DE102009041808A1 - Optical arrangement - Google Patents

Abstract

The invention relates to a receiver for serial OFDM signals with a sampling means and a Fourier transforming means. It is provided here that the Fourier transform means comprises a delay interferometer cascade and the sampling means are arranged downstream of the cascade.

Description

The present invention relates to the term claimed above and thus deals with the high-frequency signal transmission.

The transmission of signals with a large bandwidth is becoming increasingly important. Particularly high transmission rates can be achieved with optical signal transmission. For this purpose, high-frequency light signals are transmitted in optical fibers and the like. As a rule, in the case of signal transmission, parallel signals are present on the transmitter side, for example data words having a width of several bits, and data words with a width of several bits are also processed on the receiver side. Nevertheless, the transmission of these parallel present and required data takes place in a serial fashion via a single optical (glass) fiber or a fiber for the outgoing and a fiber for the return conduction of signals.

It has also been proposed to work in the field of optical signal transmission with discrete multitone methods, more precisely orthogonal frequency division multiplexing (OFDM).

The generation of a serial OFDM signal from parallel input data and the recovery of parallel data from an OFDM-like signal requires, inter alia, the performance of Fourier transforms or inverse Fourier transforms. The need to transfer data very quickly forces that the Fourier transforms and the inverse Fourier transformations also have to be executed very quickly. In principle, this is possible by making a digital electronic signal processing. However, the digital electrical signal processing suffers from the fact that with increasing frequencies of the energy consumption increases quite considerably with very broadband signals. This is disadvantageous if the highest frequencies are to be used in a simple manner and thus under narrow-band or low-frequency operating electronics for signal transmission.

It has already been shown that the optical OFDM transmission does not necessarily have to be based on digital-electronic high-frequency signal processing, but in particular the inverse Fourier transforms (which is not different from the Fourier transforms unless otherwise stated below) can be optically realized by performing the Fourier transforms with conventional coupler interferometry. How a discrete Fourier transformation with star-shaped networks for single-mode fibers can be constructed in principle is described in US Pat "Discrete Fourier transforms by single-mode star networks" by ME Marhic in Optics Letters Vol. 12, No. 1, January 1987 ,

Reference is also made to the article by Yue-Kai Huan et al. entitled "All-optical OFDM transmission with coupler based IFFT / FFT and pulse interleaving", ISBN 978-1-4244-1932-6 / 08 , It is proposed in this article that the received OFDM signal after the transmission is first split and the Fourier transform is performed to obtain the respective subcarrier coefficients; then, for each of the channels, a scan should be performed with an electroabsorption modulator to eliminate artifacts. After this optical scanning then the Subträgerdetektion should be done. Although the described structure is complicated, the achievable transmission rates are in need of improvement.

A high-frequency modulated transmitter for the generation of optical signals is otherwise off AD Ellis, FG Garcia Gunning and T. Healy "Coherent WDM: The Achievement of High Information Spectral Density Through Phase Control with the Transmitter" published in 2006 by the Optical Society of America ,

The arrangements typically used to generate electrical parallel signals from an optical high frequency OFDM signal are complicated. Typically, the serial signals are first split with splitters, the respective split-up signal components are delay-delayed and then the Fourier transform is determined on the corresponding signal-delayed parallel signals. This can be done, for example, with delay interferometers such as Mach-Zehnder interferometers. The optical effort for this is quite significant. This massively increases the costs on the receiver side.

The optical signal transmission also deals with the U.S. Patent 5,852,505 , It is stated in this document that in fiber optic signal transmission, for example when fiber optic signals have to be distributed to residential buildings, it is important that optical signals can be multiplexed and demultiplexed, ie a combination of several optical signals with different wavelengths or their separation , This should be done with a wavelength demultiplexer, in particular a wavelength spacing at wavelengths around 1.310 / 1500 nm of 0.8 nm should be achieved. In the document, such a wavelength demultiplexer for demultiplexing an optical signal into a plurality of individual channels at various wavelengths, which is intended to include a first stage with a Fourier filter for receiving the optical signal having the plurality of individual channels at different wavelengths and for demultiplexing the plurality of individual channels into a plurality of first output step paths having first passbands, the Fourier filter a multipath interference device having a transfer function representing a finite Fourier series in which each harmonic term corresponds to an interference path; and a second stage having a plurality of Mach Zehnder filters, wherein each of the Mach Zehnder filters having a respective first stage output path of the first stage Fourier filter for demultiplexing the receiving channels from the first stage into a plurality of second ones Includes step exit paths with second pass bands that are wider than the first pass bands.

