WO1992011706A1 - Frequency and time slot synchronization using adaptive filtering - Google Patents

Frequency and time slot synchronization using adaptive filtering Download PDF

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Publication number
WO1992011706A1
WO1992011706A1 PCT/US1991/009409 US9109409W WO9211706A1 WO 1992011706 A1 WO1992011706 A1 WO 1992011706A1 US 9109409 W US9109409 W US 9109409W WO 9211706 A1 WO9211706 A1 WO 9211706A1
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Prior art keywords
signal
frequency
signals
determining
produce
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PCT/US1991/009409
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French (fr)
Inventor
Arvind S. Arora
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Motorola, Inc.
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Application filed by Motorola, Inc. filed Critical Motorola, Inc.
Priority to GB9216946A priority Critical patent/GB2256993B/en
Priority to DE4193255A priority patent/DE4193255C2/en
Publication of WO1992011706A1 publication Critical patent/WO1992011706A1/en
Priority to SE9202350A priority patent/SE504792C2/en

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Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W56/00—Synchronisation arrangements
    • H04W56/0035—Synchronisation arrangements detecting errors in frequency or phase
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/24—Radio transmission systems, i.e. using radiation field for communication between two or more posts
    • H04B7/26—Radio transmission systems, i.e. using radiation field for communication between two or more posts at least one of which is mobile
    • H04B7/2662—Arrangements for Wireless System Synchronisation
    • H04B7/2671—Arrangements for Wireless Time-Division Multiple Access [TDMA] System Synchronisation
    • H04B7/2675—Frequency synchronisation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/24—Radio transmission systems, i.e. using radiation field for communication between two or more posts
    • H04B7/26—Radio transmission systems, i.e. using radiation field for communication between two or more posts at least one of which is mobile
    • H04B7/2662—Arrangements for Wireless System Synchronisation
    • H04B7/2671—Arrangements for Wireless Time-Division Multiple Access [TDMA] System Synchronisation
    • H04B7/2678—Time synchronisation
    • H04B7/2681—Synchronisation of a mobile station with one base station
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/24—Radio transmission systems, i.e. using radiation field for communication between two or more posts
    • H04B7/26—Radio transmission systems, i.e. using radiation field for communication between two or more posts at least one of which is mobile
    • H04B7/2662—Arrangements for Wireless System Synchronisation
    • H04B7/2671—Arrangements for Wireless Time-Division Multiple Access [TDMA] System Synchronisation
    • H04B7/2678—Time synchronisation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L7/00—Arrangements for synchronising receiver with transmitter
    • H04L7/04—Speed or phase control by synchronisation signals
    • H04L7/041—Speed or phase control by synchronisation signals using special codes as synchronising signal
    • H04L2007/047—Speed or phase control by synchronisation signals using special codes as synchronising signal using a sine signal or unmodulated carrier

