US20100284496A1 - Method and apparatus for dc offset compensation in a digital communication system - Google Patents
Method and apparatus for dc offset compensation in a digital communication system Download PDFInfo
- Publication number
- US20100284496A1 US20100284496A1 US10/527,783 US52778303A US2010284496A1 US 20100284496 A1 US20100284496 A1 US 20100284496A1 US 52778303 A US52778303 A US 52778303A US 2010284496 A1 US2010284496 A1 US 2010284496A1
- Authority
- US
- United States
- Prior art keywords
- matrix
- trend
- regression
- regression matrix
- path
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Images
Classifications
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
- H04L25/024—Channel estimation channel estimation algorithms
- H04L25/025—Channel estimation channel estimation algorithms using least-mean-square [LMS] method
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
- H04L25/024—Channel estimation channel estimation algorithms
- H04L25/0242—Channel estimation channel estimation algorithms using matrix methods
- H04L25/0244—Channel estimation channel estimation algorithms using matrix methods with inversion
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/06—Dc level restoring means; Bias distortion correction ; Decision circuits providing symbol by symbol detection
- H04L25/061—Dc level restoring means; Bias distortion correction ; Decision circuits providing symbol by symbol detection providing hard decisions only; arrangements for tracking or suppressing unwanted low frequency components, e.g. removal of dc offset
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/08—Modifications for reducing interference; Modifications for reducing effects due to line faults ; Receiver end arrangements for detecting or overcoming line faults
Definitions
- the present invention relates to DC offset (or biased noise) compensation in digital communication systems.
- DC offset or biased noise
- it relates to biased noise/DC offset compensation in digital communication systems where a′known training sequence of limited length is transmitted together with data burst for the estimation of a multi-path (or multi-tap) signal propagation channel, such as in a normal burst of TDMA/GSM/EDGE systems.
- blind DC estimation This is the simplest and most straightforward method.
- the received signal is averaged before de-rotation.
- this method is not accurate due to uncertainty of the data symbols in the transmission.
- Another such known method is joint channel and DC estimation. This is used when the DC offset has been treated as an extra tap in the multi-tap channel estimation, utilising the constellation rotation as a reference, for example the ⁇ /2 rotation in GSM and the 3 ⁇ /8 rotation in the EDGE modulation. It has been observed, however, that the performance of this method depends on the training sequence used. It does not perform well when a training sequence has high amplitude at the trend frequency. Further, the accuracy of channel estimation is compromised due to the fact that an extra parameter needs to be estimated with the same training sequence. In addition, the performance is also affected by the form of burst synchronisation.
- a further known method is referred to as classical trend elimination as disclosed for example in “System Modelling and Identification”; R. Johansson, in particular pages 83 to 85, pages 126 and 127 and pages 464 and 465.
- This is a method in system identification.
- a stimulating sequence ⁇ t k ⁇ of length n is applied to a linear system with m parameters, a system response ⁇ x k ⁇ of length n is collected for the system identification.
- Trend elimination modifies the system model where neutralized sequences are used for both stimulus and observation.
- the neutralized sequence of the stimulus s k and the neutralized sequence of the observation (input signal) y k are derived as follows:
- This method can be employed only if either the training sequence, the stimulus, is significantly longer than the model order n>>m, or just a single parameter is sufficient for system identification. It cannot be applied in a digital communication system where a multi-path channel is required to be estimated with a limited training sequence.
- a generalised trend elimination processing is proposed, where a single frequency trend, possibly a pure DC offset when the trend frequency is zero, is taken into consideration in an unbiased multi-path channel estimation to compensate for the biased noise/DC offset.
- the DC offset estimation/compensation of the present invention may be utilised in a radio receiver working in a multi-path channel environment with or without rotation modulation.
- the estimation/compensation method of the present invention can provide better channel estimation in the presence of biased noise or DC offset since the method of the present invention reduces the sensitivity to the distortion.
- the method of the present invention is computationally simpler since the initial channel estimation is separated from DC offset estimation.
- path-trend vectors can be pre-calculated, which further reduces the computational load.
- the invention extends trend elimination (bias/DC offset compensation) to include single frequency trends and enables multi-path channel estimation with relatively short training sequences.
- DC offset is generalised to include an additive single frequency component which causes static (zero frequency) or incremental (non-zero frequency) phase offset. Depending on the rotation scheme in the modulation, this phase offset increment can be considered as the normalised trend frequency.
- the objective of the invention is to acquire channel estimation with eliminated/suppressed trend and to obtain trend estimation for DC offSet compensation.
