DE102011103642B4 - Method and device for determining a frame start of a communication signal - Google Patents

Abstract

Method for determining a frame start of a communication signal (7, 7) to be analyzed, with the following method steps: - Detecting (S) at least one signal range (Y) from the communication signal (7, 7) to be analyzed with a detection unit (21); Generating (S) a reference signal (P) as a function of a power profile of the at least one signal range (Y) of the communication signal (7, 7) to be analyzed, with active slots and burst types within active slots being used to generate the reference signal (P), and the active slots and burst types being specified by a user; determining (S) a first metric by means of a convolution operation between the at least one signal range (Y) and the reference signal (P), the convolution operation for the magnitude of the at least one signal range (Y ) and the complex conjugate part of the reference signal (P *) is calculated; - Output (S) the position of the maximum of the first Metric as time offset (τ̂) for the frame start.

Description

The invention relates to a method and a device for determining a frame start of a digitized communication signal, in particular a GSM signal (global system for mobile communication; dt. Worldwide system for mobile communication).

In development phases it is often necessary that a communication signal, which is generated, for example, by a prototype of a communication system to be developed, for example a mobile terminal, can be analyzed for any errors. Such a communication signal is digitized so that it can then be demodulated. Within the communication signal, which is, for example, a GSM signal, the information is transmitted within individual bursts, with a burst usually being transmitted within a slot. Several slots are combined to form a frame. In order to be able to demodulate the individual bursts within the individual slots, knowledge of the start of the frame is necessary. To determine the start of the frame, there are various methods that can determine this precisely down to a fraction of a symbol. However, the computational effort with which the frame start can be determined increases with the accuracy with which it is to be determined. In many applications, e.g. in production tests, however, it is often sufficient if the frame start can be calculated with an accuracy of two to three symbols, because a subsequent synchronization process has a search area that includes several symbols.

The US 2006/0114812 A1 teaches a method and apparatus for configuring, synchronizing, and searching for cells in a cellular system based on OFDMA (Orthogonal Frequency-Division Multiple Access) downlink signals. This document describes a device for configuring a downlink signal consisting of a first preamble generator in order to generate a first preamble consisting of a first symbol and a second symbol so that a phase difference between the first and second symbol is 180 °, and thus a time and Frequency synchronization is performed. Furthermore, this document discloses a second preamble generator in order to generate a second preamble which contains at least one send symbol, so that the second preamble has cell-specific patterns for a plurality of cells for the purpose of cell search. This document also shows a pilot pattern generator that generates pilot patterns that are assigned to a plurality of pilot symbols on the time axis and frequency axis, a frame of the downlink signal containing a first slot, which is made up of the first and second preambles and a plurality of second slots containing the pilot symbols. This document also shows a downlink signal synchronizer in a mobile communication system, which consists of an initial synchronization estimator and a cell finder.

The US 2007/0217524 A1 discloses a frame timing synchronization technique for orthogonal frequency division multiplexing (OFDM) systems. This publication shows that a rough synchronization technique initially generates a rough frame timing estimate by feeding a received input signal to an autocorrelator and then processing the autocorrelated signal further by a "sliding window" differentiator and feeding it to a cross correlator. Subsequently, a fine synchronization technique produces a fine frame timing estimate, using the coarse frame timing estimate to reduce the number of cross-correlation calculations. In addition, the fine synchronization technique receives a fine frame timing estimate based on a signal-to-interference ratio (SIR metric). This reference further teaches that a fine-tuning technique produces a desired frame timing estimate by searching for a first signal path in a search window in the vicinity of the fine-frame timing to further refine the frame timing synchronization.

The US 7,764,593 B2 describes a method and a device to configure downlink signals, as well as a method and a device for synchronization and cell search in a mobile communication system. This document shows that in a downlink frame which has a large number of symbols, pilot subcarriers are arranged in a distributed manner with respect to time and frequency axes. The initial symbol and frequency synchronization is estimated using a position at which an autocorrelation between a cyclic prefix symbol of a downlink signal and a valid symbol of the downlink signal is maximum. This reference also teaches that cell search and integer time synchronization are estimated using pilot subcarriers present in the estimated symbol. This reference also discloses that fine symbol synchronization, fine frequency synchronization and downlink frame synchronization are estimated using an estimated cell search result.

The EP 2 057 855 B1 discloses a method for the synchronization of communication signals (uplink signals) which are sent from a mobile device to a base station. For data transmission from a mobile device to a base station (uplink or uplink connection), the base station must ensure that the mobile device is synchronized with the transmission scheme of the radio interface with adequate accuracy in order to use transmission resources, such as bandwidth, available time slots in To use transmission frames, as well as the transmission power, optimally. According to this publication, this is achieved by the base station analyzing received uplink signals, determining appropriate adaptation values for the uplink transmission parameters of the mobile device, and finally transmitting data to the mobile device in order to adapt its uplink transmission parameters so that the desired synchronization is achieved becomes. In mobile GSM or UMTS networks, such synchronization is implemented using what is known as a physical random access channel (RACH), which is provided by the base station. A mobile device sends a specific burst signal, the so-called access burst, to the base station via the random access channel. This access burst is used specifically for synchronization and is to be differentiated from the "normal" data transmission bursts. Said detected specific burst signals are analyzed, corresponding adaptation data are determined by the base station and transmitted to the mobile device, whereby the desired synchronization is achieved.

From the DE 101 59 911 A1 a method for processing a communication signal and for determining a frame start is known. The disadvantage of the DE 101 59 911 A1 is that the frame start is determined relatively precisely, but it also requires a high level of computing effort.

It is therefore the object of the method according to the invention and the device according to the invention to create a solution to determine the necessary frame start for a recorded, digitized communication signal as quickly as possible within a signal range of the recorded digitized communication signal with such a high level of accuracy that it is in the Search area of a subsequent synchronization process falls.

The object is achieved with regard to the method for determining the frame start by the features of claim 1 and with regard to the device for determining the frame start by the features of claim 9. Claim 17 contains a computer program with program code means in order to be able to carry out all method steps when the program is carried out on a computer or a digital signal processor. Claim 18 contains a computer program product with program code means stored in particular on a machine-readable carrier in order to be able to carry out all method steps when the program is executed on a computer or a digital signal processor. Advantageous developments of the method according to the invention for determining the frame start and the device according to the invention for determining the frame start are specified in the respective subclaims.

The method according to the invention for determining a frame start of a communication signal to be analyzed comprises several method steps. In a first method step, at least one signal range of the communication signal to be analyzed is recorded with a detection unit. In a further method step, a reference signal is generated as a function of a power profile of the at least one signal range of the communication signal to be analyzed. In a further method step, a first metric between the at least one signal range and the reference signal is determined by means of a convolution operation. In a final method step, the position of the maximum of the first metric is output as a time offset for the start of the frame.

It is particularly advantageous if a first metric can be calculated very quickly on the basis of a convolution operation of the at least one signal range and the reference signal, which has a power profile similar to that of the at least one signal range, the point or the index of the maximum of the first metric is used as a time offset for the frame start. The necessary arithmetic operations can be carried out very quickly and very efficiently, for example on a digital signal processor.

In the device according to the invention for determining a frame start of a communication signal to be analyzed, it is particularly advantageous if the device has a detection unit by which at least one signal range of the signal to be analyzed can be detected. The device preferably also has a signal generator with which a reference signal can be generated as a function of a power profile of the at least one signal range of the communication signal to be analyzed. The device preferably has a computing unit through which a first metric is generated by means of a Convolution operation between the at least one signal range and the reference signal can be determined. The computing unit can also determine the position of the maximum of the first metric and output it as a time offset for the start of the frame.

It is particularly advantageous if a reference signal can be generated within the device by a signal generator which has a performance profile that is similar to the performance profile of the at least one signal range of the communication signal to be analyzed. This allows a first metric of the convolution operation between the at least one signal range of the communication signal to be analyzed and the reference signal to be determined by means of a computing unit, the position or the index of the maximum of the first metric being able to be output as a time offset for the start of the frame. The operations shown can be carried out very simply and efficiently within a digital signal processor. The time offset for the start of the frame is estimated with sufficient accuracy so that it falls within the search range of a subsequent synchronization process.

Another advantage of the method according to the invention for determining a frame start is when the first metric of the cyclic convolution operation between the amount of the at least one signal range and the reference signal is calculated using the further method steps. Within one of the further method steps, the at least one signal range and the reference signal are transformed into the frequency range by means of a fast Fourier transformation. Furthermore, the at least one signal range of the communication signal to be analyzed which has been transformed into the frequency range is multiplied by the conjugate complex part of the reference signal. In this preferred development, the result of the multiplication of the at least one signal range of the communication signal to be analyzed with the complex conjugate part of the reference signal is then transformed back into the time domain by means of an inverse fast Fourier transformation. Finally, the position of the maximum of the first metric of the real part of the multiplication result transformed back into the time domain is output as a time offset for the start of the frame. The use of a fast Fourier transformation for the transformation into the frequency domain and into the time domain, which can be carried out very efficiently on a digital signal processor, is particularly advantageous. It is also particularly advantageous that only the real part of the multiplication result transformed back into the time domain is used for determining the maximum of the first metric because the imaginary part contains noise. This allows the time offset for the frame start to be specified even more precisely.

In addition, there is an advantage in the method according to the invention for determining a frame start if a first number of zeros is appended to the amount of the at least one signal range and to the reference signal, so that the amount of the at least one signal range and the reference signal have a length that is equal to one Is a power of two and if a second number of all elements that are located before the attached zeros within the reference signal, with the exception of a first element, are copied and if this second number of elements are inserted at the end of the reference signal without lengthening it. This allows the use of a cyclic convolution operation, which can be calculated particularly efficiently using a fast Fourier transformation, provided the length is a power of two.