Definitions

  • the present invention relates generally to the field of communications and particularly to frequency and time slot synchronization in a mobile communication environment.
  • TDMA time domain multiple access
  • the different base stations in a cellular radiotelephone system maintain very accurate frequency references, but utilize different transmission frequencies, and possibly different time slot alignments.
  • a mobile radiotelephone is handed off from one cell to another in a cellular
  • the mobile may need some minor frequency adjustment, as well as complete time slot
  • FCCH frequency correction channel
  • BCCH broadcast control channel
  • the base band signal of the FCCH is a frequency correction burst (FCB), a pure tone (sine wave) at 67.5 kHz, consisting of 148 samples, sent priodically and it always occurs in time slot zero of the data stream.
  • FCB frequency correction burst
  • the offset between the carrier frequencies of the base station and the mobile radiotelephone is translated to the base band as a deviation from 67.5 kHz.
  • the boundaries of the FCB delineate the time slots of the TDMA structure. From the FCCH detected, the mobile radiotelephone synchronizes its local oscillator frequency and time slot boundaries with those of the base station using the frequency correction burst in the FCCH time slot.
  • the synchronizing process of the present invention is comprised of the steps of filtering a received signal with adaptive filtering means, buffering this signal in storage means, and determining if the frequency correction tone is present, (the detection process). This also establishes the boundaries of the TDMA time slots. When this frequency correction tone is present, filtering the buffered signal and determining the difference between the frequency of this filtered signal and 67.5 kHz, (the carrier frequency offset estimation process).
  • FIG. 1 shows a block diagram of the process of the present invention.
  • FIG. 2 shows the TDMA, multiframe, broadcast control channel format.
  • FIG. 3 shows a typical radiotelephone, using the process of the present invention, for use in a TDMA type system.
  • the process of the present invention provides rapid frequency and time slot synchronization between a mobile radiotelephone and the base station with which it is
  • the input to this process is one of the two base band quadrature signals, the I or Q data stream, sampled at one sample per bit-time, from the receiver of the radiotelephone.
  • This signal, labeled x n in FIG. 1, is initially filtered by a second order, infinite impulse response
  • IIR bandpass filter 1031
  • Both the gain and the pole of this filter are adaptive.
  • the gain is adjusted in order to maintain substantially unity gain through the filter, that is, the energy at the output is equal to the energy at the input.
  • the pole of the filter is moved so that the passband of the filter encompasses the received signal.
  • the signal output from the filter is labeled y n .
  • the energy of the input signal and the energy of the filtered signal are then estimated in the energy estimation blocks (103 and 104).
  • the input and the output energies, E(x) n+1 and E(y) n+1 , are compared in the gain adaptation block (105) and the gain of the filter is adapted to match the input and filtered signal energies. This adapted gain is then fed back to the filter.
  • This comparison and adaptation is performed as follows:
  • b n+1 b n (1+ ⁇ b (g n+ ⁇ -1)) where b n+1 is the gain in the adaptive filter and ⁇ b is the gain adaptation coefficient and is set to 0.077 for the gain adaptation operation.
  • the pole adaptation block (102) estimates the
  • the pole of the adaptive filter is adapted toward this frequency and the new pole location is fed back to the filter (101). This operation is as follows:
  • a n+1 ⁇ p a n +(1- ⁇ p )r ⁇ n+1
  • ⁇ n is an instaneous pole estimate and ⁇ p is the pole adaptation coefficient and is set to 0.083 for the pole adaptation operation.
  • the adaptive filter tracks a pure tone, such as in the frequency correction burst, all the energy in the input signal is in the band of the bandpass filter. Unit gain can thus be achieved through the filter (101) with the lowest value of the filter gain. This condition is checked to determine the instantaneous presence of a tone in the tone detection block (106). If g n+1 is less than a threshold of 1.2 and b n+1 is less than a threshold of f(a n ), then the tone is present.
  • the timer block (107) measures the length of time for which the tone present condition persists. If this tone is present for at least 100 samples in the preferred embodiment, the presence of the frequency correction burst has been verified. This integration prevents the algorithm from falsely detecting a signal, that, for short periods, may appear like a narrowband signal.
  • the signal, x n that was input to the filter (101), is also stored in a shift registered buffer (108). Once it has been determined that this stored signal is the frequency correction burst, the signal from the buffer (108) is input to the band-pass filter (101) again using optimum coefficients, a * and b * , determined during the detection process. Since the passband of the filter (101) is now tuned to the frequency of the frequency correction burst, after the above adaptation process, it passes this signal without attenuation, and filters out the background noise, thus improving the effective signal-to-noise ratio.
  • y n+1 b * X n+1 + a * y n + (- r 0 2 ) y n-1
  • the filtered signal, y n is next processed using a Least Squared Error estimation process to generate a frequency estimate, q * , of the base band tone.
  • the difference between q * and p/2 (67.5 kHz) is the frequency offset between the carrier frequencies of the base station and the mobile radiotelephone. This is entered to the local oscillator circuit of the radiotelephone to compensate for the carrier frequency offset. The above described process is performed periodically to keep the mobile radiotelephone locked to the base station carrier frequency.
  • the I and Q decoder block contains the

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  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Mobile Radio Communication Systems (AREA)
  • Time-Division Multiplex Systems (AREA)
  • Synchronisation In Digital Transmission Systems (AREA)

