WO2002028041A2 - Method for reducing the peak-to-average power ratio of a modulated signal - Google Patents

Method for reducing the peak-to-average power ratio of a modulated signal Download PDF

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Publication number
WO2002028041A2
WO2002028041A2 PCT/BE2001/000171 BE0100171W WO0228041A2 WO 2002028041 A2 WO2002028041 A2 WO 2002028041A2 BE 0100171 W BE0100171 W BE 0100171W WO 0228041 A2 WO0228041 A2 WO 0228041A2
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WO
WIPO (PCT)
Prior art keywords
signal
bit stream
peak
modulated
modulated signal
Prior art date
Application number
PCT/BE2001/000171
Other languages
French (fr)
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WO2002028041A3 (en
Inventor
Jan Mennekens
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M-Tec Wireless
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Filing date
Publication date
Application filed by M-Tec Wireless filed Critical M-Tec Wireless
Priority to AU2001291533A priority Critical patent/AU2001291533A1/en
Publication of WO2002028041A2 publication Critical patent/WO2002028041A2/en
Publication of WO2002028041A3 publication Critical patent/WO2002028041A3/en

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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00Modulated-carrier systems
    • H04L27/26Systems using multi-frequency codes
    • H04L27/2601Multicarrier modulation systems
    • H04L27/2614Peak power aspects
    • H04L27/2623Reduction thereof by clipping
    • H04L27/2624Reduction thereof by clipping by soft clipping