Furthermore, the method according to the invention for determining a frame start has an advantage if the magnitude of the at least one signal range and the reference signal is filtered and decimated in such a way that an integer number of samples is retained for the two signals. This means that it is no longer necessary to process the entire number of recorded samples, so that the number of necessary arithmetic operations is reduced.

Finally, the method according to the invention for determining the start of the frame has an advantage if a further time offset can be determined by interpolating the time offset and if this further time offset can be added to the time offset. By interpolating the time offset, the accuracy of the estimated time offset for the frame start can be increased, which became lower in the course of the decimation.

The inventive device for determining a frame start is advantageous if the communication signal to be analyzed is a digitized GSM signal and / or if the at least one signal range is at least one frame and / or if the convolution operation for the at least one signal range and the reference signal can be calculated and / or if the convolution operation is a cyclic convolution operation. Because mainly periodic GSM signals are analyzed during production tests, the one to be analyzed can at least one Signal range can be reduced to a frame that necessarily contains a frame start, wherein the determined frame start can be used to determine the position of the further frame starts of the following frames. One period here preferably corresponds to one frame of a GSM signal. It is also advantageous if the convolution operation uses the complex conjugate part of the reference signal and if the convolution operation is a cyclic convolution operation, because this can then be calculated very efficiently by means of a fast Fourier transform.

mit u = Abtastwert, g = Gewichtsfunktion, Pref = Referenzssignal, F = Anzahl der Abtastwerte in einer Periode oder in einem Rahmen multiplizierbar ist, wenn durch die dritte Additionseinheit das Quadrat des Realteils der ersten Metrik von dem Ergebnis der sechsten Multiplikationseinheit subtrahierbar ist und wenn durch eine sechste Verarbeitungseinheit die Stelle des Maximums des Ergebnisses der Subtraktion als Zeitversatz für den Rahmenstart ausgebbar ist. Für den Fall, dass innerhalb der Produktionsumgebung bekannt ist, dass ein Rahmenstart bevorzugt innerhalb eines GSMK-modulierten Bursts innerhalb des zumindest einen Signalbereichs auftritt, kann dieser Bereich des Referenzsignals beispielsweise stärker gewichtet werden. Dies erhöht die Wahrscheinlichkeit, dass ein gültiger Zeitversatz für den Rahmenstart geschätzt werden kann.There is also an advantage in the device according to the invention if a weighting function can be generated by the arithmetic unit in order to weight individual areas within the reference signal to different degrees and if the reference signal can be multiplied by the weighting function by a third multiplication unit and if the arithmetic unit uses a second metric a convolution operation of the weighting function with the squared at least one signal range of the communication signal to be analyzed can be determined and if the real part of the second metric with the result of the formula by a sixth multiplication unit $${\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}{\left(\upsilon -\tau \right)}^2}$$

with u = sample, g = weight function, Pref = reference signal, F = number of samples in a period or in a frame can be multiplied if the square of the real part of the first metric can be subtracted from the result of the sixth multiplication unit by the third addition unit and if the position of the maximum of the result of the subtraction can be output as a time offset for the frame start by a sixth processing unit. In the event that it is known within the production environment that a frame start occurs preferably within a GSMK-modulated burst within the at least one signal range, this range of the reference signal can be weighted more heavily, for example. This increases the probability that a valid time offset for the frame start can be estimated.

Finally, there is an advantage in the device according to the invention if the second metric can be determined in such a way that the at least one signal range of the communication signal to be analyzed can be squared by a squaring unit and that a first number of zeros can be appended to the reference signal by a fourth processing unit and that by a fifth processing unit a second number of all elements that are located before the appended zeros within the reference signal, with the exception of a first element, can be copied and that this second number of elements can be inserted at the end of the reference signal by the fifth processing unit and that by a third and fourth Fourier transform unit, the at least one squared signal range and the weighting function can be transformed into the frequency range and that the at least one squared transformed in the frequency range by the fourth multiplication unit Signal range can be multiplied with the conjugate complex part of the weighting function transformed into the frequency range and that the multiplication result can be transformed into the time domain by a further inverse Fourier transformation unit and that this can be output as a second metric by the further inverse Fourier transformation unit. The appending of a first number of zeros and a second number of elements allows the convolution operation by means of a cyclic convolution operation using a fast Fourier transform to be calculated very efficiently and quickly within a digital signal processor, the reference signal not being due to the appending of the second number of elements may be extended.

• 1 ein Ausführungsbeispiel eines Blockschaltbilds, das den Aufbau der erfindungsgemäßen Vorrichtung zeigt;
• 2 ein Ausführungsbeispiel eines Blockschaltbilds, das den Aufbau der erfindungsgemäßen Messeinheit zeigt;
• 3 ein Modell, das den Zusammenhang zwischen dem idealen Leistungsprofil und dem gemessenen Signal erläutert;
• 4 ein erfindungsgemäßes Modell zur groben Berechnung eines Zeitversatzes für den Rahmenstart;
• 5A ein Ausführungsbeispiel, das Abtastwerte von verschiedenen Signalen enthält;
• 5B ein erfindungsgemäßes Ausführungsbeispiel, das beschreibt, wie die Abtastwerte von verschiedenen Signalen mit Nullen ergänzt werden;
• 5C ein erfindungsgemäßes Ausführungsbeispiel, das beschreibt, wie eine zweite Anzahl an Elementen zu den mit Nullen ergänzten Abtastwerten von verschiedenen Signalen eingefügt werden;
• 6 ein verfeinertes erfindungsgemäßes Ausführungsbeispiel eines Modells zur Berechnung eines Zeitversatzes für den Rahmenstart;
• 7 ein weiteres verfeinertes erfindungsgemäßes Ausführungsbeispiel eines Modells zur Berechnung eines Zeitversatzes für den Rahmenstart;
• 8 ein weiteres verfeinertes erfindungsgemäßes Ausführungsbeispiel eines Modells zur Berechnung eines Zeitversatzes für den Rahmenstart;
• 9 ein Ausführungsbeispiel eines Flussdiagramms, welches die Funktionsweise der erfindungsgemäßen Vorrichtung zum Ermitteln eines Rahmenstarts erläutert;
• 10 ein weiteres Ausführungsbeispiel eines Flussdiagramms, welches die Funktionsweise der erfindungsgemäßen Vorrichtung zum Ermitteln eines Rahmenstarts genauer erläutert;
• 11 ein weiteres Ausführungsbeispiel eines Flussdiagramms, welches die Funktionsweise der erfindungsgemäßen Vorrichtung zum Ermitteln eines Rahmenstarts genauer erläutert;
• 12 ein weiteres Ausführungsbeispiel eines Flussdiagramms, welches die Funktionsweise der Filterung und der Dezimation innerhalb der erfindungsgemäßen Vorrichtung zum Ermitteln eines Rahmenstarts genauer erläutert;
• 13 ein weiteres Ausführungsbeispiel eines Flussdiagramms, welches die Funktionsweise der quadratischen Interpolation innerhalb der erfindungsgemäßen Vorrichtung zum Ermitteln eines Rahmenstarts erläutert;
• 14 ein weiteres Ausführungsbeispiel eines Flussdiagramms, welches die Funktionsweise einer Gewichtungsfunktion innerhalb der erfindungsgemäßen Vorrichtung zum Ermitteln eines Rahmenstarts genauer erläutert; und
• 15 ein weiteres Ausführungsbeispiel eines Flussdiagramms, welches die Funktionsweise der quadratischen Interpolation innerhalb der erfindungsgemäßen Vorrichtung zum Ermitteln eines Rahmenstarts genauer erläutert.

Various exemplary embodiments of the invention are described below by way of example with reference to the drawing. The same items have the same reference symbols. The corresponding figures in the drawing show in detail:

• 1 an embodiment of a block diagram showing the structure of the device according to the invention;
• 2 an embodiment of a block diagram showing the structure of the measuring unit according to the invention;
• 3 a model that explains the relationship between the ideal power profile and the measured signal;
• 4th a model according to the invention for roughly calculating a time offset for the frame start;
• 5A an embodiment that includes samples from various signals;
• 5B an embodiment according to the invention, which describes how the samples of different signals are supplemented with zeros;
• 5C an exemplary embodiment according to the invention, which describes how a second number of elements are inserted into the zero-supplemented sample values of different signals;
• 6th a refined embodiment according to the invention of a model for calculating a time offset for the frame start;
• 7th a further refined exemplary embodiment according to the invention of a model for calculating a time offset for the frame start;
• 8th a further refined exemplary embodiment according to the invention of a model for calculating a time offset for the frame start;
• 9 an exemplary embodiment of a flow chart which explains the mode of operation of the device according to the invention for determining a frame start;
• 10 a further exemplary embodiment of a flow chart which explains in more detail the mode of operation of the device according to the invention for determining a frame start;
• 11 a further exemplary embodiment of a flow chart which explains in more detail the mode of operation of the device according to the invention for determining a frame start;
• 12 a further exemplary embodiment of a flowchart which explains in more detail the functioning of the filtering and the decimation within the device according to the invention for determining a frame start;
• 13 a further exemplary embodiment of a flow diagram which explains the mode of operation of the quadratic interpolation within the inventive device for determining a frame start;
• 14th a further exemplary embodiment of a flow chart which explains in more detail the functioning of a weighting function within the inventive device for determining a frame start; and
• 15th a further exemplary embodiment of a flow chart which explains in more detail the mode of operation of the quadratic interpolation within the inventive device for determining a frame start.