- FIG. 1 is a flow diagram illustrating the method according to an embodiment of the present invention.
- the digital communication system comprises a modulator and transmitter (not shown here).
- the modulator modulates a signal for transmission using known techniques.
- the signal to be transmitted comprises a plurality of data bits and a plurality of training sequence bits which constitute a normal burst.
- the training sequence being a sequence of bits known by the receiver of the digital communication system allows the receiver to determine precisely the position of the data bits within a burst, and to enable the receiver to derive the distortion caused by transmission etc.
- transmission of the burst is made over a multi-path propagation channel comprising m-taps.
- the distortion is derived, in part, from an estimation of the propagation channel.
- Application of the training sequence to the channel estimation provides the distortion when the result is compared to the actual received training sequence.
- each column vector in the regression matrix is defined as the-path-regression vector
- ⁇ k [t m-1-k t m-k . . . t n-2-k t n-1-k ] T
- the regression matrix ⁇ is constructed 104 from samples of a known training sequence of a received signal by minimising the least-square error, without DC compensation, channel estimation with LS results in
- a trend matrix ⁇ of the same dimension as ⁇ is introduced 106 , in which each column is defined as a path-trend vector of size n ⁇ m+1
- ⁇ degenerates to a unit matrix with every element equal to 1
- the path-trend vector degenerates to a unit vector in the regression matrix as
- the method according to an embodiment of the present invention constructs 108 a new “neutralized” path-regression vectors:
- the new model can then be described as
- the offset vector can be then calculated 112 as
- the amplitude of the offset can be determined as
- ⁇ DC ⁇ DC ⁇ ⁇ n - m + 1
- the method above therefore, constructs path trend vectors for each path from rotation vector and path regression vector.
- the method provides a path trend elimination/suppression model for channel estimation, using a modified “neutralized” regression matrix in LS channel estimation. It separates the channel estimation and DC estimation by eliminating/suppressing DC offset in the channel estimation. Implicit DC offset estimation is obtained by combination of the de-trended path—regression and de-trended receiving signal.
- Application of the method of the present invention in linear system identification can be achieved with short stimulus and biased/single frequency offset noise.
Abstract
Description
- The present invention relates to DC offset (or biased noise) compensation in digital communication systems. In particular, but not exclusively, it relates to biased noise/DC offset compensation in digital communication systems where a′known training sequence of limited length is transmitted together with data burst for the estimation of a multi-path (or multi-tap) signal propagation channel, such as in a normal burst of TDMA/GSM/EDGE systems.
- The problem with biased noise/DC offset exists in,' among others, homodyne receivers that convert radio frequency signal directly into base band signal. Various factors such as components mismatch, local oscillator leakage and interferences may contribute to this distortion. When the modulation of the transmitted signal consists of a rotation operation, for example in GSM/EDGE systems, the DC offset will causes a single frequency trend in the received signal after de-rotation (demodulation). If this frequency trend is left uncompensated, the DC offset can cause significant receiver performance degradation.
- Several methods are known and are currently used for compensation of the DC offset.
- One such known method is blind DC estimation. This is the simplest and most straightforward method. The received signal is averaged before de-rotation. When this is applied to TDMA systems which have limited symbols in a burst, this method is not accurate due to uncertainty of the data symbols in the transmission.
- Another such known method is joint channel and DC estimation. This is used when the DC offset has been treated as an extra tap in the multi-tap channel estimation, utilising the constellation rotation as a reference, for example the π/2 rotation in GSM and the 3π/8 rotation in the EDGE modulation. It has been observed, however, that the performance of this method depends on the training sequence used. It does not perform well when a training sequence has high amplitude at the trend frequency. Further, the accuracy of channel estimation is compromised due to the fact that an extra parameter needs to be estimated with the same training sequence. In addition, the performance is also affected by the form of burst synchronisation.
- A further known method is referred to as classical trend elimination as disclosed for example in “System Modelling and Identification”; R. Johansson, in particular pages 83 to 85, pages 126 and 127 and pages 464 and 465. This is a method in system identification. When a stimulating sequence {tk} of length n is applied to a linear system with m parameters, a system response {xk} of length n is collected for the system identification. Trend elimination modifies the system model where neutralized sequences are used for both stimulus and observation. The neutralized sequence of the stimulus sk and the neutralized sequence of the observation (input signal) yk are derived as follows:
-
- This method, however, can be employed only if either the training sequence, the stimulus, is significantly longer than the model order n>>m, or just a single parameter is sufficient for system identification. It cannot be applied in a digital communication system where a multi-path channel is required to be estimated with a limited training sequence.