Definitions

  • the present invention relates to a method for reducing the peak-to-average power ratio of a telecommunication signal according to the preamble of the first claim.
  • OFDM Orthogonal Frequency Division Multiplex
  • LAN wireless local area networks
  • use is made of around 50 orthogonal subcarrier frequencies which are evenly distributed over a bandwidth of about 20 MHZ in a 5GHz frequency band.
  • the signal is cut into a plurality of data blocks, which are distributed and transmitted over the plurality of subcarriers. In this way, it can be ensured that most of the signal is receivable anywhere in the network. A small portion of the signal may be lost on certain locations: where a dead spot is present for one of the subcarriers, the data block carried on this subcarrier will be lost.
  • This loss of signal can be compensated by transmitting an amount of error correction along with the signal.
  • This error correction is also provided to correct bit errors which may be introduced into the signal between the modulation in the sender and the demodulation in the receiver and which may originate from interference of the transmitted signal with noise, propagation losses and multipath fading.
  • a bit change from "0" to "1” or vice versa is modulated as a phase and/or amplitude change of one of the subcarriers.
  • PAP peak-to-average power ratio
  • clipping is a non-linear operation which introduces non-linearities into the signal. These non-linearities adversely affect the orthogonality of the subcarriers, which means that the subcarriers of the signal interfere with each other to a certain extent. Furthermore, the clipping of the signal creates out-of-band frequency components, i.e. unwanted spectral components outside the bandwidth in which the subcarriers are comprised. Upon transmittal of the clipped signal, the loss of orthogonality causes interference between the subcarriers, so that they can no longer be demodulated independently in the receiver.
  • the additional signals which are transmitted on frequencies outside the bandwidth may cause further disturbance of the subcarriers or disturb the operation of any other signal receiving devices.
  • the bit stream which is derived from the transmitted signal after demodulation may contain a too high amount of errors to be correctable by the error correction, which is transmitted along with the signal.
  • the method of the invention is explained for an OFDM modulated signal, which comprises a plurality of orthogonal subcarriers.
  • the method of the invention is applicable to any modulation technique in which the modulated signal comprises a plurality of orthogonal components (subcarriers, codes or other) and in which the PAP problem is experienced, such as for example Orthogonal Code Division Multiplexing (OCDM) or other.
  • OCDM Orthogonal Code Division Multiplexing
  • step b) of introducing non-linearities in the modulated signal in such a way that the peak-to-average power ratio of the modulated signal is reduced, adversely affects the orthogonality of the subcarriers of the signal in a similar way as in the prior art.
  • the method of the invention comprises an additional step c) before the signal with non-linearities is applied to the amplifier. In this additional step c), the orthogonality between the subcarriers is restored.
  • the method of the invention ensures that the signal which is amplified and subsequently transmitted is composed of orthogonal subcarriers, as opposed to the prior art methods described above.
  • the amount of error correction which has to be transmitted along with the signal can be reduced, which reduces the cost and power consumption of the transmittal.
  • the predetermined value to which the amplitude of the modulated signal is reduced can be chosen in respect of the amount of error correction which is transmitted along with the signal. A trade off is possible between the amount of error correction and the PAP ratio of the transmitted signal.
  • step c) of the method of the invention further comprises the removal of unwanted spectral components from the signal achieved after the introduction of non-linearities in step b).
  • unwanted spectral components may be created into the modulated signal in a similar way as in the prior art methods mentioned above. By removing these unwanted spectral components before applying the signal to the amplifier, it can be obtained that the signal which is transmitted does not comprise spectral components outside the bandwidth of the subcarriers, so that interference or disturbance by such spectral components can be avoided.
  • step c) comprises demodulating and subsequently modulating the signal achieved after the introduction of non-linearities in step b).
  • This demodulation and modulation are carried out according to the same modulation technique as used for modulating the signal from the original bit stream.
  • a bit stream is achieved which is substantially equal to the original bit stream, except that it contains a number of bit errors, which result from the introduction of non-linearities in step b).