1 shows an embodiment of a block diagram showing the structure of the device according to the invention 1 describes in more detail. The device 1 for determining a frame start of a communication signal to be analyzed 7 ₁ , 7 ₂ , in particular a GSM signal, comprises at least one central data processing unit 3 . The at least one central data processing unit 3 can have one or more processors and / or FPGAs (field programmable gate array; dt. in the (application) field programmable (logic) gate arrangement) and / or DSP (digital signal processor; dt. digital signal processor ) exhibit. With the at least one central data processing unit 3 are at least one unit of measurement 2 , a storage unit 4th , a screen unit 5 and an input unit 6th connected.

In the at least one storage unit 4th it can be, for example, a main memory and / or a hard disk storage that is within the device 1 is formed and / or with the device 1 is connected via a network interface, for example.

The one with the at least one central data processing unit 3 connected measuring unit 2 receives, as will be explained in detail later, a communication signal to be analyzed 7 ₁ , 7 ₂ in order to determine or estimate a frame start for this. At the communication signal to be analyzed 7 ₁ , 7 ₂ it can be a GSM signal, for example. The device according to the invention 1 , which is used to determine a frame start, becomes a measured digitized communication signal 7 ₁ , 7 ₂ to hand over. Such a digitized communication signal 7 ₁ , 7 ₂ can for example with a signal analyzer 8th or an oscilloscope.

In 1 is a simplified block diagram of a signal analyzer 8th shown. A high-frequency communication signal to be analyzed 9 , in particular a GSM signal, is passed through an amplifier 10 amplified in its amplitude. Then the amplified high frequency communication signal 9 through a mixer 11 by means of a local oscillator signal to an intermediate frequency 12 mixed down. That on an intermediate frequency 12 Down-mixed high-frequency communication signal 9 becomes then through a band pass 13 filtered before going through an analog to digital converter 14th is digitized. Via a digital sales converter 15th (English. digital down converter) the digitized high-frequency signal is mixed down into the baseband. The communication signal mixed down to baseband is the communication signal to be analyzed 7 ₁ , 7 ₂ , which of the device according to the invention 1 is fed. The device according to the invention 1 preferably the in-phase (dt. in-phase) and the quadrature component are supplied. In the event that it is the communication signal to be analyzed 9 a communication signal 9 which is transmitted, for example, by a GSM base station, is used instead of an amplifier 10 an attenuator or a coupler is used, at the output of which a signal with a much smaller amplitude is present.

The advantage is that a communication signal to be analyzed 7 ₁ , 7 ₂ , of which it is only known that it is a GSM signal, can be demodulated and evaluated as automatically as possible. A GSM signal has several frames, with one frame having eight slots in which the user data of a mobile subscriber is transmitted in the form of bursts. The bursts, one of which can each be transmitted within a slot, can have a large number of different parameters.

So that a frame can be demodulated, these parameters and the exact position within the slot must be known for each burst within a slot. The length of the individual slots is standardized by the GSM standard and as soon as the start of a frame has been determined, the position of the individual slots can be calculated.

2 shows an embodiment of a block diagram showing the structure of the measuring unit according to the invention 2 within the device according to the invention 1 describes in more detail. The measuring unit according to the invention 2 within the device according to the invention 1 consists of at least one processing unit 20th , a registration unit 21st , a signal generator 22nd and a processing unit 23 . At the arithmetic unit 20th it can be the central data processing unit 3 act or another central data processing unit, or another FPGA or another DSP. The one with the at least one computing unit 20th connected registration unit 21st takes the communication signal to be analyzed 7 ₁ , 7 ₂ opposite.

The signal generator 22nd serves, as will be explained later, to generate a reference signal. The at least one computing unit 20th , the registration unit 21st , the signal generator 22nd and the processing unit 23 can each be designed in independent computing units that are connected to one another via electrically conductive connections or they can be within the central data processing unit 3 be trained.

3 shows a model which explains the relationship between the ideal power profile Pref and the measured signal Y _meas . The measured signal Y _meas is obtained by the acquisition unit by calculating the absolute value from the IQ recording memory 21st won. The communication signal to be analyzed is located in the IQ recording memory 7 ₁ , 7 ₂ which was recorded, being from the communication signal to be analyzed 7 ₁ , 7 ₂ a signal range Y _{meas is picked} out which, for example, covers a frame, or is preferably only one period long. The frame start is _sought within the measured signal Y _meas , for example in the middle of the slot 0 can be accepted. P _ref is a reference signal with a power profile that does not contain any noise.

The power profile of the reference signal Pref is transmitted via the input unit 6th within the device according to the invention 1 set by a user. From the communication signal to be analyzed 7 ₁ , 7 ₂ it is known which slots are active within a frame. It can be via the input unit 6th The type of modulation that is present in the individual slots can also be entered. The communication signal to be analyzed 7 ₁ , 7 ₂ is a periodic signal, ie the same slots are always active in consecutive frames and the same slots have the same modulation, even if different data are transmitted at the same time. The signal generator 22nd generated from the in the input unit 6th input data, the reference signal Pref with a corresponding power profile.

The generation of the reference signal Pref is explained in more detail below. The goal is that the power profile of the reference signal Pref is similar to the power profile of the communication signal to be analyzed 7 ₁ , 7 ₂ is, so the reference signal P _ref as a function of the power profile of the at least one signal range Y _{meas of} the communication signal to be analyzed 7 ₁ , 7 ₂ is produced. The course of the power profile of a reference signal is for a GSM signal in the corresponding standard 3GPP TS 45.005 Annex B (German appendix) (English 3rd Generation Partnership Project; German third-generation partnership project), which is fully included in the description. For example, a user can enter which slots in a frame within the communication signal to be analyzed 7 ₁ , 7 ₂ are active, i.e. in which slots a burst is transmitted and which burst type is present within the active slot. Different types of bursts differ, among other things, in their length, for example there is the normal burst, the dummy burst and the access burst. This information allows the signal generator 22nd that a reference signal P _ref with a power profile as a function of the power profile for the at least one signal range Y _{meas of} the communication signal to be analyzed 7 ₁ , 7 ₂ is generated. Furthermore, it can optionally be entered how the rise or fall of the edges of the power profile of the reference signal is to take place. If the signal is to be applied immediately, the edge is infinitely steep; alternatively, a linear or cosine-shaped increase in power (power ramping) or decrease in power can be set. Preferably, however, a linear power curve or edge curve is always selected here because a sufficiently accurate time offset for the frame start can always be determined with this, regardless of the actual edge of the power curve of the communication signal to be analyzed 7 ₁ , 7 ₂ . The correspondingly selected edge profile applies both to the increase in power at the beginning of the burst and to the decrease in power at the end of the burst.

Inside the model 3 there is also a delay element 30th with the desired time offset τ _c . The signal at the output of the delay element 30th can still with a constant C by the multiplication unit 31 be scaled. Following this, the signal can be sent via the addition unit 32 A noise AWGN (English Additive White Gaussion Noise; German Additive White Gaussian Noise) can be added. From the signal at the output of the addition unit 32 is in the amount unit 33 still the amount formed so that the registration unit 21st measured signal Y _{meas is} obtained.

The signal Y _meas is the magnitude of the communication signal to be analyzed 7 ₁ , 7 ₂ , where: $$Y_{meas}\left(t\right)=\sqrt{\underset{{\mathrm{<figure-callout\; id="1"\; label="7th"\; filenames="DE102011103642B4\_0030.png,DE102011103642B4\_0031.png"\; state="\{\{state\}\}">7th</figure-callout>}}_1}{\underbrace{\mathrm{I.}{\left(t\right)}^2}}+\underset{{\mathrm{<figure-callout\; id="1"\; label="7th"\; filenames="DE102011103642B4\_0030.png,DE102011103642B4\_0031.png"\; state="\{\{state\}\}">7th</figure-callout>}}_1}{\underbrace{Q{\left(t\right)}^2}}}.$$

The aim of the measuring unit according to the invention 2 and the device according to the invention 1 It is now to estimate the time offset τ _c for the frame start as quickly as possible and with sufficient accuracy so that a synchronization unit (not shown) can then determine the exact frame start based on the estimated time offset τ _c and thus the estimated frame start.

One possibility to estimate this time offset τ _c is with the least squares method. This approach is shown in equation (1). $$\begin{array}{l}\mathrm{L.}\left(\tau ,\mathrm{C.}\right)={\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot {\left|Y_{meas}\left(\upsilon \right)-\mathrm{C.}\cdot P_{ref}\left(\upsilon -\tau \right)\right|}^2}\\ \begin{array}{ll}\mathrm{M.}it\hfill & \to \upsilon :Zeit-\mathrm{I.}ndex\left(t=\upsilon \cdot T_{\mathrm{A.}btastvert}\right)\hfill \\ \hfill & \to \tau :VerzöGerunGin\mathrm{A.}btastwerten{\tau }_c=\tau \cdot T_{\mathrm{A.}btastwert}\hfill \\ \hfill & \to \mathrm{F.}:\mathrm{D.}auereinerPeriOde\left(Hie\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="DE102011103642B4\_0030.png,DE102011103642B4\_0031.png"\; state="\{\{state\}\}">r</figure-callout>}1\mathrm{R.}aHmen\right)\text{i}n\mathrm{A.}btastwerten\hfill \\ und\hfill & \to G\left(\upsilon \right):GewicHtsfunktiOnG\left(\upsilon \right)\ge \mathrm{0,}\forall \upsilon \hfill \end{array}\end{array}$$