- A generalised trend elimination processing is proposed, where a single frequency trend, possibly a pure DC offset when the trend frequency is zero, is taken into consideration in an unbiased multi-path channel estimation to compensate for the biased noise/DC offset.
- The DC offset estimation/compensation of the present invention may be utilised in a radio receiver working in a multi-path channel environment with or without rotation modulation. The estimation/compensation method of the present invention can provide better channel estimation in the presence of biased noise or DC offset since the method of the present invention reduces the sensitivity to the distortion.
- This is achieved by adjusting the trend suppression level such that the channel estimation is less variant when different training sequences, or different training sequence segments are used.
- The method of the present invention is computationally simpler since the initial channel estimation is separated from DC offset estimation. In addition, path-trend vectors can be pre-calculated, which further reduces the computational load.
- The invention extends trend elimination (bias/DC offset compensation) to include single frequency trends and enables multi-path channel estimation with relatively short training sequences. The term DC offset is generalised to include an additive single frequency component which causes static (zero frequency) or incremental (non-zero frequency) phase offset. Depending on the rotation scheme in the modulation, this phase offset increment can be considered as the normalised trend frequency. The objective of the invention is to acquire channel estimation with eliminated/suppressed trend and to obtain trend estimation for DC offSet compensation.
-
FIG. 1 is a flow diagram illustrating the method according to an embodiment of the present invention. - An embodiment of the present invention will now be described with reference to
FIG. 1 . The digital communication system comprises a modulator and transmitter (not shown here). The modulator modulates a signal for transmission using known techniques. The signal to be transmitted comprises a plurality of data bits and a plurality of training sequence bits which constitute a normal burst. The training sequence being a sequence of bits known by the receiver of the digital communication system allows the receiver to determine precisely the position of the data bits within a burst, and to enable the receiver to derive the distortion caused by transmission etc. In the digital communication system in which the method of the present invention is utilised, transmission of the burst is made over a multi-path propagation channel comprising m-taps. The distortion is derived, in part, from an estimation of the propagation channel. Application of the training sequence to the channel estimation provides the distortion when the result is compared to the actual received training sequence. - In general, linear regression with Least-Squares (LS) error criterion is used to obtain channel estimation in digital communication systems. In LS estimation, the estimation model can be expressed as
-
x=Φh+v - which includes a channel vector (m is the span of the channel),
-
h=[h0h1 . . . hm-1]T - a received signal vector
-
x=[x0s1 . . . xn-m]T - a noise vector
-
v=[v0v1 . . . vn-m]T - and a regression matrix
-
- where each column vector in the regression matrix is defined as the-path-regression vector
-
Φk=[tm-1-ktm-k . . . tn-2-ktn-1-k]T - Therefore, the regression matrix Φ is constructed 104 from samples of a known training sequence of a received signal by minimising the least-square error, without DC compensation, channel estimation with LS results in
-
ĥ=(ΦTΦ)−1ΦT x - In the presence of DC offset, this equation gives erroneous results.
- In the method of an embodiment of the present invention, a trend matrix Ψ of the same dimension as Φ is introduced 106, in which each column is defined as a path-trend vector of size n−m+1
-
- where ( )* notifies conjugate transposition, and Ω is a Toeplitz matrix generated by the rotation vector ω, (the de-rotation vector having the form of ω*), where
-
ω=[1e jβ e j2β . . . e j(n-m)β]T - The phase shift (the nominal trend frequency) Pin the rotation vector is system dependent. For example, in GSM β=π/2 while in EDGE β=3π/8. When β=0, i.e. the constellation does not rotate in the modulation, Ω degenerates to a unit matrix with every element equal to 1, and the path-trend vector degenerates to a unit vector in the regression matrix as
-
- The method according to an embodiment of the present invention constructs 108 a new “neutralized” path-regression vectors:
-
θk=φk−ψk , k=0, 1, . . . , m−1 - and a new regressor matrix
-
Θ=Φ−Ψ=[θ0, θ1 . . . θm-1] - Utilising this new regression matrix and the neutralised receiving signal,
-
- where the receiving trend vector p depends also on the modulation rotation and can degenerate to an average when β=0, the new model can then be described as
-
y=Θh+v - and an unbiased channel estimation is obtained 110.