  • the bit stream after demodulation is altered in such a way with respect to the original bit stream that, when it is modulated again, the amplitude of the newly modulated signal does not exceed the predetermined value.
  • the signal obtained, which is applied to the amplifier is composed of orthogonal subcarriers.
  • step b) The adverse effect to the orthogonality by introducing the non-linearities in step b) is removed from the signal. Furthermore, by demodulating and subsequently modulating, any unwanted spectral components present in the signal after step b) are removed. So by demodulating and subsequently modulating again, it can be simultaneously achieved for the newly modulated signal that the orthogonality of the subcarriers is ensured, that the unwanted spectral components are removed and that the amplitude remains below the predetermined value.
  • Step b) of the method of the invention preferably comprises the clipping of the amplitude of the signal on the peak locations.
  • the amplitude of the signal on the peak locations is clipped to the predetermined value in order to reduce the PAP ratio to the desired extent.
  • the invention further relates to a method for modulating a bit stream to a signal by using a multicarrier modulation technique and subsequently reducing the peak-to-average power ratio of the modulated signal by using the method described above. Furthermore, the invention also relates to a wireless local area network comprising a transmitting device for transmitting a signal which is modulated from a bit stream using the method of the former paragraph, and a receiving device for receiving the modulated signal.
  • Figure 1 shows a schematic representation of a preferred embodiment of the method according to the invention.
  • the method shown in figure 1 is suitable for reducing the PAP-ratio of a signal modulated using the OFDM scheme. This is shown on figure 1 in that a set of original bits is applied to an "OFDM modulator", which outputs an "original signal" to be transmitted.
  • the OFDM modulator divides the original bit stream into a plurality of data blocks which are distributed over a plurality of subcarriers. These subcarriers are orthogonal frequencies, which do substantially not interfere with each other when transmitted.
  • a bit change from "0" to "1” or vice versa is modulated as a phase and/or amplitude change of one of the subcarriers.
  • PAP peak-to-average power ratio
  • a "hard clipping” device In order to reduce the PAP ratio of the original signal, it is applied to a "hard clipping" device.
  • This hard clipping device analyses the amplitude of the original signal and detects peak locations where the amplitude rises above a predetermined value. On occurrence of such a peak, the device clips the amplitude to the predetermined value, so that the PAP ratio of the signal being output by the hard clipping device is reduced with respect to the original signal.
  • the clipping is a non-linear operation, i.e. it introduces non-linearities in the original signal. These non-linearities may affect the orthogonality of the subcarriers of the signal and create unwanted frequency components.
  • this "clipped, non- linear signal" prior to transmittal it is first applied to an "OFDM demodulator” and subsequently to an "OFDM modulator".
  • the OFDM demodulator demodulates the clipped, non-linear signal and returns it to a bit stream ("bits with errors"), which is substantially the same as the original bit stream apart from a number of bit errors. These bit errors are the result of the introduction of the non-linearities into the original signal by clipping the peaks.
  • the OFDM modulator then (re-)modulates the "bits with errors" into the "clipped, but linear signal".
  • This clipped linear signal differs from the clipped non-linear signal in that any loss of orthogonality between the subcarriers is restored and that any unwanted spectral components are removed.
  • As the final step in the method of figure 1 is an OFDM modulation, it is obtained that all subcarriers in the final signal, i.e. the "clipped, linear signal”, are orthogonal and no unwanted spectral components are present.
  • the "clipped, linear signal” differs from the
  • a signal with a low PAP ratio can be obtained which has a high spectral purity, i.e. it comprises orthogonal subcarriers and no unwanted spectral components.
  • a device for transmitting the signal in a local area network can have an amplifier which is lower in power consumption and cost.
  • a receiving device can have less difficulty in retrieving the original bit stream from the signal it receives.
  • the bit stream obtained in the receiving device after demodulation of the received signal may have bit errors, which originate from the introduction of non-linearities prior to transmittal, but the risk of causing further bit errors during transmittal is reduced by the high spectral purity of the transmitted signal.
  • the retrieval of the original bit stream from the received bit stream i.e. the removal of bit errors, is obtained by transmitting an amount of error correction along with the signal.
  • the amount of bit errors in the received bit stream can be reduced with the method of the invention, also the amount of error correction transmitted along with the signal can be reduced.