The noise n (t) can be neglected. Furthermore, for Y _meas (t) = | IQ (t) |. The actual value of the scaling constant C is unknown, so the metric L depends on both τ and C. The weighting function g (υ-τ) allows certain slots to be weighted higher than others. The weighting function g (υ-τ) is synchronous with the reference signal P _ref (υ-τ) and is therefore the same in time, which is expressed by the same indices. All signals g (υ-τ), Y _meas (υ) and P _ref (υ-τ), as well as the scaling constant C, are real-valued, so that the amount can be resolved in brackets as shown in equation (2). $$\mathrm{L.}\left(\tau ,\mathrm{C.}\right)={\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot {\left(Y_{meas}\left(\upsilon \right)-\mathrm{C.}\cdot P_{ref}\left(\upsilon -\tau \right)\right)}^2}$$

When multiplied, equation (3) results: $$\mathrm{L.}\left(\tau ,\mathrm{C.}\right)={\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot \left(Y_{meas}{\left(\upsilon \right)}^2-2\cdot \mathrm{C.}\cdot P_{ref}\left(\upsilon -\tau \right)\cdot Y_{meas}\left(\upsilon \right)+{\mathrm{C.}}^2\cdot P_{ref}{\left(\upsilon -\tau \right)}^2\right)}$$

This can be expanded further: $$\begin{array}{c}\mathrm{L.}\left(\tau ,\mathrm{C.}\right)={\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot Y_{meas}{\left(\upsilon \right)}^2-2\cdot \mathrm{C.}\cdot {\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}}}\left(\upsilon -\tau \right)\cdot Y_{meas}\left(\upsilon \right)+\\ {\mathrm{C.}}^2\cdot {\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}{\left(\upsilon -\tau \right)}^2}\end{array}$$

The metric L should now be minimized with respect to the scaling constant C. This is achieved by differentiating the metric L from equation (4) into C, as shown in equation (5). $$\frac{d\mathrm{L.}}{d\mathrm{C.}}=-2\cdot {\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}\left(\upsilon -\tau \right)\cdot Y_{meas}\left(\upsilon \right)+2\cdot \mathrm{C.}\cdot {\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}{\left(\upsilon -\tau \right)}^2}}$$

The time offset τ is found once the derivative is set to zero, as shown in equation (6). $$-2\cdot {\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}\left(\upsilon -\tau \right)\cdot Y_{meas}\left(\upsilon \right)+2\cdot \mathrm{C.}\cdot {\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}{\left(\upsilon -\tau \right)}^2}=0}$$

Now it is possible to solve for the scaling constant C. $$\Rightarrow \mathrm{C.}\left(\tau \right)=\frac{{\displaystyle {\sum }_{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}\left(\upsilon -\tau \right)\cdot Y_{meas}\left(\upsilon \right)}}{{\displaystyle {\sum }_{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}{\left(\upsilon -\tau \right)}^2}}$$

The result for the scaling constant C from equation (7) is inserted into equation (4), resulting in equation (8). $$\begin{array}{l}\mathrm{L.}\left(\tau \right)={\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)}\cdot Y_{meas}{\left(\upsilon \right)}^2-2\cdot \frac{{\left({\displaystyle {\sum }_{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}\left(\upsilon -\tau \right)Y_{meas}\left(\upsilon \right)}\right)}^2}{{\displaystyle {\sum }_{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}{\left(\upsilon -\tau \right)}^2}}+\\ \frac{{\left({\displaystyle {\sum }_{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}\left(\upsilon -\tau \right)\cdot Y_{meas}\left(\upsilon \right)}\right)}^2}{{\displaystyle {\sum }_{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}{\left(\upsilon -\tau \right)}^2}}\end{array}$$

The maximum of the metric L and thus the time offset for the frame start sought results from the following equation (9). $$\begin{array}{l}\widehat{\tau }=\text{bad}\left({\text{min}}_{\tau }\mathrm{L.}\left(\tau \right)\right)=\\ \text{bad}\left({\text{min}}_{\tau }\left\{\underset{\left(1\right)}{\underbrace{{\left({\displaystyle {\sum }_{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot Y_{meas}\left(\upsilon \right)}\right)}^2}}-\frac{{\left\{{\displaystyle {\sum }_{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}\left(\upsilon -\tau \right)\cdot Y_{meas}}\left(\upsilon \right)\right\}}^2}{\underset{\left(2\right)}{\underbrace{{\displaystyle {\sum }_{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}{\left(\upsilon -\tau \right)}^2}}}}\right\}\right)\end{array}$$

As already mentioned, the frames repeat themselves cyclically with the period F. This means that the power profile of the reference signal Pref and the weighting function g also repeat themselves cyclically with the period F. The expression (2) in the denominator within equation (9) is therefore related to the Estimation parameter τ constant because it adds up all signal elements within a period and therefore only has to be calculated once.

To find the minimum of the expression in equation (9), the weight function is initially assumed to be one for the sake of simplicity, g (υ-τ) = 1. See equation (10). $$\underset{\left(1\right)}{\underbrace{{\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot Y_{meas}{\left(\upsilon \right)}^2}}}={\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}{Y}_{meas}}{\left(\upsilon \right)}^2=KOnstant$$

To find the minimum, the maximum of the expression from equation (11) can alternatively be determined. $${\mathrm{L.}}_1\left(\tau \right)={\left\{{\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot Y_{meas}\left(\upsilon \right)}\right\}}^2$$

Because Pref and Y _meas are greater than or equal to zero anyway, equation (11) can be simplified to equation (12). $${\mathrm{L.}}_2\left(\tau \right)={\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}{P}_{ref}\left(\upsilon -\tau \right)\cdot Y_{meas}\left(\upsilon \right)}$$

The problem is that the calculation of equation (12) can require a great deal of computing time if a frame is scanned with a high resolution. In the event that a framework 30000 Containing sampled values are necessary according to equation (12) for the calculation of a hypothesis of τ 30000 summations with one multiplication each. Taking into account the fact that there are 30,000 hypotheses, it can be seen that a high computing power or computing time is required for the conventional calculation of equation (12). The computing unit according to the invention 20th therefore does not calculate the summations of equation (12), but cleverly uses a convolution operation.

Basically: $$f\left(\tau \right)=a\left(\tau \right)\ast b\left(\tau \right)=f\left(\tau \right)={\displaystyle \sum _{\upsilon =\infty }^{+\infty }a\left(\upsilon \right)\cdot b\left(\tau -\upsilon \right)}$$

The following also applies: $$c\left(\tau \right)=b\left(-\tau \right)\iff b\left(\tau -\upsilon \right)=c\left(\upsilon -\tau \right)$$

Equation (15) results from equations (13) and (14): $$\Rightarrow f\left(\tau \right)={\displaystyle \sum _{\upsilon =-\infty }^{+\infty }a\left(\upsilon \right)\cdot c\left(\upsilon -\tau \right)\text{With}c\left(\tau \right)=b\left(-\tau \right)}$$

Applying equation (15) to equation (12) results in equation (16): $${\displaystyle \sum _{\upsilon =-\infty }^{+\infty }{P}_{ref}\left(\upsilon -\tau \right)\cdot Y_{meas}\left(\upsilon \right)=Y_{meas}\left(\tau \right)\ast P_{ref}\left(-\tau \right)}$$

ausgeführt. Dies kann Gleichung (17) entnommen werden. Eine Periode F des zu analysierenden Kommunikationssignals Y_meas wird auch als ein Signalbereich des zu analysierenden Kommunikationssignals Y_meas bezeichnet. $$L_2\left(\tau \right)={\displaystyle \sum _{\upsilon =0}^{F-1}{P}_{ref}}\left(\upsilon -\tau \right)Y_{meas}\left(\upsilon \right)=Y_{meas}\left(\tau \right)⊛P_{ref}\left(-\tau \right)$$

As already described, the signals Pref and Y _{meas are} periodic, so that the sum can be reduced to one period. Instead of a convolution operation (*) there is now a cyclic convolution operation

executed. This can be seen in equation (17). A period F of the communication signal to be analyzed Y _meas is also referred to as a signal range of the communication signal to be analyzed Y _meas . $${\mathrm{L.}}_2\left(\tau \right)={\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}{P}_{ref}}\left(\upsilon -\tau \right)Y_{meas}\left(\upsilon \right)=Y_{meas}\left(\tau \right)⊛P_{ref}\left(-\tau \right)$$

Such a cyclic convolution operation is most efficiently calculated by means of a Fourier transform, preferably a fast Fourier transform. In the frequency domain, a convolution can be described by a multiplication. This fact is shown in equation (18). $${\mathrm{L.}}_2\left(\tau \right)=Y_{meas}\left(\tau \right)⊛P_{ref}{\left(-\tau \right)}_{\overleftarrow{\mathrm{I.}\mathrm{D.}\mathrm{F.}T}}^{\underrightarrow{\mathrm{D.}\mathrm{F.}T}}{\mathrm{L.}}_2\left(n\right)=Y_{meas}\left(n\right)\cdot P_{ref}\left(-n\right)$$

Due to the fact that the signals Pref and Y _meas , as already described, are real-valued signals in the time domain, equation (18) can be simplified further. $$\mathrm{W.}enny\left(\upsilon \right)reell\iff Y\left(-n\right)=Y*\left(n\right)$$

Equation (19) leads to equation (20). $${\mathrm{L.}}_2\left(n\right)=Y_{meas}\left(n\right)\cdot P_{ref}^{*}\left(n\right)$$

Using the calculation steps shown, equation (9) for determining the time offset of the frame start has been very elegantly simplified to equation (18) or (20). Then L ₂ (n) still has to be transformed back into the time domain in order to then determine the maximum. This fact is shown, for example, in equation (21). $${\mathrm{L.}}_2\left(\tau \right)=\mathrm{I.}\mathrm{D.}\mathrm{F.}T\left\{{\mathrm{L.}}_2\left(n\right)\right\}$$

As soon as the first metric is obtained by means of the convolution operation from equation (18) between the at least one signal range Y _{meas of} the communication signal to be analyzed 7 ₁ , 7 ₂ and the reference signal Pref is calculated, the position or the index of the maximum of the first metric can be output as the start of the frame. The result of the convolution operation is understood as the metric.

