DE4220524A1 - Separate estimation of power in two superimposed stochastic processes - by sampling and filtering to identify inputs for processing to identify separate signal and noise components - Google Patents

Abstract

The separate power content of two stochastic processes that are superimposed upon each other are identified in an evaluation process. The method can be used to determine the signal to noise ratio when a signal has superimposed noise. The input signal(x) is subjected to digital sampling to generate second and fourth order components (E2, E4) that are provided as an input to a processor. The processor executes specific mathematical formula (14) to separate the signal and noise components (S, N). ADVANTAGE - Allows signal noise to be estimated.

Description

Procedure for the separate estimation of the individual performances of two stochastic processes from the observation of the sum process created by additive superposition are used, among other things, to estimate the signal-to-noise ratio (signal-to-noise ratio, SNR) of a disturbed signal, that is the quotient of the power a desired part (signal) and an undesirable part (disturbance). In Following this application, one of the addendum processes is described below Utility process with the associated useful power, the other as a disturbance process with the associated Interference power, and that from the additive superposition of the two processes resulting time function called signal. The signal is used for further processing scanned. The resulting samples consist of the additive Superposition of a time-discrete usage process (usage samples) and a time-discrete Interference process (interference samples).

1. State of the art

So far, methods for estimating the SNR have mainly been found in digital data transmission Use. The process is i. a. cyclostationary with the symbol step speed as a period, while the disturbance process is assumed to be weakly stationary can be. In addition to simple geometric shapes that can only be used to a very limited extent One of the main considerations was a split symbol moments SNR estimation Procedures a practical meaning (B. Shah, S. Hinedi, "The split symbol moments SNR estimator in narrow band channels ", IEEE Trans. Aerospace and Electronic Systems, vol. 26, no. 5, pp. 737-747, September 1990). An estimate for the SNR is included by arithmetic operations from the first and second order time averages of the Absolute amount of the samples determined. However, this procedure has two serious ones Disadvantages: On the one hand, it is necessary to sample the signal so that several samples are available per symbol step (oversampling). The quality of the estimate depends directly on the amount of oversampling. On the other hand leads mutual Superposition of the signal curves of adjacent symbol steps (inter-symbol interference, IS) to no longer meet expectations, d. H. erroneous estimate.

2. Principle of the invention

The invention is based on the calculation of the SNR from the time averages second and fourth order of the amount of the sampled (and possibly digitized) signal. If the method in digital transmission technology for determining the signal-to-interference ratio is used, the sampling of the receiver input signal is sufficient after the receive filter in symbol cycle. The calculation is then carried out by solving an i.a. quadratic system of two equations. To set up this system of equations it is sufficient if the forms of probability density distributions (i.e. up to the performance of the process) the amplitudes of useful and interference samples are known. These are e.g. B. in digital transmission by the modulation method (e.g. phase shift keying) and the type of interference (e.g. Gaussian noise or  Crosstalk given by another signal with phase shift keying). The time averaging and the calculation (i.e. solving the system of equations) can be done by integrated or discretely constructed hardware or by running on a processor Program.

3. Mode of operation of the procedure

Bold italic letters b subsequently denote stochastic processes, italic letters b one of their pattern sequences and subscripted Greek letters b _γ the temporal numbering of the sequences. The probability density function (WDF) of the random variables of a real-valued stochastic process b is denoted by f _b (b) and is assumed to be time-invariant. For complex valued stochastic processes b∈C there is a composite probability density

a complex random variable. The expected value is defined as

for real processes (order n) or

for complex processes (order n + m). The kurtosis k _{b of} a stochastic process b is defined as

and remains constant for a given form of WDF, regardless of the performance of the Process.

In the following the sampled signal is called i. a. complex, time-discrete stochastic Process x is understood to be the additive superimposition of a, as a useful process designated discrete-time stochastic process e and a discrete-time discrete stochastic process n, so that:

It is assumed that

• 1. Usage and disturbance processes are uncorrelated:
• 2. Real and imaginary part of at least one of the two processes. B. the disturbance process, orthogonal are:
• 3. Both processes are free of mean values: or the first and third moments of one of the two processes disappear:

Formation of the second and fourth order expected values of the observed summation process x provides

in which

the desired average energy of the discrete-time process and

is the mean energy of the discrete-time disruptive process that is also to be determined. For the fourth order moment arises

Using the requirements (3) to (6), all expected values disappear, in which one of the processes occurs in an odd power. Using the Abbreviations (8) and (9) give the following for complex valued processes e and n System of equations for S and N:

Insertion of the kurtoses (1) of the useful and disruptive process leads to

For real-valued processes e and n, the following results accordingly:

Solving this system of equations according to S and N leads to

With

The solutions (14) exist if D {x} 0 was for many known digital transmission methods with noise or crosstalk interference or adjacent channel interference given is.

For a specific application, it must first be determined whether real or complex processes are available. Correspondingly, choose c in (15). In the next step, the kurtoses of useful and disruptive processes k _e and k _{n are} to be determined according to (1). Inserting in (15) gives C and an expression for D {x}. By inserting in (14), an equation for S and N is created.

5. Technical implementation

A technical implementation of the method consists of the implementation of the Expected value formation and the arithmetic unit for (14). This can be the case through discrete, digital circuits, partially or fully integrated circuits or by a program running on a processor. In all three cases the function is completely described by a signal flow graph.

The expected value operator used in the section above is replaced by a time averaging. Is suitable for. B. an AR filter of the first order, resulting in a structure according to Fig. 3.

If the WDFs of useful and disturbance process have properties so that no solution to (14) exists (e.g. if it is a Gaussian process in both cases), the WDF can do one or both processes by partitioning the The quantity of values in subsets and the use of only those samples contained in one of these subsets are changed so that (14) can be solved. Fig. 4 shows an example of a receiver for data transmission in the baseband. The decision maker divides the alphabet of the transmitted symbols into two subsets A and B, of which only one (subset B) is used to determine the signal-to-noise ratio.

Claims (5)

1. A method for determining the individual powers of the signals of two additively superimposed stochastic processes from the observation of the sampled sum signal, characterized in that the mean values of the second and fourth powers of the amount of the sampled values of the sum signal are used for the determination. 2. The method according to claim 1, characterized, by taking advantage of the performance-invariant kurtoses of the two superimposed ones Processes whose individual performances are the solution of a quadratic system of equations result as a function of the mean values according to claim 1. 3. The method according to claims 1 and 2 applied in transmission systems, characterized in that the signal breaks down at least one individual process into signal elements, the quantity this signal element is then partitioned into disjoint subsets, and only the signal elements that are in one or more of these subsets are included to determine the individual services according to claim 1 or 2 be used. 4. Device for determining the individual powers of the signals of two additively superimposed stochastic processes from the observation of the sampled sum signal at the input, characterized in that the method according to claims 1 and 2 or 3 is used and the input signal in the shown by Fig. 1 to 3 Is processed in a manner or in a manner resulting from redrawing the signal flow graphs from FIGS. 1 to 3. 5. Device according to claim 4 for determining the signal-to-noise ratio, characterized in that the useful signal as one process and the disturbance as the other process, subsequently determined according to claims 1 and 2 or 3, the individual services and the signal-to-noise ratio is determined from this.