It should also be noted in this connection that, if in the present case a Fourier transformation is mentioned, the determination of only a finite number of terms of a Fourier series is always meant in practice.

It is desirable to provide a receiver for OFDM signals that can easily handle high frequency signals.

The object of the present invention is to provide new products for commercial use.

The solution to this problem is claimed in an independent form. Preferred embodiments can be found in the subclaims.

The present invention thus proposes, in a first aspect, a receiver for serial OFDM signals with a sampling means and a Fourier transform means, in which it is provided that the Fourier transform means comprises a delay interferometer cascade and the sampling means are arranged downstream of the cascade.

The present invention has recognized that in receivers for serial OFDM signals it is possible to carry out a fast Fourier transformation (FFT, fast Fourier transformation) analogously, in particular preferably optically, without great efforts for tuning the corresponding Fourier transform-forming (optical) elements must be undertaken and without the need for the most elaborate electronic (digital) circuits.

In principle, it would be possible to implement a conversion of the Fourier transforms with optical, typically two-path delay interferometer cascades of the invention also in receivers for electrical signals. In such a case, the conversion from an electrical signal to an optical signal, then the optical execution of the Fourier transform and then a conversion into electrical signals could take place. However, it will be typical for the receiver to be designed as a receiver for optical signals, for example for connection to an optical fiber line, such as a glass fiber. Nevertheless, the implementation of the invention would also be possible with purely electrical elements such as delay lines, adders and / or subtractors.

The receiver may optionally output a serial signal again, which is important, for example, when repeaters or the like are required in wide area networks; typically, however, the receiver will output parallel signals such as data words or the like.

The scanning means will scan optically or electrically. For this purpose, either an electro-optical or electro-absorptive modulator, but also a purely optical scanning or the like may be provided in the optical path, in particular behind each delay interferometer cascade output, or respective outputs are scanned with photodiodes. On the - in principle, but practically not or only in exceptional cases preferred - possibility to make both an optical scan for some channels as well as an electrical scan for other channels, it should be mentioned. In particular, it is possible to convert the optical signal into an electrical signal by means of a photodiode and to subsequently scan it by means of a smart-and-hold circuit. Also, a sampling window could be determined both optically and photoelectrically by sampling.

The sampling means is preferably designed such that a signal sampling takes place in each case only during a specific sampling interval and is synchronized to the OFDM signals. The synchronization to signals according to certain frequencies and / or modulation properties is known per se and need not be explained in more detail. However, the sampling takes into account that the signals obtained from the delay interferometer cascade can only be viewed in a certain short time window, since the signals are severely disturbed at other times.

If .DELTA.f is the distance of the sampling points in the frequency domain, then it must be taken into account in the cascading of delay interferometers for the mathematical determination of an FFT that, for a physical realization in practice, the output signal of the cascade for the longest period is overlaid by disturbances. A sole synchronization is therefore not sufficient; rather, the sampling time must be selected short against the symbol duration and selected phase correct. For example, if a 16-point FFT is implemented and an ideal OFDM signal with a symbol duration T _s = 1 / Δf is used, the output of the passive filter structure (ie the delay interferometer mask) is up to a fraction of 1/16 of the symbol duration T _s interference superimposed. The sampling with the sampling means will be carried out for intervals which are short against the symbol duration and are appropriately synchronized therewith. It is particularly preferred in this case for the sampling means to scan for a sampling duration based on the OFDM symbol duration T _s , for a fraction of the symbol duration, the fraction being determined by the cascade depth.

It should be noted that in non-ideal OFDM signals, such as may occur due to absorption of certain frequency components in the optical fiber, dispersion, etc., the sampling intervals may need to be further shortened. However, a sample interval extension can be achieved by introducing a Guard Interval to extend the possible sample period. It should be mentioned, moreover, that optionally one or more of the photoelectric converters can provide a multi-stage conversion of the optical into an electrical signal, so do not simply make a simple light-dark distinction, but approximately capture the brightness value with multiple bits. This may be preferred in order to enable even better synchronization in the case of strongly disturbed signals and / or to reduce a bit error rate.