4th shows a model according to the invention for roughly calculating a time offset for the frame start. The model from 4th shows a possible implementation of equation (21). The model from 4th is preferably in the computing unit 20th educated. At least one signal range Y _meas from the communication signal to be analyzed 7 ₁ , 7 ₂ , which is a frame, becomes a first Fourier transform unit 40 ₁ fed. The reference signal P _ref , which preferably also has the length of a frame, is sent to a second Fourier transform unit 40 ₂ fed. The output of the second Fourier transform unit 40 ₂ is with a first processing unit 41 connected. The first processing unit 41 forms the complex conjugate part of the reference signal Pref (n) transformed into the frequency domain.

The output of the first processing unit 41 becomes just like the output of the first Fourier transform unit 40 ₁ one input each of a further multiplication unit 42 fed. By the further multiplication unit 42 the convolution operation in the time domain is calculated by means of a multiplication in the frequency domain. The result of the further multiplication unit 42 is applied to an inverse Fourier transform unit 43 forwarded. The inverse Fourier transform unit 43 transforms the signal supplied to it from the frequency domain back into the time domain. The first Fourier transform units work to save computing time 40 ₁ , the second Fourier transform unit 40 ₂ and the inverse Fourier transform unit 43 preferably according to the principle of the fast Fourier transformation or the inverse fast Fourier transformation. From that by the inverse Fourier transform unit 43 The signal transformed back into the time domain is processed in a second processing unit 44 the real part is searched for and output. The imaginary part contains unwanted noise and is not used to determine the time offset τ for the frame start. In a sixth processing unit 64 the maximum of the expression of L ₂ (τ) is now searched for, as shown in equation (12). At the output of the sixth processing unit 64 the estimated frame start τ̂ is output. The estimated frame start is the index or the point at which the metric L (τ) becomes maximum.

5A Figure 3 shows an embodiment containing samples from various signals. An exemplary period of the reference signal P _ref , of the at least one signal range Y _{meas of} the communication signal to be analyzed is shown 7 ₁ , 7 ₂ and the weighting function g. It can be seen that in this exemplary embodiment a period comprises a total of six samples. In this example, the sample values have the same sample value (a, b, c, d, e, f) for all signals at a given point in time. However, this is only intended to simplify matters. However, a fast Fourier transformation can preferably be calculated for a signal with a number of sampled values if the number of sampled values corresponds to a power of two, that is to say 2 ⁿ , where n is a natural number and where n 1. A fast Fourier transform cannot be calculated from a signal with six sample values any more than from a signal with 30,000 sample values.

5B shows an exemplary embodiment according to the invention which describes how the sampled values of various signals must be supplemented with zeros so that a fast Fourier transformation can be calculated from these signals. Are shown in 5B the signals off 5A with the known sampling values for the first six sampling times. The signals P _ref , Y _meas and g are padded with zeros so that they reach a length which corresponds to a power of two, i.e. 2 ⁿ . In the case of the signals, which have six sample values by way of example, it should be assumed that these would be padded with zeros up to the next power of two. The next power of two would be reached with eight samples for each signal. However, studies have shown that an aliasing error can occur in such a case. To avoid this, the length L of the signals P _ref , Y _meas and g must preferably be chosen such that the relationship L 2 · F-1 applies, where F represents the number of samples within a frame or within a period and L is also the length of the fast Fourier transform. In this case, F has the value six, so the length of the zero-padded signals must be at least eleven. Since a length of eleven does not represent a power of two, the signals P _ref , Y _meas and g are padded with zeros up to the next power of two, consequently L = 16 = 2 ⁴ .

5C shows an exemplary embodiment according to the invention, which describes how a second number of elements are inserted into the sampled values supplemented with zeros within the various signals P _ref and g. If the signals P _ref and Y _meas 5 are multiplied with one another in the frequency domain, which corresponds to a convolution in the time domain, this convolution would not be over the entire at least one signal range Y _{meas of} the communication signal to be analyzed 7 ₁ , 7 ₂ respectively. For this reason, with the signals Pref and g, i.e. the reference signal and the weighting function, a second number of all elements that are in front of the attached zeros, with the exception of the first element, are copied and pasted at the end of the respective signals without them be extended. In the example 5C are the samples 1 to F-1 of the reference signal Pref and the weighting function g and copied to the locations for the samples 11 to 15th inserted.

6th shows a refined exemplary embodiment according to the invention of a model for calculating the time offset τ for the frame start. At the beginning is the recording memory 60 shown. The recording memory 60 is preferably in the storage unit 4th educated. From the recording memory 60 , the communication signal to be analyzed 7 ₁ , 7 ₂ contains is processed by a third processing unit 61 cut out at least one signal area. This at least one signal range comprises the length of a frame or the length of a period F, which do not necessarily have to match in length. Subsequently, at least one signal range of the cut out is given by a unit of amount 33 the amount formed. This fact is already over 3 known. A fourth processing unit then determines 62 the number of zeros which must be appended to the at least one signal range Y _meas (t) so that the total number of elements within the at least one signal range Y _meas (t) reaches the length of a power of two, with at least as many zeros having to be added, that the length L of the at least one signal range corresponds to Y _meas 2 · F-1, or is rounded up to the next power of two. The first Fourier transform unit then transforms 40 ₁ the at least one signal range Y _meas (U) of the communication signal to be analyzed 7 ₁ , 7 ₂ in the frequency domain.

On the other hand, the signal generator generates 22nd a reference signal P _ref , which has the length of a period or a frame. The power profile of the reference signal P _ref corresponds approximately to the power profile of the at least one signal range Y _{meas of} the communication signal to be analyzed 7 ₁ , 7 ₂ . Information (active slots, burst type per active slot) that are necessary for generating the reference signal P _ref can be accessed by a user in the input unit 6th be entered so that this reference signal P _ref can be generated according to the GSM standard.

The stronger the reference signal P _ref corresponds to the at least one signal range Y _{meas of} the communication signal to be analyzed 7 ₁ , 7 ₂ is similar, the more precisely the time offset τ can be determined for the frame start. The reference signal P _ref , which is generated by the signal generator 22nd is also generated within a fourth processing unit 62 added a certain number of zeros. As already described, so many zeros are appended to the end of the reference signal Pref that the reference signal P _{ref has} a length L which is equal to a power of two. It should be noted that the length L of the reference signal P _ref must have at least 2 · F-1 elements, so that the fourth processing unit 62 must add a corresponding number of zeros until the length L reaches a power of two.

This is followed by the fifth processing unit 63 all elements are copied with the exception of the first element, which are before the trailing zeros. These copied elements are then inserted at the end of the reference signal Pref without the length L of the reference signal Pref being increased. This fact was already too 5C explains what is hereby referred to. The reference signal P _ref (U) is then sent to a second Fourier transform unit 40 ₂ to hand over. The second Fourier transform unit 40 ₂ preferably calculates a fast Fourier transform using the reference signal P _ref (U). After the second Fourier transform unit 40 ₂ has transformed the reference signal P _ref (U) into the frequency domain, forms the first processing unit 41 the complex conjugate part of the reference signal P _ref (n) transformed into the frequency domain.

The further multiplication unit 42 multiplies the at least one signal range, transformed into the frequency range, of the communication signal Y _meas (n) to be analyzed by the conjugate complex part of the reference signal P _ref * (n) transformed into the frequency range. The result of this multiplication is sent to the inverse Fourier transform unit 43 to hand over. This inverse Fourier transform unit 43 transforms the signal fed to it, preferably by means of an inverse fast Fourier transformation, back into the time domain. The result of this inverse Fourier transform unit 43 becomes the second processing unit 44 supplied, which determines the real part from the result of the inverse transformation. A sixth processing unit 64 determines the maximum of the metric from the real part of the multiplication result transformed back into the time domain and outputs the index or the position of the maximum of the metric as a time offset τ̂ for the frame start.

7th shows a further refined exemplary embodiment according to the invention of a model for calculating a time offset τ for the frame start. The embodiment from 7th is very similar to the exemplary embodiment 6th on, which is why the in 6th processing units already explained in 7th to describe again. Please refer to the description of the figures 6th referenced. In order to reduce the computing time, it makes sense to use the samples of the at least one signal range Y _{meas of} the communication signal to be analyzed 7 ₁ , 7 ₂ and to decimate the samples of the reference signal P _ref . For this reason, Y _{meas of} the communication signal to be analyzed is used for the at least one signal range 7 ₁ , 7 ₂ according to the unit of amount 33 a rectangular decimation filter unit 70 integrated. The at least one signal range Y _{meas of} the communication signal to be analyzed becomes 7 ₁ , 7 ₂ filtered with a square filter, which in the frequency range, the longer the square, the smaller the bandwidth.

This filter can be compared to a low-pass filter, which leads to a smaller spectrum, which is why the sampling rate can be reduced. The width L of the rectangle corresponds, for example, to an integer factor of the decimation factor D; the width of the rectangle is preferably twice as large as the decimation factor. When choosing the decimation factor, it is advantageous that an integer number of samples is retained after the decimation of the signal. The decimation factor must be an integer divisor of the length L. By using a rectangular decimation filter unit 70 the filtering and decimation of the at least one signal range Y _meas (t) can take place at once, which in turn leads to a time saving. Investigations have shown that a decimation factor of 125 represents the best compromise between required computing time and efficiency if it is assumed that 30,000 samples are stored for one frame and thus 3750 samples for a slot. The first Fourier transform unit 40 ₁ in this case calculates a fast Fourier transform with a size of 512. After the rectangular decimation filter unit 70 This leaves 240 measured values with 272 zeros appended to the end.