Abstract

The synchronization process of the present invention filters the received signal with an adaptive band-pass filter (101) while buffering the received signal in memory (108). The energies of the input signal and the filtered signal are estimated (103 and 104) and the gain of the filter is adapted (105) based on the difference between the energies. The pole of the filter is adapted (102) to center the frequency of the input signal in the filter's pass-band. If a tone is detected (106), the length of the tone is determined (107) to ascertain if it is a frequency correction burst (FCB). If the tone detected is an FCB, the signal in the memory is also the FCB that is then filtered in the band-pass filter (101) and the difference between the frequency of this signal and 67.5 kHz is determined (109). This difference represents the frequency offset between the base station carrier frequency and that of the mobile radiotelephone, and can be fed into the local oscillating means to compensate for the frequency offset. The boundaries of the FCB establish the time slot alignment of the TDMA structure being received from the base station.

Description

FREQUENCY AND TIME SLOT SYNCHRONIZATION USING ADAPTIVE FILTERING
Field of the Invention
The present invention relates generally to the field of communications and particularly to frequency and time slot synchronization in a mobile communication environment. Background of the Invention
Since a mobile radiotelephone does not have an accurate enough frequency reference internally, it must make fine frequency adjustments to achieve the required frequency synchronization to a base station frequency. In a time domain multiple access (TDMA) system, multiple logical channels are transmitted on the same frequency, but separated in time, FIG 2. To communicate with a base station, the mobile radiotelephone must also find the boundaries of these time slots, called time slot synchronization.
The different base stations in a cellular radiotelephone system maintain very accurate frequency references, but utilize different transmission frequencies, and possibly different time slot alignments. When a mobile radiotelephone is handed off from one cell to another in a cellular
radiotelephone system, the mobile may need some minor frequency adjustment, as well as complete time slot
synchronization to communicate with the new base station.
To accomplish this in a digital cellular radiotelephone system, the radiotelephone first finds a frequency correction channel (FCCH), which is part of the broadcast control channel (BCCH). FIG. 2 illustrates the FCCH slots (201) and other data control channels that make up the multiframe
TDMA structure of the BCCH. This format is described in greater detail in the digital cellular standard specification GSM Recommendation 5.02, Version 3.3.1, October 13, 1989. The base band signal of the FCCH is a frequency correction burst (FCB), a pure tone (sine wave) at 67.5 kHz, consisting of 148 samples, sent priodically and it always occurs in time slot zero of the data stream. The offset between the carrier frequencies of the base station and the mobile radiotelephone is translated to the base band as a deviation from 67.5 kHz. The boundaries of the FCB delineate the time slots of the TDMA structure. From the FCCH detected, the mobile radiotelephone synchronizes its local oscillator frequency and time slot boundaries with those of the base station using the frequency correction burst in the FCCH time slot.
Since the burst is relatively short, the mobile must find it in the data stream and synchronize with it in this short period. There is a resulting need for a process that can detect the presence and boundaries of the FCB very rapidly, and estimate the frequency offset very accurately, even when signals are received in the presence of noise. Summary of the Invention
The synchronizing process of the present invention is comprised of the steps of filtering a received signal with adaptive filtering means, buffering this signal in storage means, and determining if the frequency correction tone is present, (the detection process). This also establishes the boundaries of the TDMA time slots. When this frequency correction tone is present, filtering the buffered signal and determining the difference between the frequency of this filtered signal and 67.5 kHz, (the carrier frequency offset estimation process).
Brief Description of the Drawings FIG. 1 shows a block diagram of the process of the present invention. FIG. 2 shows the TDMA, multiframe, broadcast control channel format.
FIG. 3 shows a typical radiotelephone, using the process of the present invention, for use in a TDMA type system.
Detailed Description of the Preferred Embodiment
The process of the present invention provides rapid frequency and time slot synchronization between a mobile radiotelephone and the base station with which it is
communicating. This is accomplished by detecting the presence and boundaries of the frequency correction burst and determining the frequency of this base band tone.