It is not necessary to carry out the entire Fourier transformation and / or signal processing by optical means.

Rather, electronic filters and / or digital signal processing, in particular for signal bandwidth limiting and / or pulse shaping of received pulses and / or for performing a (continued) Fourier transformation, d. H. the determination of further terms of the Fourier series, to be arranged downstream of a photoelectric converter. It should be noted that by performing an optical Fourier transformation of the later required further signal processing effort drops significantly, so that this further signal processing with only low clock rates of digital electronics, etc. can be performed. It is particularly preferred if additional electronic (analogue) or digital signal processing takes place when the modulation rate in the OFDM signal is substantially smaller than the channel spacing.

The delay interferometer cascades, which are multi-level, typically have delays in each stage, which are determined by the OFDM symbol duration T _s and the cascade stage, where for the first stage the delay is (1/2 * T), in the second stage ( 1/4 · T), in the third stage (1/8 · T) and so on. Each delay interferometer will typically comprise in one of the branches a phase link tunable or tuned to the carrier. It should be noted that possibly when using coherent receivers, ie receivers which mix the light signal to be detected before its detectors with a signal from a local source, one or more cascade stages, in particular the first, may be unnecessary.

It should be noted that the delay interferometers may be constructed as two-path delay interferometers and are preferred and that they may also be constructed as integrated delay interferometers or as a free-jet delay interferometer. For example, unless all stages are constructed with interferometer cascades, integrated delay interferometers may be constructed with a waveguide grating router (WGR), free-jet delay interferometer followed by, for example, a free-jet liquid crystal waveguide grating router (LCWGR), etc.

The invention makes it possible to greatly reduce the optical complexity for the Fourier filtering. Unlike the prior art as described, for example, in Marhic's paper, which requires optical couplers to compute a fast optical Fourier transform O (N) = N * log (N), i. H. given a complexity of O (N), wherein the optical phase in groups of each N waveguides of the coupler structure is to be stabilized relative to each other, in the present case only 2 (N-1) optical couplers must be used and only the relative phases in each case two arms of the delay interferometer are controlled. This becomes more advantageous the larger N is. On the other hand, simulations show that the overall performance of a system is most affected by the first stages. This applies in particular to the first two delay interferometer cascade stages, so that passive splitter and bandpass filters can also be used for N> 4 components in the OFDM signal to be considered without great loss of quality, which further facilitates the optical design. In particular, the possibility of using arrayed waveguide gratings instead of splitter standard wavelength demultiplexers or more specific implementations should be mentioned.

It should be noted that this is considered particularly advantageous to simple To realize the receiver. It should also be pointed out that the optimum number of cascade stages may also change over the next few years, even with a large number of channels of the OFDM signal to be taken into account, because possibly digital signal processing could become more favorable in terms of energy due to new semiconductor technologies or in the future even better modulation options on a transmitter side exist, glass fiber transmission properties are improved and the like. All this can have an influence on the preferred number of cascade stages connected in series.

It is therefore preferred, at least for the moment, if the cascade comprises no more than four cascaded delay interferometers.

As can be seen, the individual cascades are constructed in a signal-splitting manner and typically a plurality of the split signals are sampled individually with the sampling means.

Reference has already been made to the possibility of providing at least one wavelength demultiplexer between cascade and sampling means which is not constructed as and / or with delay interferometers. The implementation of filter or splitting means by elements differing from cascaded delay integrators makes it possible, in particular, to provide filters with specific characteristics, such as Gaussian or Lorentz filter transmission characteristics, but also flat-top or armchair characteristics. This can bring considerable advantages in the further processing of the signals, such as when signals are particularly disturbed.

It should be noted that where it is not necessary to extract all channels from a serial OFDM signal, the construction of only a portion of the delay interferometer cascade is sufficient without departing from the basic principles of the invention. Protection is therefore also claimed for a subcarrier extracting receiver for serial OFDM signals with a sampling means and a Fourier transform means, in which the Fourier transform means comprises paths of a delay interferometer cascade corresponding to the subcarrier to be extracted and wherein the sampling means are downstream of the paths of the cascade ,

The receivers of the present invention can be used for end-user access devices in networks, as routing arrangements for signal routing and / or signal division in networks with a receiver as described above, but also for other arrangements, such as for (future) LAN networks, communication of digital signal processing units with each other, etc.