Abstract

A method is disclosed for the reduction of the peak-to-average power ratio of a multicarrier signal. The method comprises the following steps: (a) detecting locations at which the amplitude of the signal is above a predetermined value; (b) applying a non-linear process, so that the amplitudes at those locations are below or equal to the predetermined value; (c) restoring orthogonality between the subcarriers.

Description

Method for reducing the peak-to-average power ratio of a modulated signal
The present invention relates to a method for reducing the peak-to-average power ratio of a telecommunication signal according to the preamble of the first claim.
Nowadays, a frequency band around 5 GHz has been reserved for implementing wireless LAN networks. At frequencies around 5GHz, however, some difficulties are experienced on transmitting signals from a sender to a receiver, as the signal is reflected on almost any object. As a result, the receiver not only receives the original signal, but also reflected signals, resulting in echoes on the original signal or in so-called dead spots, i.e. locations where the reflected and original signals are in counterphase and cancel each other. The difficulties mentioned above can be overcome by using the Orthogonal Frequency Division Multiplex (OFDM) modulation scheme. This scheme makes uses of a plurality of "orthogonal" frequencies or "subcarriers" for transmitting the signal, i.e. frequencies which do substantially not mutually interfere. For example, for some new-generation wireless local area networks (LAN), use is made of around 50 orthogonal subcarrier frequencies which are evenly distributed over a bandwidth of about 20 MHZ in a 5GHz frequency band. The signal is cut into a plurality of data blocks, which are distributed and transmitted over the plurality of subcarriers. In this way, it can be ensured that most of the signal is receivable anywhere in the network. A small portion of the signal may be lost on certain locations: where a dead spot is present for one of the subcarriers, the data block carried on this subcarrier will be lost. This loss of signal can be compensated by transmitting an amount of error correction along with the signal. This error correction is also provided to correct bit errors which may be introduced into the signal between the modulation in the sender and the demodulation in the receiver and which may originate from interference of the transmitted signal with noise, propagation losses and multipath fading.
In the OFDM scheme, a bit change from "0" to "1" or vice versa is modulated as a phase and/or amplitude change of one of the subcarriers. When the bit-combination to be transmitted results in many subcarriers having the same phase, an amplitude peak occurs in the signal to be transmitted. This results in a high peak-to-average power ratio (PAP), which is unfavourable for amplification of the signal prior to its transmittal. One could solve this problem by using an amplifier powerful enough to perform linearly on the whole amplitude range of the modulated signal, but such an amplifier is expensive and has a high power consumption, so that this solution is commercially unattractive.
It is therefore desirable to reduce the PAP-ratio of the signal to be transmitted, before it is applied to the amplifier, so that a less powerful amplifier can be used. The following are some proposed prior art solutions for reducing the high PAP-ratio of the signal to be transmitted.
One prior art solution is to remove the signal peaks by clipping. However, clipping is a non-linear operation which introduces non-linearities into the signal. These non-linearities adversely affect the orthogonality of the subcarriers, which means that the subcarriers of the signal interfere with each other to a certain extent. Furthermore, the clipping of the signal creates out-of-band frequency components, i.e. unwanted spectral components outside the bandwidth in which the subcarriers are comprised. Upon transmittal of the clipped signal, the loss of orthogonality causes interference between the subcarriers, so that they can no longer be demodulated independently in the receiver. Furthermore, the additional signals which are transmitted on frequencies outside the bandwidth may cause further disturbance of the subcarriers or disturb the operation of any other signal receiving devices. As a result, the bit stream which is derived from the transmitted signal after demodulation may contain a too high amount of errors to be correctable by the error correction, which is transmitted along with the signal.
Another prior art solution is to remove the peaks in the signal to be transmitted by replacing them with the average signal. This is also a non-linear approach which leads to the same difficulties as mentioned above.
It is an aim of the present invention to provide a method for reducing the peak-to-average power ratio of a telecommunication signal with which the amount of bit errors created can be reduced.
This aim is achieved according to the invention with the method showing the technical characteristics of the characterising part of the first claim. For the sake of clarity, the method of the invention is explained for an OFDM modulated signal, which comprises a plurality of orthogonal subcarriers. However, the method of the invention is applicable to any modulation technique in which the modulated signal comprises a plurality of orthogonal components (subcarriers, codes or other) and in which the PAP problem is experienced, such as for example Orthogonal Code Division Multiplexing (OCDM) or other.
In the method of the invention, step b) of introducing non-linearities in the modulated signal, in such a way that the peak-to-average power ratio of the modulated signal is reduced, adversely affects the orthogonality of the subcarriers of the signal in a similar way as in the prior art. However, the method of the invention comprises an additional step c) before the signal with non-linearities is applied to the amplifier. In this additional step c), the orthogonality between the subcarriers is restored. As a result, the method of the invention ensures that the signal which is amplified and subsequently transmitted is composed of orthogonal subcarriers, as opposed to the prior art methods described above. In this way it can be avoided that the subcarriers interfere with each other, so that a receiver has less difficulty in demodulating the signal it receives. Consequently, the number of bit errors which are created during demodulation of the signal in the receiver can be reduced, so that the bit stream obtained after demodulation has less bit errors. Furthermore, with the method of the invention, the amount of error correction which has to be transmitted along with the signal can be reduced, which reduces the cost and power consumption of the transmittal. The predetermined value to which the amplitude of the modulated signal is reduced can be chosen in respect of the amount of error correction which is transmitted along with the signal. A trade off is possible between the amount of error correction and the PAP ratio of the transmitted signal. Preferably, step c) of the method of the invention further comprises the removal of unwanted spectral components from the signal achieved after the introduction of non-linearities in step b). Such spectral components may be created