502519A (en) |
CA (1) | CA2094612A1 (en) |
WO (1) | WO1992008307A2 (en) |
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US5590158A (en) * | 1993-01-28 | 1996-12-31 | Advantest Corporation | Method and apparatus for estimating PSK modulated signals |
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1991
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- 1991-10-23 EP EP91920304A patent/EP0555348A1/en not_active Withdrawn
- 1991-10-23 WO PCT/US1991/007819 patent/WO1992008307A2/en not_active Application Discontinuation
- 1991-10-23 CA CA002094612A patent/CA2094612A1/en not_active Abandoned
-
1994
- 1994-04-11 US US08/225,759 patent/US5491724A/en not_active Expired - Fee Related
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1995
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Also Published As
Publication number | Publication date |
---|---|
US5619537A (en) | 1997-04-08 |
JPH06502519A (en) | 1994-03-17 |
CA2094612A1 (en) | 1992-05-02 |
WO1992008307A3 (en) | 1992-07-09 |
US5491724A (en) | 1996-02-13 |
EP0555348A1 (en) | 1993-08-18 |
US5303269A (en) | 1994-04-12 |
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