It should be noted that the simple optical structure with inexpensive elements without requiring high investment in complex electronic signal processing opens up a very wide range of applications and that here as exemplary specified preferred embodiments such as end user access devices and routing arrangements (hubs, routers, switches) not are to be construed limited. Moreover, protection is also claimed for a transmitter with which serial OFDM signals are generated, wherein a sensing means and a forcing transform means are provided, wherein the sensing means is adapted to generate a plurality of optical signals comprising a plurality of cascaded delay interferometers subordinate to or forming part of a Fourier filter means for realizing an (inverse) Fourier transform. As a feeler are in particular, but not exclusively electro-absorptive modulators into consideration. It should be noted that there are similar advantages as in the receivers and that typically where receivers are realized in devices according to the principles of the present invention, such transmitters can be realized. This allows two-way communication over one or more paths.

The invention will now be described by way of example only with reference to the drawings. In this is represented by

1 a receiver with a two-stage delay interferometer cascade here 1 and a sampling means downstream of the delay interferometer cascade;

2 a transmitter for serial OFDM signals with a sensing means and a downstream Fourier filter means with cascade-coupled delay interferometers;

3 an alternative embodiment for a transmitter according to the present invention, wherein an optical signal from a light source formed here as a pulsed laser source is split, differently modulated and fed to a delay interferometer cascade to implement an IFFT;

4 a variation of a receiver of 1 in which four conventional wavelength demultiplexers are provided between a two-stage delay interferometer cascade, the outputs of which are in turn fed to sampling elements;

5 another variation too 1 in which, in order to reduce the number of required scanning elements of a delay interferometer cascade, first the scanning elements and then wavelength demultiplexers are connected downstream;

6 a subcarrier-extracting receiver for serial optical OFDM signals with one of a delay interferometer cascade as a Fourier transform means and a here as a bandpass realized filter arrangement downstream scanning means;

7 a structure of a transmitter and a receiver according to the present invention, wherein the recorded at respective points A, B, C, D, E, F, G, H, J spectra and for selected points D, G, H, J, the intensity or eye diagrams are shown;

8th the bit error rate for differently coded carriers, depending on the input power at the receiver of the array of 7 for different vehicles, etc .;

9a to 9e Prior art arrangements in which no delay interferometer cascades are used.

In the figures, especially in the 1 to 6 uwsnd 9 certain elements are shown only schematically. Not all identical elements are always provided with the same reference numerals.

In 1 means reference number 1 a coupler, reference number T / 2 refers to a delay line which delays by half a symbol interval T, the symbol T / 4 designates a delay line delaying by a quarter interval, and the box denoted by "-j" denotes one to the respective carrier matched phase shifter. This use of designations for delay lines with couplers and phase shifters runs through the 1 . 2 . 3 . 4 . 5 such as 6 and 9 through, even if in the 9 the delay lines in particular T / 2 and 3 T / 4 are symbolized by a plurality of loops.

It means further in 1 the reference number 21 a scanning element, wherein the scanning elements 21 together form a scanning means; the reference number 21 is for the sensing elements in the 9a and 9b used.

In 1 denotes reference number 22 and 23 a serial-to-parallel converter and the FFT computation by the out of the couplers 1 , the delay lines T / 2 and T / 4 and the phase shifter -j built delay Interferometer cascade, which is constructed here in two stages and the reference numerals D1 to D4 denote the outputs of the parallelized portions of a very left fed into the optical coupler serial optical OFDM signal Scanning and parallelization.

In the 4 and 5 are the scanning elements that form the scanning, with 51 designated. The reference number 52 denotes a four-point FFT arrangement of two cascaded delay interferometers. In 4 are sixteen scanning elements 51 shown and in 5 only four sensing elements, where the reference number 53 each wavelength demultiplexer called. The 4 and 5 differ in the arrangement of the scanning elements 51 and the wavelength demultiplexer 53 in that in one case the wavelength demultiplexer 53 the scanning elements 51 are preset so that here sixteen sensing elements 51 are while in 5 only four sensing elements are needed to scan because the sensing elements are upstream of the wavelength demultiplexers. In both cases, the principles of the invention are implemented.