As in 7th is shown, the reference signal P _ref (t) is also decimated. Due to the fact that the reference signal is free of any noise, the decimation can be carried out by means of a cyclic decimation filter unit 71 respectively. The reference signal is preferably given the same decimation factor as in the rectangular decimation filter unit 70 decimated. In the fourth processing unit 62 will be in this If preferred, 272 zeros are appended to the samples. Then in the fifth processing unit 63 of the 240 samples the last 239 samples are copied and inserted at the end. This leaves 33 zeros in the middle.

Furthermore, in 7th another interpolation unit 72 shown. The interpolation unit 72 is preferably connected to the output of the second processing unit 44 and to the output of the sixth processing unit 64 connected. With the interpolation unit 72 it is preferably a square interpolation unit 72 . Other interpolation methods can also be used. Due to the fact that through the rectangular decimation filter unit 70 and by the cyclic decimation filter unit 71 the resolution has been reduced, the resolution with which the time offset τ can be estimated also decreases. For this reason, the square interpolation unit 72 the course of the time offset τ is interpolated between two values of the time offset τ. This additional further time offset τ ₂ is used in a second addition unit 73 added to the time offset τ which is determined by the sixth processing means 64 is issued. At the output of the second addition unit 73 the entire time offset that is used to determine the frame start is retained.

8th shows a further refined exemplary embodiment according to the invention of a model for calculating a time offset τ for the frame start, in which the weighting function g is taken into account. When considering equation (9) it becomes clear that in addition to the constant term ( 2 ) another term ( 1 ), which contains a weighting function g. Consequently, the time offset τ to be determined is calculated from the term ( 1 ) minus another term, which is in the numerator and is represented by the constant term ( 2 ) is divided. The weighting function g also appears within this further term. Because the model is out 8th on the models 6th and 7th based, the similarities will not be discussed again separately. Instead, reference is made to the description of the figures for the 6th and 7th made.

Equation (9) can be expanded to a fraction with a common denominator, as shown in Equation (22). The term ( 2 ) is constant. $$\begin{array}{c}\mathrm{L.}\left(\tau \right)=\frac{\stackrel{\left(1\right)}{\overbrace{\left({\displaystyle {\sum }_{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot Y_{meas}{\left(\upsilon \right)}^2}\right)}}\cdot \stackrel{\left(2\right)}{\overbrace{\left({\displaystyle {\sum }_{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}{\left(\upsilon -\tau \right)}^2}\right)}}}{\underset{\left(2\right)}{\underbrace{\left({\displaystyle {\sum }_{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}{\left(\upsilon -\tau \right)}^2}\right)}}}\\ \stackrel{\left(3\right)}{\overbrace{\frac{{\left({\displaystyle {\sum }_{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}\left(\upsilon -\tau \right)\cdot P_{ref}\left(\upsilon -\tau \right)\cdot Y_{meas}\left(\upsilon \right)}\right)}^2}{\underset{\left(2\right)}{\underbrace{\left({\displaystyle {\sum }_{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)\cdot P_{ref}{\left(\upsilon -\tau \right)}^2}\right)}}}}}\end{array}$$

The weighting function g is used within the computing unit 20th generated and preferably has the length of a frame. These are preferably likewise 30,000 samples, as is the case, for example, with the at least one signal range Y _meas of the communication signal to be analyzed 7 ₁ , 7 ₂ and the reference signal Pref is the case. In a further step, one frame becomes the weighting function g by means of the cyclic decimation filter unit 71 filtered and decimated. A value of, for example, is preferred 125 used as a decimation factor. The decimated and filtered weighting function g is then combined with the filtered and decimated reference signal Pref by means of the third multiplication unit 82 multiplied. This multiplication can be assigned to the term ( 3 ) can be taken from equation (22).

Furthermore, the filtered and decimated weight function g is obtained by means of the fourth processing unit 62 and the fifth processing unit 63 processed in such a way that zeros are inserted after the sample values of the weight function g and the sample values, with the exception of the first sample value, are copied to the end of the weight function without the weight function g being increased in the process. By the fourth processing unit 62 and the fifth processing unit 63 the weight function is so large that it corresponds to a power of two and is preferred 512 Having samples.

The weight function g is then calculated by means of a fourth Fourier transformation unit 40 ₄ preferably transformed into the frequency domain by means of a fast Fourier transformation. Subsequently, the first processing unit 41 the complex conjugate part of the weight function g (n) transformed into the frequency domain is formed.

Of the at least one signal range Y _meas (U) of the communication signal to be analyzed 7 ₁ , 7 ₂ at the output of the fourth processing unit 62 is by means of the squaring unit 83 formed the square. This fact is in the term ( 1 ) shown by equation (22). The squared part of the at least one signal range Y _meas (U) ^{2 of} the communication signal to be analyzed is then used 7 ₁ , 7 ₂ transformed into the frequency range by means of a third Fourier transformation unit 40 _3, preferably by means of a fast Fourier transformation. The at least one signal range Y _meas (n) of the communication signal to be analyzed, transformed into the frequency range 7 ₁ , 7 ₂ is by the fourth multiplication unit 84 multiplied by the conjugate complex part of the weight function g * (n) transformed into the frequency domain. This multiplication in the frequency domain corresponds to the cyclical convolution in the time domain. The sum over the product of the weight function and the squared at least one signal range from the communication signal to be analyzed 7 ₁ , 7 ₂ , like this in the term ( 1 ) is shown in equation (22) is calculated.

Via another inverse Fourier transform unit 85 the result is preferably transformed back into the time domain by means of a fast Fourier transformation. The second processing unit 44 forms the real part of the result transformed back into the time domain.

The following explains how the term ( 2 ) is calculated from equation (22). The filtered and decimated reference signal Pref is by means of a squaring unit 83 squared to this then with a fifth multiplication unit 90 to be multiplied by the decimated and filtered weighting function g. This is followed by the summation unit 91 the sum of the multiplication results of all samples of the decimated and filtered weighting function g is calculated with the filtered and decimated reference signal P _ref . The sum of term ( 2 ) from equation (22) is calculated directly without transforming individual signals into the frequency domain, because the term ( 2 ) is independent of Y _meas . The calculation of the sum can be done once, with the result in the memory unit 4th is filed. The result of the sum is a scalar value. The calculated term ( 2 ) is by means of the sixth multiplication unit 92 with the result of the second processing unit 44 multiplied. This becomes the calculated term ( 2 ) of equation (22) with the real part term ( 1 ) multiplied by equation (22).

As in 7th the at least one signal range Y _meas (n) of the communication signal to be analyzed is shown, transformed into the frequency range 7 ₁ , 7 ₂ multiplied by the conjugate complex part of the reference signal P _ref * (n) transformed into the frequency domain. The result is in turn using the inverse Fourier transform unit 43 transformed back into the time domain. With the result at the output of the inverse Fourier transform unit 43 it is the first metric, whereas it is the result of the further inverse Fourier transform unit 85 is a second metric.

From the result at the output of the inverse Fourier transform unit 43 is by means of the second processing unit 44 the real part is determined to thereby remove the numerical noise. Then another squaring unit is used 87 the real part of the result transformed back into the time domain, as in term ( 3 ) represented by equation (22), squared.

Then the result of the further squaring unit is used 87 from the result of the sixth multiplication unit 92 in a third addition unit 86 subtracted. This fact is also shown in equation (22), with the assumption that the constant term ( 2 ) is already included in the denominator of the fraction.

The result of this third addition unit 86 becomes the sixth processing unit again 64 and optionally the interpolation unit 72 supplied, which is preferably a square interpolation unit 72 acts. The output of the sixth processing unit 64 can also be the interpolation unit 72 are supplied, the result of the interpolation unit 72 to the result at the output of the sixth processing unit 64 by means of the second addition unit 73 is added. At the output of the second addition unit 73 is obtained in 8th a time offset τ̂ in whose calculation the weight function g is included. This time offset τ̂ can be output as the frame start.

9 shows an embodiment of a flowchart showing the functioning of the device according to the invention 1 to determine a frame start. In a first process step S ₁ becomes at least one signal range Y _meas of the communication signal to be analyzed 7 ₁ , 7 ₂ with one registration unit 21st detected. The at least one signal range has a length that is preferably that of a frame or a period of the communication signal to be analyzed 7 ₁ , 7 ₂ corresponds, where it is the communication signal to be analyzed 7 ₁ , 7 ₂ preferably a GSM signal.

Subsequently, in a method step S _2, a reference signal Pref with a power profile is generated as a function of the signal range Y _meas of the communication signal to be analyzed 7 ₁ , 7 ₂ generated. This reference signal Pref is preferably generated by means of a signal generator 22nd generated. A valid reference signal Pref is preferably already generated when it is known which slots within the at least one signal range Y _meas of the communication signal to be analyzed 7 ₁ , 7 ₂ are active and which burst type is present within the corresponding active slots. A linear increase in power is preferably assumed, although other forms of increase in power can also be taken into account. Such information can be provided via the input unit 6th the signal generator 22nd are supplied, which generates the reference signal Pref according to the corresponding GSM standard. At the communication signal to be analyzed 7 ₁ , 7 ₂ it is a periodic signal, with the slot configuration of the slots being identical in successive frames.