The preferred embodiment of the process of the present invention is illustrated in FIG. 1. The input to this process is one of the two base band quadrature signals, the I or Q data stream, sampled at one sample per bit-time, from the receiver of the radiotelephone. This signal, labeled xn in FIG. 1, is initially filtered by a second order, infinite impulse response
(IIR) bandpass filter (101). Both the gain and the pole of this filter are adaptive. The gain is adjusted in order to maintain substantially unity gain through the filter, that is, the energy at the output is equal to the energy at the input. The pole of the filter is moved so that the passband of the filter encompasses the received signal. The signal output from the filter is labeled yn. The filtering is performed as follows: yn+1 = bn xn+1 + an yn + (- r2 0) yn-1 The energy of the input signal and the energy of the filtered signal are then estimated in the energy estimation blocks (103 and 104). The estimation for the input energy is accomplished as follows: E(x)n+1 = (1-αe) E(x)n + αe x2 n+1 The estimate for the filtered signal energy is as follows: E(y)n+1=(1-αe)Eyn+αe yn 2 +1 where αe is the energy adaptation coefficient and is set equal to 0.091 for the estimation operations.
The input and the output energies, E(x)n+1 and E(y)n+1, are compared in the gain adaptation block (105) and the gain of the filter is adapted to match the input and filtered signal energies. This adapted gain is then fed back to the filter. This comparison and adaptation is performed as follows:
Figure imgf000006_0001
bn+1=bn (1+αb(gn+ι-1)) where bn+1 is the gain in the adaptive filter and αb is the gain adaptation coefficient and is set to 0.077 for the gain adaptation operation.
The pole adaptation block (102) estimates the
instantaneous frequency of the filtered signal. The pole of the adaptive filter is adapted toward this frequency and the new pole location is fed back to the filter (101). This operation is as follows:
If (yn 2>0.15E(y)n+1) then If ( |2yn| > lyn-1+yn+1l ) then θn+1=(yn-1+yn+1)/(yn)
an+1=αpan+(1-αp)rθn+1
End If
End if where θn is an instaneous pole estimate and αp is the pole adaptation coefficient and is set to 0.083 for the pole adaptation operation. When the adaptive filter tracks a pure tone, such as in the frequency correction burst, all the energy in the input signal is in the band of the bandpass filter. Unit gain can thus be achieved through the filter (101) with the lowest value of the filter gain. This condition is checked to determine the instantaneous presence of a tone in the tone detection block (106). If gn+1 is less than a threshold of 1.2 and bn+1 is less than a threshold of f(an), then the tone is present.
The timer block (107) measures the length of time for which the tone present condition persists. If this tone is present for at least 100 samples in the preferred embodiment, the presence of the frequency correction burst has been verified. This integration prevents the algorithm from falsely detecting a signal, that, for short periods, may appear like a narrowband signal.
The signal, xn, that was input to the filter (101), is also stored in a shift registered buffer (108). Once it has been determined that this stored signal is the frequency correction burst, the signal from the buffer (108) is input to the band-pass filter (101) again using optimum coefficients, a* and b*, determined during the detection process. Since the passband of the filter (101) is now tuned to the frequency of the frequency correction burst, after the above adaptation process, it passes this signal without attenuation, and filters out the background noise, thus improving the effective signal-to-noise ratio. yn+1 =b* Xn+1 + a* yn + (- r0 2) yn-1
The filtered signal, yn, is next processed using a Least Squared Error estimation process to generate a frequency estimate, q*, of the base band tone.
The difference between q* and p/2 (67.5 kHz) is the frequency offset between the carrier frequencies of the base station and the mobile radiotelephone. This is entered to the local oscillator circuit of the radiotelephone to compensate for the carrier frequency offset. The above described process is performed periodically to keep the mobile radiotelephone locked to the base station carrier frequency.
An example of the receive portion of a typical mobile radiotelephone for use in a TDMA system is illustrated in FIG. 3. The I and Q decoder block contains the
synchronization process of the present invention disclosed herein. This type of radiotelephone is discussed in greater detail in copending U.S. patent application serial No. 590,415 "Interference Reduction Using an Adaptive Receiver Filter, Signal Strength, and BER Sensing filed September 28, 1990 on behalf of Cahill.
In summary, a novel process has been shown that will synchronize a mobile radiotelephone's local oscillator frequency and time slot positioning with those of the received signal from a base station. This synchronization occurs in real time and with significantly enhanced accuracy.