In 6 a receiver for extracting only certain subcarrier components of an OFDM signal is shown, wherein the reference number 51 again represents a scanning element, the reference number 52 a part of a delay element cascade and the reference number 54 refers here to a realized as a band-pass filter filter element.

It refers to the rest in the 1 as well as the 9a and 9b the reference number 22 respectively 23 the serial-parallel conversion or the (optical) FFT. As can be seen, according to the invention, the serial-to-parallel conversion and the fast optical Fourier transformation are combined into one unit, while in the prior art the serial-parallel conversion with delay then the Fourier transformation and only after the sampling is performed, which leads to significantly more complex structures.

It should be mentioned, moreover, that it is particularly in the embodiment according to 5 is not required, the sampling by the sampling means 51 make visually. In particular, it is possible to coherently detect several carriers after a few, here two, delay interferometer stages, and subsequently the filtering by electronic post-processing in the filter elements 53 make. Coherent detection, in which the incident optical signal is mixed with light from a local source, ie, a frequency stable local laser, helps to eliminate those subcarriers that are more than the bandwidth of the local oscillator the photodiode or its associated electronics deviate to attenuate and filter out. It can, for example, in the case of coherent detection, for example, with a subcarrier distance of 50 GHz and a photodiode bandwidth of 50 GHz, be stopped after two delay interferometer stages and be dispensed with further filtering, since the mixing products of the remaining carrier with the Local oscillator at over 150 GHz. Wavelength demultiplexing can be realized by electronic implementation of an FFT, bandpass filter, or the like.

In 2 For example, a transmitter is shown which, in a simplified manner, illustrates how an OFDM signal can be generated according to the invention. Provided is an input with a plurality of bits D1 to D4, which are fed to respective sampling (or Tast) elements whose outputs are in turn applied to the cascade end of a delay interferometer cascade, in which delays, here T / 4 or T / 2, Phase shifts j and merging optical signals in coupling elements 1 in a backward cascade, so that a serial OFDM signal is output on the right. This is indicated by the reference numerals 44 and 45 indicated, wherein the reference numeral 44 an IFFT and the reference numeral denotes a serial-to-parallel conversion, that is to say the backward-passing delay-interferometer cascade designates a combined IFFT-parallel-serial-conversion structure.

In 3 is the same IFFT-serial conversion structure as in 2 but is an optical pulse source 47 provided an optical splitter 48 goes through and then into a modulator array 49 is fed to generate the inputs to the backward passing delay interferometer cascade.

In 7 Among other things, a structure is shown with which it is easy to generate OFDM-like signals, for testing purposes for example, without requiring a large number of modulators. This arrangement uses a comb generator "comb generator" whose spectrum A is fed into a disinterleaver, the outputs of which are fed into modulator units DBPSK and DQPSK, the abbreviations being known for differential binary phase shift keying and differential quadrature phase shift keying " stand. The respective output signals from the DBPSK or DQPSK units B and C are also illustrated in the figure. The ODFM signals generated in this way can be fed together into a glass fiber and after merging have the spectrum D and the associated, in 7 also shown intensity distribution. In 7 It is further shown that with a multi-stage delay interferometer cascade, a serial-to-parallel conversion can be carried out by performing an FFT, the spectra obtained at different points of the delay interferometer cascade are shown at E and F. The outputs from the delay interferometer cascade are fed to bandpass filters, behind which the spectrum G is obtained, and then sampled with an electro-absorptive modulator EAM to be translated in the receiver-side DBPSK and DQPSK units, respectively. The eye diagrams obtained at the respective outputs are denoted as j and h and in 7 also shown.

The bit error rates for different carriers available with this arrangement are dependent on the input power from the receiver side in FIG 8th shown. The different types of bit errors can be recognized for different subcarriers. The adjacent DBPSK carriers have no adverse behavior, ie they do not experience any deterioration compared to a direct measurement ("back to back"), the central DQPSK carriers also have no significant disadvantages or impairments. There is a deterioration of the receiver sensitivity of 5 dB or an error background for the two outer DQPSK subcarriers which have 11 dB less power in the optical comb. The lower power means the signal-to-noise ratio is poor and bandpass filtering is no longer effective enough.