This is followed by the process step S ₃ executed. Within the process step S ₃ a first metric is established by means of a convolution operation between the at least one signal range Y _{meas of} the communication signal to be analyzed 7 ₁ , 7 ₂ and the reference signal Pref determined. This fact can be found in equation (18). The convolution operation is a cyclic convolution.

This is followed by the process step S ₄ executed. Within the process step S ₄ the position or the index of the maximum of the first metric is output as a time offset τ̂ for the start of the frame, the result of the convolution operation being understood as the metric.

10 shows a further exemplary embodiment of a flow chart which shows the functioning of the device according to the invention 1 for determining a frame start explained in more detail. 10 explains how the process step S ₃ can be calculated particularly efficiently. Within the process step S _{3_1} , which at the beginning of the process step S ₃ can be carried out, the at least one signal range Y _meas (U) of the communication signal to be analyzed 7 ₁ , 7 ₂ and the reference signal P _ref (U) preferably transformed into the frequency domain by means of a fast Fourier transformation.

This is followed by the process step S _{3_2} executed. In the process step S _{3_2} the at least one signal range Y _meas (n) transformed into the frequency range is multiplied by the conjugate complex part of the reference signal P _ref * (n) transformed into the frequency range. This fact can be taken from equation (20).

This is followed by the process step S _{3_3} executed. In this process step S _{3_3} the first metric of the convolution operation between the at least one signal range Y _meas (n) and the reference signal P _ref * (n) is determined. This convolution operation is now the multiplication within the method step S _{3_2} that runs in the frequency domain.

Finally, the process step S _{3_4} executed. Within the process step S _{3_4} the position or the index of the maximum of the first metric of the real part is output as a time offset τ̂ for the start of the frame. It is particularly advantageous that only the real part of the first metric is output as a time offset τ̂, because the imaginary part contains additional noise.

11 shows a further exemplary embodiment of a flow chart showing the mode of operation of the device according to the invention 1 for determining a frame start explained in more detail. As in 10 has been described, a fast Fourier transformation is preferably used so that the cyclic convolution operation can be calculated by means of a multiplication in the frequency domain. So that a fast Fourier transformation can be used, the signal to be transformed must have a length that preferably corresponds to a power of two, that is to say 2 ⁿ . The process step S ₅ carried out, in which a first number of zeros to the amount of the at least one signal range Y _{meas of} the communication signal to be analyzed 7 ₁ , 7 ₂ and is appended to the reference signal P _ref , so that the magnitude of the at least one signal range Y _{meas of} the communication signal to be analyzed 7 ₁ , 7 ₂ and the reference signal P _{ref have} a length which is equal to a power of two.

The process step S ₆ executed, in which a second number of all elements that are located before the appended zeros within the reference signal P _ref , with the exception of a first element, are copied and the second number of all elements, with the exception of the first element, to the end of the reference signal P _ref can be inserted without lengthening it. This allows a cyclic convolution operation to be computed instead of a convolution operation.

12 describes a further exemplary embodiment of a flow chart which shows the functioning of the filtering and decimation within the device according to the invention 1 for determining a frame start explained in more detail. Within method step S ₇ , the magnitude of the at least one signal range Y _meas and of the reference signal P _{ref is} filtered and decimated in such a way that an integer number of samples of the two signals Y _meas , P _ref is retained. The at least one signal range Y _{meas of} the communication signal to be analyzed 7 ₁ , 7 ₂ is preferably filtered and decimated with a rectangular decimation filter. Due to the fact that the reference signal P _ref does not contain any noise, it can be filtered and decimated by means of a cyclic decimation filter. The filtering reduces the spectrum in the frequency range so that the time offset τ can be determined significantly faster and with a sufficiently high degree of accuracy even with a smaller number of samples. A value of, for example, is preferred for a decimation factor 125 selected, for the case that a frame comprises, for example, 30000 samples.

13 shows a further exemplary embodiment of a flow diagram which shows the mode of operation of the interpolation, preferably the quadratic interpolation, within the device according to the invention 1 to determine a frame start. Due to the fact that the at least one signal range Y _meas of the communication signal to be analyzed 7 ₁ , 7 ₂ and the reference signal P _{ref have been} decimated, the time offset τ can only be specified with a resolution that corresponds to the reduced resolution. For this reason, the first metric that results from the cyclic convolution operation is interpolated so that a more precise time offset τ̂ can be determined for the start of the frame. This interpolation is a quadratic interpolation.

14th shows a further exemplary embodiment of a flow chart which shows the functioning of a weighting function g within the device according to the invention 1 for determining a frame start explained in more detail. Such a weighting function g is used to weight certain slots more strongly than other slots. The weighting function g is just as long as the reference signal P _ref . In the process step S ₉ is such a weighting function g by the computing unit 20th generated.

In the following process step S ₁₀ the reference signal P _{ref is} multiplied by the weighting function g.

multipliziert. Eine Transformation in den Frequenzbereich und eine anschließende Multiplikation sind nicht notwendig, weil die oben genannte Gleichung, die auch den Term (2) aus Gleichung (22) darstellt von dem gemessenen Signal befreit sind. Die oben genannte Gleichung kann muss daher nur einmalig, beispielsweise beim Start der Vorrichtung 1 berechnet werden.In the following process step S ₁₁ a second metric is obtained by means of a convolution operation of the weighting function g (n) with the squared at least one signal range Y _meas (n) ² of the communication signal to be analyzed 7 ₁ , 7 ₂ determined. The underlying calculation step can be derived from the term ( 1 ) in equation (22). Furthermore, the real part of the second metric is determined by a sixth multiplication unit 92 with the result of the equation $$\left({\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)}\cdot P_{ref}{\left(\upsilon -\tau \right)}^2\right)$$

multiplied. A transformation into the frequency domain and a subsequent multiplication are not necessary because the above equation, which also includes the term ( 2 ) from equation (22) are exempt from the measured signal. The above equation can therefore only have to be used once, for example when the device is started 1 be calculated.

In the following process step S ₁₂ becomes the square of the real part of the first metric of the result of the sixth multiplication unit 92 by the third addition unit 86 subtracted. This fact is also shown in equation (22). As already explained, the summation symbols in equation (22) can be described by a cyclic convolution.

In the following process step S ₁₃ the position or the index of the maximum of the result of the subtraction is output as a time offset τ̂ for the start of the frame.

15th shows a further exemplary embodiment of a flow diagram which shows the mode of operation of the quadratic interpolation within the device according to the invention 1 for determining a frame start explained in more detail. Within 15th becomes the procedural step S ₁₁ explained in more detail. Within the process step S ₁₁ is at the beginning of the process step S ₁₁ _ ₁ executed. In the process step S _{11_1} becomes the at least one signal range Y _meas (U) of the communication signal to be analyzed 7 ₁ , 7 ₂ squared. This at least one signal range Y _meas (U) has already been extended in advance to a length that is suitable for calculating a fast Fourier transform.

This is followed by the process step S _{11_2} executed. In the process step S _{11_2} the procedural steps are attached S ₅ and copying S ₆ also carried out for the weighting function. Then the process step S _{11_3} carried out, in which the at least one squared signal range Y _meas (U) ^{2 of} the communication signal to be analyzed 7 ₁ , 7 ₂ and the weighting function g (u) are transformed into the frequency domain.

This is followed by the process step S _{11_4} executed, in which the transformed in the frequency range at least one squared signal range Y _meas (n) ^{2 of} the communication signal to be analyzed 7 ₁ , 7 ₂ is multiplied by the conjugate complex part of the weighting function g * (n) transformed into the frequency domain.

Finally the process step S _{11_5} carried out, in which the multiplication result is transformed back into the time domain and this is output as a second metric.

A third processing unit is preferred 61 cut out at least one signal area. This signal area has a length that corresponds to that of a frame. If, for example, it is a GSM signal which is also periodic within a frame, only one period by the third processing unit is preferred 61 cut out, which further reduces the computational effort. If, for example, slots zero to three, with the exception of the transmitted data, are identical to slots four to seven, then all that has to be cut out is a time interval which has the length of one period, i.e. is four slots long.

The signal generator 22nd , with which the reference signal P _{ref is} generated, can be implemented in software but also in hardware. There can also be different profiles for the reference signal P _ref within the at least one memory unit 4th be stored, of which depending on the input within the input unit 6th the corresponding reference signal P _{ref is} loaded.

Within the scope of the invention, all of the features described and / or identified can be combined with one another as desired. In particular, the sub-claims relating to the method can also relate to the device claims, the device 1 concerning and vice versa.