into the modulated signal in a similar way as in the prior art methods mentioned above. By removing these unwanted spectral components before applying the signal to the amplifier, it can be obtained that the signal which is transmitted does not comprise spectral components outside the bandwidth of the subcarriers, so that interference or disturbance by such spectral components can be avoided. In a preferred embodiment of the method of the invention, step c) comprises demodulating and subsequently modulating the signal achieved after the introduction of non-linearities in step b). This demodulation and modulation are carried out according to the same modulation technique as used for modulating the signal from the original bit stream. By demodulating the signal achieved after step b), a bit stream is achieved which is substantially equal to the original bit stream, except that it contains a number of bit errors, which result from the introduction of non-linearities in step b). As these non-linearities are introduced in step b) to reduce the PAP-ratio, the bit stream after demodulation is altered in such a way with respect to the original bit stream that, when it is modulated again, the amplitude of the newly modulated signal does not exceed the predetermined value. Furthermore, by demodulating and subsequently modulating, the signal obtained, which is applied to the amplifier, is composed of orthogonal subcarriers. The adverse effect to the orthogonality by introducing the non-linearities in step b) is removed from the signal. Furthermore, by demodulating and subsequently modulating, any unwanted spectral components present in the signal after step b) are removed. So by demodulating and subsequently modulating again, it can be simultaneously achieved for the newly modulated signal that the orthogonality of the subcarriers is ensured, that the unwanted spectral components are removed and that the amplitude remains below the predetermined value.
Step b) of the method of the invention preferably comprises the clipping of the amplitude of the signal on the peak locations. The amplitude of the signal on the peak locations is clipped to the predetermined value in order to reduce the PAP ratio to the desired extent.
The invention further relates to a method for modulating a bit stream to a signal by using a multicarrier modulation technique and subsequently reducing the peak-to-average power ratio of the modulated signal by using the method described above. Furthermore, the invention also relates to a wireless local area network comprising a transmitting device for transmitting a signal which is modulated from a bit stream using the method of the former paragraph, and a receiving device for receiving the modulated signal.
The invention will be further elucidated by means of the following description and the appended figure.
Figure 1 shows a schematic representation of a preferred embodiment of the method according to the invention. The method shown in figure 1 is suitable for reducing the PAP-ratio of a signal modulated using the OFDM scheme. This is shown on figure 1 in that a set of original bits is applied to an "OFDM modulator", which outputs an "original signal" to be transmitted.
The OFDM modulator divides the original bit stream into a plurality of data blocks which are distributed over a plurality of subcarriers. These subcarriers are orthogonal frequencies, which do substantially not interfere with each other when transmitted. In the OFDM scheme, a bit change from "0" to "1" or vice versa is modulated as a phase and/or amplitude change of one of the subcarriers. When the original bit-combination produces many subcarriers having the same phase, an amplitude peak occurs in the original signal which is output by the OFDM modulator. This results in a high peak-to-average power ratio (PAP), which is unfavourable for amplification of the signal prior to its transmittal. In order to reduce the PAP ratio of the original signal, it is applied to a "hard clipping" device. This hard clipping device analyses the amplitude of the original signal and detects peak locations where the amplitude rises above a predetermined value. On occurrence of such a peak, the device clips the amplitude to the predetermined value, so that the PAP ratio of the signal being output by the hard clipping device is reduced with respect to the original signal. The clipping is a non-linear operation, i.e. it introduces non-linearities in the original signal. These non-linearities may affect the orthogonality of the subcarriers of the signal and create unwanted frequency components. In order to improve this "clipped, non- linear signal" prior to transmittal, it is first applied to an "OFDM demodulator" and subsequently to an "OFDM modulator".
The OFDM demodulator demodulates the clipped, non-linear signal and returns it to a bit stream ("bits with errors"), which is substantially the same as the original bit stream apart from a number of bit errors. These bit errors are the result of the introduction of the non-linearities into the original signal by clipping the peaks.
The OFDM modulator then (re-)modulates the "bits with errors" into the "clipped, but linear signal". This clipped linear signal differs from the clipped non-linear signal in that any loss of orthogonality between the subcarriers is restored and that any unwanted spectral components are removed. As the final step in the method of figure 1 is an OFDM modulation, it is obtained that all subcarriers in the final signal, i.e. the "clipped, linear signal", are orthogonal and no unwanted spectral components are present. The "clipped, linear signal" differs from the
"original signal" in that the subcarriers no longer have undesirably high peaks. In other words, the PAP ratio of the "clipped, linear signal" is reduced with respect to the "original signal". This results from the fact that the "clipped, linear signal" is modulated from a bit stream, the "bits with errors", which contains no bit-combinations giving rise to such unwanted peaks. The "bits with errors" are demodulated from the "clipped, non-linear signal", so from a signal from which the peaks have been removed.
So with the method of reducing the PAP ratio shown in figure 1 , a signal with a low PAP ratio can be obtained which has a high spectral purity, i.e. it comprises orthogonal subcarriers and no unwanted spectral components. As a result, a device for transmitting the signal in a local area network can have an amplifier which is lower in power consumption and cost. Furthermore, because of the high spectral purity of the signal, a receiving device can have less difficulty in retrieving the original bit stream from the signal it receives. The bit stream obtained in the receiving device after demodulation of the received signal may have bit errors, which originate from the introduction of non-linearities prior to transmittal, but the risk of causing further bit errors during transmittal is reduced by the high spectral purity of the transmitted signal.
The retrieval of the original bit stream from the received bit stream, i.e. the removal of bit errors, is obtained by transmitting an amount of error correction along with the signal. As the amount of bit errors in the received bit stream can be reduced with the method of the invention, also the amount of error correction transmitted along with the signal can be reduced.