The experiment has also shown that the presented OFDM implementation does not require extensive phase stabilization of the transmitter.

With an arrangement like in 7 Transfer rates of almost 400 GB / s have already been achieved on the filing date under laboratory conditions.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• US 5852505 [0009]

Cited non-patent literature

• "Discrete Fourier transforms by single-mode star networks" by ME Marhic in Optics Letters Vol. 12, No. 1, January 1987 [0005]
• Yue-Kai Huan et al. entitled "All-optical OFDM transmission with coupler based IFFT / FFT and pulse interleaving", ISBN 978-1-4244-1932-6 / 08 [0006]
• AD Ellis, FG Garcia Gunning and T. Healy "Coherent WDM: The Achievement of High Information Spectral Density Through Phase Control with the Transmitter" published in 2006 by the Optical Society of America [0007]

Claims (19)

Receiver for serial OFDM signals with a sampling means and a Fourier transform means, characterized in that the Fourier transform means comprises a delay interferometer cascade and the sampling means are arranged downstream of the cascade. Receiver according to the preceding claim, characterized in that it has an optical input. Receiver according to one of the preceding claims, characterized in that it is designed to output a parallel signal. Receiver according to one of the preceding claims, characterized in that the scanning means comprises at least one optical scanning means, preferably at least one electro-acoustic modulator (EAM), preferably for all outputs of the delay interferometer cascade means for optical scanning. Receiver according to one of the preceding claims, characterized in that the scanning means comprises at least one photoelectric converter, preferably at least one photodiode, more preferably a photodiode for each output of the delay interferometer cascade, and, in photodiode use, a respective electrical scanning member. Receiver according to the preceding claim, characterized in that a plurality of photoelectric transducers is provided, to which an electronic filter and / or a digital signal processing for signal bandwidth limiting and / or for pulse shaping and / or for carrying out a Fourier transformation is arranged downstream. Receiver according to the preceding claim, characterized in that the modulation rate is smaller, preferably significantly smaller than the channel spacing. Receiver according to one of the preceding claims, characterized in that the scanning means for sampling with a on the OFDM symbol duration (T _s ) and thus preferably synchronized related sampling period scans, in particular with a sampling period corresponding to ≈ T _s · (1/2 ⁿ ), where n is the number of cascade stages. Receiver according to one of the preceding claims, characterized in that the delay interferometer cascades are constructed n-stage and the delay in the first interferometer T / 2, in the second interferometer T / (2 ² ) and in the n-point T interferometer T / (2 ⁿ ), where T preferably corresponds to the OFDM symbol duration T _s . Receiver according to one of the preceding claims, characterized in that the delay interferometer comprises a phase element (j) tuned to the carrier. Receiver according to one of the preceding claims, characterized in that the cascade is constructed at least three stages. Receiver according to one of the preceding claims, characterized in that the cascade comprises not more than six, preferably not more than four cascaded delay interferometer. Receiver according to one of the preceding claims, characterized in that the delay interferometer cascade is constructed by multiple signals splitting by their cascading and a plurality of the split signals are scanned individually with the scanning means. Receiver according to one of the preceding claims, characterized in that between the cascade and the scanning means, a wavelength demultiplexer is provided which is not constructed as and / or with two-path delay interferometers. Receiver according to one of the preceding claims, characterized in that the Fourier transformation means is arranged downstream of at least one filter whose filter characteristic is preferably selected from Gaussian, Bessel and Lorentz or flat-top filter characteristics. Subcarrier extracting receiver for serial OFDM signals with a sampling means and a Fourier transform means, characterized in that the Fourier transform means comprises paths of a delay interferometer cascade which correspond to the subcarrier to be extracted and the sampling means are arranged downstream of the paths of the cascade. Transmitter for serial OFDM signals with a sensing means and a Fourier transform means, characterized in that the sensing means is adapted to generate a plurality of optical signals, which is followed by a Fourier filter means comprising a plurality of cascade-coupled delay interferometers. End-user access device for networks, in particular wide-area, metro and / or Access networks with a receiver or a transmitter according to one of the preceding claims. Forwarding arrangement for signal forwarding and / or signal division in networks with a receiver according to one of the preceding receiver claims or a transmitter according to claim 17.

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