Claims

Claims
1. A method for frequency synchronization between a cellular communication base station that transmits a plurality of signals, at least one of the plurality of signals having a frequency correction tone, and a mobile communication device that receives the plurality of signals, the mobile
communication device having local oscillating means with a variable frequency, the method characterized by the steps of: a) filtering a first signal of the plurality of signals to produce a first filtered signal (101);
b) buffering the first signal to produce a buffered signal (108);
c) determining if the frequency correction tone is present in the first signal by determining an energy of the first signal and an energy of the filtered signal and a duration for which a relationship between these energies exists (102-107); d) when the frequency correction tone is present, filtering the buffered signal to produce a second filtered signal which contains carrier frequency offset information (110); and the method further characterized by the step of
e) when the frequency correction tone is present, determining from the second filtered signal a frequency difference between the carrier frequency of the signal from the base station and the frequency of the local oscillating means of the mobile communication device (109).
2. The method of claim 1 and further characterized by the step of adjusting the local oscillating means of the mobile
communication device in response to the frequency difference.
3. The method of claim 1 characterized in that the
relationship between the input and output energies is equality.
4. A method for frequency synchronization in a time division multiple access (TDMA) cellular communication system between a communication base station that transmits a plurality of TDMA signals at a plurality of frequencies, and a mobile communication device that receives the plurality of signals, each signal comprised of a plurality of samples and at least one of the signals having a frequency correction tone, the mobile communication device having local oscillating means with a variable frequency that varies in response to the frequency correction tone, the method characterized by the steps of:
a) filtering a first signal of the plurality of signals with an adaptive filter to produce a filtered signal, the adaptive filter having a variable gain and a variable pole (101);
b) buffering the first signal to produce a buffered signal
(108);
c) determining a first energy level of the first signal (103);
d) determining a second energy level of the filtered signal (104);
e) varying the gain of the adaptive filter in response to a difference between the first and second energy levels (105); f) varying the pole of the adaptive filter in response to the frequency of the second signal (102);
g) when the first energy level is equal to the second energy level, determining a quantity of samples of the first signal for which a relationship between the first and the second energies exists (106-107);
h) when the quantity of samples is substantially the predetermined number, filtering the buffered signal to produce a second filtered signal having carrier frequency offset information (110); and the method further characterized by the step of i) if the quantity of samples is substantially a
predetermined number, determining from the second filtered signal a frequency difference between the carrier frequency of the signal from the base station and the frequency of the local oscillating means of the mobile communication device (109).
5. The method of claim 4 and further characterized by the step of adjusting the local oscillating means of the mobile
communication device in response to the frequency difference.
6. A radiotelephone for use in a TDMA type cellular communication system, the radiotelephone having
demodulation means for generating I and Q signals, the radiotelephone characterized by:
a) means for transmitting a first signal;
b) means for receiving a second signal, coupled to the TDMA demodulation means, the TDMA demodulation means processing the second signal to generate the I and Q signals; and the radiotelephone further characterized by
c) processing means for processing the I or Q signals, the processing means performing the steps of:
filtering a first signal of the plurality of signals with an adaptive filter to produce a first filtered signal (101);
buffering the first signal to produce a buffered signal (108) ;
determining if the frequency correction tone is present in the first signal by determining an energy of the first signal and an energy of the filtered signal and a duration for which a relationship between these energies exists (102-107);
when the frequency correction tone is present, filtering the buffered signal to produce a second filtered signal containing carrier frequency offset information (110); and the processing means further performing the step of
when the frequency correction tone is present, determining from the second filtered signal a frequency difference between the carrier frequency of the signal from the base station and the frequency of the local oscillating means of the mobile communication device (109).
PCT/US1991/009409 1990-12-17 1991-12-11 Frequency and time slot synchronization using adaptive filtering WO1992011706A1 (en)