Claims

Claims
1. A method of reducing the peak-to-average power ratio of a telecommunication signal modulated from an original bit stream by a modulation technique, the modulated signal comprising a plurality of orthogonal components, the method comprising the steps of: a) detecting peak locations in the modulated signal on which the signal has an amplitude above a predetermined value, b) introducing non-linearities on the peak locations in such a way that the amplitude of the modulated signal is reduced to a value below or equal to the predetermined value, characterised in that the method further comprises the step of c) restoring orthogonality between the components of the signal achieved after the introduction of non-linearities in step b).
2. A method according to claim 1 , characterised in that step c) further comprises the removal of unwanted spectral components from the signal achieved after the introduction of non-linearities in step b).
3. A method according to claim 1 or 2, characterised in that step c) comprises demodulating and subsequently modulating the signal achieved after the introduction of non-linearities in step b), the demodulation and modulation being carried out according to the same modulation technique as used for modulating the signal from the original bit stream.
4. A method according to any one of the claims 1-3, characterised in that step b) comprises clipping of the amplitude on the peak locations to the predetermined value.
5. A method according to any one of the claims 1-4, characterised in that the multicarrier modulation technique is orthogonal frequency division multiplexing.
6. A method for modulating a bit stream comprising the steps of modulating the bit stream into a modulated signal according to a modulation technique and subsequently reducing a peak- to-average power ratio of the modulated signal by using the method according to any one of the claims 1-5.
7. A wireless local area network comprising a transmitting device for transmitting a signal which is modulated from a bit stream using the method according to claim 6, and a receiving device for receiving the modulated signal.
PCT/BE2001/000171 2000-09-28 2001-09-28 Method for reducing the peak-to-average power ratio of a modulated signal WO2002028041A2 (en)

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US7697414B2 (en) 2005-09-30 2010-04-13 Meshnetworks, Inc. System and method for achieving crest factor reduction for multi-carrier modulation in a wireless communication network
US10911141B1 (en) 2019-07-30 2021-02-02 Microsoft Technology Licensing, Llc Dynamically selecting a channel model for optical communications
US10911284B1 (en) 2019-07-16 2021-02-02 Microsoft Technology Licensing, Llc Intelligent optimization of communication systems utilizing error correction
US11031961B2 (en) 2019-07-16 2021-06-08 Microsoft Technology Licensing, Llc Smart symbol changes for optimization of communications using error correction
US11044044B2 (en) 2019-07-16 2021-06-22 Microsoft Technology Licensing, Llc Peak to average power ratio reduction of optical systems utilizing error correction
US11063696B2 (en) 2019-07-16 2021-07-13 Microsoft Technology Licensing, Llc Increasing average power levels to reduce peak-to-average power levels using error correction codes
US11075656B2 (en) 2019-07-16 2021-07-27 Microsoft Technology Licensing, Llc Bit error reduction of communication systems using error correction
US11086719B2 (en) 2019-07-16 2021-08-10 Microsoft Technology Licensing, Llc Use of error correction codes to prevent errors in neighboring storage
US11172455B2 (en) 2019-07-16 2021-11-09 Microsoft Technology Licensing, Llc Peak to average power output reduction of RF systems utilizing error correction

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Cited By (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7697414B2 (en) 2005-09-30 2010-04-13 Meshnetworks, Inc. System and method for achieving crest factor reduction for multi-carrier modulation in a wireless communication network
US10911284B1 (en) 2019-07-16 2021-02-02 Microsoft Technology Licensing, Llc Intelligent optimization of communication systems utilizing error correction
US11031961B2 (en) 2019-07-16 2021-06-08 Microsoft Technology Licensing, Llc Smart symbol changes for optimization of communications using error correction
US11044044B2 (en) 2019-07-16 2021-06-22 Microsoft Technology Licensing, Llc Peak to average power ratio reduction of optical systems utilizing error correction
US11063696B2 (en) 2019-07-16 2021-07-13 Microsoft Technology Licensing, Llc Increasing average power levels to reduce peak-to-average power levels using error correction codes
US11075656B2 (en) 2019-07-16 2021-07-27 Microsoft Technology Licensing, Llc Bit error reduction of communication systems using error correction
US11086719B2 (en) 2019-07-16 2021-08-10 Microsoft Technology Licensing, Llc Use of error correction codes to prevent errors in neighboring storage
US11172455B2 (en) 2019-07-16 2021-11-09 Microsoft Technology Licensing, Llc Peak to average power output reduction of RF systems utilizing error correction
US10911141B1 (en) 2019-07-30 2021-02-02 Microsoft Technology Licensing, Llc Dynamically selecting a channel model for optical communications

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AU2001291533A1 (en) 2002-04-08

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