Claims (18)

Method for determining a frame start of a communication signal to be analyzed (7 ₁ , 7 ₂ ), with the following method steps: - Detection (S ₁ ) of at least one signal range (Y _meas ) of the communication signal (7 ₁ , 7 ₂ ) to be analyzed with a Detection unit (21); - Generating (S ₂ ) a reference signal (P _ref ) as a function of a power profile of the at least one signal range (Y _meas ) of the communication signal (7 ₁ , 7 ₂ ) to be analyzed, with active slots and burst types for generating the reference signal (P _ref ) are used within active slots, and the active slots and burst types are specified by a user; - Determination (S ₃ ) of a first metric by means of a convolution operation between the at least one signal range (Y _meas ) and the reference signal (P _ref ), the convolution operation for the magnitude of the at least one signal range (Y _meas ) and the complex conjugate part of the reference signal (P _ref *) is calculated; - Output (S ₄ ) the position of the maximum of the first metric as a time offset (τ̂) for the start of the frame. Procedure according to Claim 1 , characterized in that the communication signal (7 ₁ , 7 ₂ ) to be analyzed is a digitized GSM signal and / or that the at least one signal range (Y _meas ) is at least one frame and / or that the convolution operation is a cyclic convolution operation. Procedure according to Claim 1 or 2 , characterized in that the first metric of the convolution operation between the magnitude of the at least one signal range (Y _meas ) and the reference signal (P _ref ) is determined by the following method _steps : - Transforming (S _{3_1} ) the at least one signal range (Y _meas ) and the Reference signal (P _ref ) into the frequency domain by means of a fast Fourier transform; - Multiplying (S _{3_2} ) the at least one signal range (Ymeas (n)) transformed into the frequency range by the conjugated complex part of the reference signal (P _ref * (n)) transformed into the frequency range; - Transforming (S _{3_3} ) the result of the multiplication of the at least one signal range (Y _meas (n)) with the conjugated complex part of the reference signal (P _ref * (n)) by means of an inverse fast Fourier transformation into the time domain; - Output (S _{3_4} ) the position of the maximum of the first metric of the real part as a time offset (τ̂) for the frame start. Procedure according to Claim 3 , characterized by the following method steps: appending (S ₅ ) a first number of zeros to the amount of the at least one signal range (Y _meas ) and to the reference signal (P _ref ) so that the amount of the at least one signal range (Y _meas ) and the reference signal (P _ref ) have a length which is equal to a power of two; - copying (S ₆ ) a second number of all elements that are located before the appended zeros within the reference signal (P _ref ), with the exception of a first element, and inserting the second number of elements at the end of the reference signal (P _ref ), without extending it. Method according to one of the preceding claims, characterized by the following method step: filtering (S ₇ ) and decimating (S ₇ ) the magnitude of the at least one signal range (Y _meas ) and the reference signal (P _ref ) in such a way that an integer number of samples of the two signals (Y _meas , P _ref ) is retained. Method according to one of the preceding claims, characterized by the following method step: - Interpolating (S ₈ ) the time offset (τ) and adding the interpolated further time offset (τ ₂ ) to the time offset (τ). Method according to one of the preceding claims, characterized by the following method steps: - generating (S ₉ ) a weighting function (g) in order to weight individual areas within the reference signal (P _ref ) to different degrees; - Multiplying (S ₁₀ ) the reference signal (P _ref ) by the weighting function (g); - Determining (S ₁₁ ) a second metric by means of a convolution operation of the weighting function (g) with the squared at least one signal range (Y _meas ² ) from the communication signal (7 ₁ , 7 ₂ ) to be analyzed and multiplying the real part of the second metric by a sixth Multiplying unit (92) with the result of the formula: $${\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)}\cdot P_{ref}{\left(\upsilon -\tau \right)}^2,$$

where υ = sample, g = weight function, P _ref = reference signal, F = number of samples in a period or in a frame, τ = delay in samples; - Subtracting (S ₁₂ ) the square of the real part of the first metric from the result of the sixth multiplication unit (92) by the third addition unit (86); - Output (S ₁₃ ) the position of the maximum of the result of the subtraction as a time offset (τ̂) for the frame start. Procedure according to Claim 4 and Claim 7 , characterized in that the method step of determining a second metric (S ₁₁ ) contains the following partial method _steps : - squaring (S _{11_1} ) the at least one signal range (Y _meas ) of the communication signal to be analyzed (7 ₁ , 7 ₂ ); - _Execution (S _{11_2} ) of the method _steps appending (S ₅ ) and copying (S ₆ ) for the weighting function (g); - Transforming (S _{11_3} ) the at least one squared signal range (Y _meas ² ) and the weighting function (g) into the frequency range; - Multiplying (S _{11_4} ) the at least one squared signal range (Y _meas (n) ² ) transformed into the frequency range by the conjugated complex part of the weighting function (g * (n)) transformed into the frequency range; - Transforming (S _{11_5} ) the multiplication result into the time domain and outputting this as a second metric. Device (1) for determining a frame start of a communication signal (7 ₁ , 7 ₂ ) to be analyzed, the device (7 ₁ , 7 ₂ ) having a detection unit (21) through which at least one signal range (Y _meas ) of the to be analyzed Communication signal (7 ₁ , 7 ₂ ) can be detected, the device (1) having a signal generator (22) with which a reference signal (P _ref ) as a function of a power profile of the at least one signal range (Y _meas ) of the communication signal to be analyzed (7 ₁ , 7 ₂ ) can be generated, with active slots and burst types within active slots being used to generate the reference signal (P _ref ), the active slots and burst types being specified by a user, the device (1) having a computing unit ( 20), by means of which a first metric can be determined by means of a convolution operation between the at least one signal range (Y _meas ) and the reference signal (P _ref ), the Re Calculation unit (20) calculates the convolution operation for the amount of the at least one signal range (Y _meas ) and the complex conjugate part of the reference signal (P _ref *), and the position of the maximum of the first metric as a time offset (τ̂ ) can be output for the frame start. Device according to Claim 9 , characterized in that the communication signal (7 ₁ , 7 ₂ ) to be analyzed is a digitized GSM signal and / or that the at least one signal range (Y _meas ) is at least one frame and / or that the convolution operation is a cyclic convolution operation. Device according to Claim 9 or 10 , characterized in that the first metric of the convolution operation between the absolute value of the at least one signal range (Y _meas ) and the reference signal (P _ref ) can be determined in that a first and a second Fourier transform unit (40 ₁ , 40 ₂ ) of the at least one The signal range (Y _meas ) and the reference signal (P _ref ) can be transformed into the frequency range by means of a fast Fourier transformation, so that the at least one signal range (Y _meas (n)) transformed into the frequency range and the conjugated complex part by a further multiplication unit (42) of the reference signal (P _ref * (n)) can be multiplied with one another, so that the result of the multiplication of the at least one signal range (Y _meas (n)) and the complex conjugate part of the reference signal (P _ref * (n )) can be transformed into the time domain by means of an inverse fast Fourier transformation and that by an s The first processing unit (64) can output the position of the maximum of the first metric of the real part as a time offset (τ) for the start of the frame. Device according to Claim 11 , characterized in that the device (1) has a fourth processing unit (62) and a fifth processing unit (63) and that the fourth processing unit (62) adds a first number of zeros to the amount of the at least one signal range (Y _meas ) and can be appended to the reference signal (P _ref ), so that the magnitude of the at least one signal range (Y _meas ) and the reference signal (P _ref ) have a length that is equal to a power of two, and that the fifth processing unit (63) has a second number of the elements that are located before the appended zeros within the reference signal (P _ref ), with the exception of a first element, can be copied and that this second number of elements can be inserted at the end of the reference signal (P _ref ) by the fifth processing unit (63) without lengthening the reference signal (P _ref ). Device according to one of the Claims 9 to 12 , characterized in that by a rectangular decimation filter unit (70) and a cyclic decimation filter unit (71) the magnitude of the at least one signal range (Y _meas ) and the reference signal (P _ref ) can be filtered and decimated in such a way that an integral number of samples of the two signals (Y _meas , P _ref ) is retained. Device according to one of the Claims 9 to 13 , characterized in that the time offset (τ) can be interpolated by an interpolation unit (72) and that the interpolated further time offset (τ ₂ ) can be added to the time offset (τ) by a second addition unit (73). Device according to one of the Claims 9 to 14th , characterized in that a weighting function (g) can be generated by the arithmetic unit (20) in order to weight individual areas within the reference signal (P _ref ) differently so that the reference signal (P _ref ) with the by a third multiplication unit (82) Weighting function (g) can be multiplied so that the arithmetic unit (20) can determine a second metric by means of a convolution operation of the weighting function (g) with the squared at least one signal range (Y _meas ² ) of the communication signal (7 ₁ , 7 ₂ ) to be analyzed that by a sixth multiplication unit (92) the real part of the second metric with the result of the formula $${\displaystyle \sum _{\upsilon =0}^{\mathrm{F.}-1}G\left(\upsilon -\tau \right)}\cdot P_{ref}{\left(\upsilon -\tau \right)}^2,$$

with υ = sample, g = weight function, P _ref = reference signal, F = number of samples in a period or in a frame, τ = delay in samples, it is possible to multiply that by the third addition unit (86) the square of the real part of the first Metric can be subtracted from the result of the sixth multiplication unit (92) and that a sixth processing unit (64) can output the position of the maximum of the result of the subtraction as a time offset (τ̂) for the start of the frame. Device according to Claim 12 and Claim 15 , characterized in that the second metric can be determined in such a way that the at least one signal range (Y _meas ) of the communication signal (7 ₁ , 7 ₂ ) to be analyzed can be squared by a squaring unit (83), so that a fourth processing unit (62) a first number of zeros can be appended to the reference signal (P _ref ) and that, by a fifth processing unit (63), a second number of all elements that are located before the appended zeros within the reference signal (P _ref ), with the exception of a first element, is copied and that _(ref P) by the fifth processing unit (63), this second number of elements to the end of the reference signal is inserted, that by a third and fourth Fourier transform unit (40 _3, 40 ₄₎ of the at least one squared signal portion (Y _meas ² ) and the weighting function (g) can be transformed into the frequency range that a fourth multiplication unit (84) converts into the frequency range nzbereich transformed at least one squared signal range (Y _meas ² (n)) can be multiplied by the complex conjugate part of the weighting function transformed into the frequency domain (g * (n)), and that the multiplication result in the time domain by a further inverse Fourier transform unit (85) can be transformed and that this can be output as a second metric by the further inverse Fourier transformation unit (85). Computer program with program code means to carry out all steps according to one of the Claims 1 to 8th perform when the program is run on a computer or digital signal processor. Computer program product with program code means stored in particular on a machine-readable carrier, in order to carry out all steps according to one of the Claims 1 to 8th perform when the program is run on a computer or digital signal processor.

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