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GB9216946A GB2256993B (en) 1990-12-17 1991-12-11 Frequency and time slot synchronization using adaptive filtering
DE4193255A DE4193255C2 (en) 1990-12-17 1991-12-11 Frequency synchronization method and mobile radio telephone for use in a TDMA-type cellular communication system
SE9202350A SE504792C2 (en) 1990-12-17 1992-08-14 Frequency and time slot synchronization using adaptive filtering

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US62853590A 1990-12-17 1990-12-17
US628,535 1990-12-17

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WO2000001095A1 (en) * 1998-06-29 2000-01-06 Telefonaktiebolaget Lm Ericsson (Publ) Method, apparatus and system for determining a location of a frequency synchronization signal
SG79976A1 (en) * 1997-05-28 2001-04-17 Nec Corp Radiotelephone unit
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EP1472812A2 (en) * 2001-02-16 2004-11-03 Harris Corporation Wideband ranging process for frequency acquisition

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FR2709894A1 (en) * 1993-09-10 1995-03-17 Alcatel Mobile Comm France A method of determining, by a mobile station of a cellular radio system, the type of the cell to which it is attached, mobile station and base station.
US5535424A (en) * 1993-09-10 1996-07-09 Alcatel Mobile Communication France Method enabling a mobile station of a cellular mobile radio system with more than one type of cell to determine the type of cell it is accessing, and mobile station and base transceiver station for implementing this method
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EP0762698A3 (en) * 1995-08-15 2000-09-27 Conexant Systems, Inc. Frequency estimation using iterative filtering, particularly for cellular telephony system
EP0762698A2 (en) * 1995-08-15 1997-03-12 Rockwell International Corporation Frequency estimation using iterative filtering, particularly for cellular telephony system
EP0881849A3 (en) * 1997-05-28 2001-02-07 Alcatel Radio communication system with fixed and mobile radio equipment
EP0881849A2 (en) * 1997-05-28 1998-12-02 Alcatel Radio communication system with fixed and mobile radio equipment
SG79976A1 (en) * 1997-05-28 2001-04-17 Nec Corp Radiotelephone unit
US6278699B1 (en) 1998-06-22 2001-08-21 Telefonaktiebolaget Lm Ericsson (Publ) Synchronization techniques and systems for spread spectrum radiocommunication
WO2000001095A1 (en) * 1998-06-29 2000-01-06 Telefonaktiebolaget Lm Ericsson (Publ) Method, apparatus and system for determining a location of a frequency synchronization signal
US6356608B1 (en) 1998-06-29 2002-03-12 Telefonaktiebolaget Lm Ericsson (Publ) Method, apparatus, and system for determining a location of a frequency synchronization signal
AU757757B2 (en) * 1998-06-29 2003-03-06 Optis Wireless Technology, Llc Method, apparatus and system for determining a location of frequency synchronization signal
MY120816A (en) * 1998-06-29 2005-11-30 Ericsson Telefon Ab L M Method, apparatus and system for determining a location of a frequency synchronization signal.
EP1472812A2 (en) * 2001-02-16 2004-11-03 Harris Corporation Wideband ranging process for frequency acquisition
EP1472812A4 (en) * 2001-02-16 2005-05-04 Harris Corp Wideband ranging process for frequency acquisition

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SE9202350D0 (en) 1992-08-14
SE9202350L (en) 1992-08-14
FR2671248B1 (en) 1994-11-04
AU9169291A (en) 1992-07-22
DE4193255C2 (en) 1997-02-20
IL100366A (en) 1995-05-26
CA2071552A1 (en) 1992-06-18
DE4193255T (en) 1992-12-10
SE504792C2 (en) 1997-04-28
IL100366A0 (en) 1992-09-06
IT1250962B (en) 1995-04-24
AU636263B2 (en) 1993-04-22
ITRM910944A0 (en) 1991-12-17
GB2256993B (en) 1995-06-21
CA2071552C (en) 1997-02-25
GB9216946D0 (en) 1992-10-07
GB2256993A (en) 1992-12-23
FR2671248A1 (en) 1992-07-03
ITRM910944A1 (en) 1993-06-17

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