-
ĥ=(ΘTΘ)−1ΘT y - Further, the equation above also provides an implicit DC (i.e. the trend) estimation. The offset vector can be then calculated 112 as
-
δDC=αDC ω*=ρ−Ψĥ - The amplitude of the offset can be determined as
-
- In practise, complete trend elimination may be not desirable since it can damage the quality of the cross correlation between original and de-trended training sequence E{φψ*} which is essential to the accuracy of the channel estimation. Computational considerations will also prefer a real, instead.of complex, training sequence in the operation. A compromised modification of the new “neutralized” patin-regression vectors is thus
-
θk=φk −μRe(ψk) - where the real part of the trend vector is taken out and scaled down (0<μ<1) before subtracted from the path regression vector. Trend suppression, instead of trend elimination is incorporated in the processing. For different training sequences, which have different amplitude at the trend frequency, different suppression level may be applied by choosing different μ.
- The method above, therefore, constructs path trend vectors for each path from rotation vector and path regression vector. The method provides a path trend elimination/suppression model for channel estimation, using a modified “neutralized” regression matrix in LS channel estimation. It separates the channel estimation and DC estimation by eliminating/suppressing DC offset in the channel estimation. Implicit DC offset estimation is obtained by combination of the de-trended path—regression and de-trended receiving signal. Application of the method of the present invention in linear system identification can be achieved with short stimulus and biased/single frequency offset noise.
- Although a preferred embodiment of the method and apparatus of the present invention has been illustrated in the accompanying drawing and described in the forgoing detailed description, it will be understood that the invention is not limited to the embodiment disclosed, but is capable of numerous variations, modifications without departing from the scope of the invention as set out in the following claims.
Claims (10)
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US10/527,783 US7839956B1 (en) | 2002-09-16 | 2003-09-15 | Method and apparatus for DC offset compensation in a digital communication system |
Applications Claiming Priority (6)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
EP02256376A EP1401163B1 (en) | 2002-09-16 | 2002-09-16 | Method and apparatus for DC offset compensation in a digital communication system |
EP02256376 | 2002-09-16 | ||
EP02256376.1 | 2002-09-16 | ||
US41379802P | 2002-09-25 | 2002-09-25 | |
PCT/EP2003/010245 WO2004034661A1 (en) | 2002-09-16 | 2003-09-15 | Method and apparatus for dc offset compensation in a digital communication system |
US10/527,783 US7839956B1 (en) | 2002-09-16 | 2003-09-15 | Method and apparatus for DC offset compensation in a digital communication system |
Publications (2)
Publication Number | Publication Date |
---|---|
US20100284496A1 true US20100284496A1 (en) | 2010-11-11 |
US7839956B1 US7839956B1 (en) | 2010-11-23 |
Family
ID=31896960
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
US10/527,783 Expired - Fee Related US7839956B1 (en) | 2002-09-16 | 2003-09-15 | Method and apparatus for DC offset compensation in a digital communication system |
Country Status (7)
Country | Link |
---|---|
US (1) | US7839956B1 (en) |
EP (1) | EP1401163B1 (en) |
KR (1) | KR100978703B1 (en) |
AT (1) | ATE416544T1 (en) |
AU (1) | AU2003273880A1 (en) |
DE (1) | DE60230141D1 (en) |
WO (1) | WO2004034661A1 (en) |
Families Citing this family (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
ATE416544T1 (en) | 2002-09-16 | 2008-12-15 | Ericsson Telefon Ab L M | METHOD AND DEVICE FOR DC VOLTAGE OFFSET COMPENSATION IN A DIGITAL COMMUNICATIONS SYSTEM |
CN101404518B (en) * | 2008-11-21 | 2012-07-04 | 北京天碁科技有限公司 | Frequency deviation estimation method and apparatus used for radio communication system |
Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US6571090B1 (en) * | 1999-10-06 | 2003-05-27 | Fujitsu Limited | Radio receiver and diversity receiver |
US6967992B1 (en) * | 1997-11-19 | 2005-11-22 | Interuniversitair Micro-Elektronica Centrum (Imec) | Method and apparatus for receiving GPS/GLONASS signals |
Family Cites Families (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
EP1224781A1 (en) * | 1999-10-27 | 2002-07-24 | Nokia Corporation | Dc offset correction in a mobile communication system |
ATE416544T1 (en) | 2002-09-16 | 2008-12-15 | Ericsson Telefon Ab L M | METHOD AND DEVICE FOR DC VOLTAGE OFFSET COMPENSATION IN A DIGITAL COMMUNICATIONS SYSTEM |
-
2002
- 2002-09-16 AT AT02256376T patent/ATE416544T1/en not_active IP Right Cessation
- 2002-09-16 DE DE60230141T patent/DE60230141D1/en not_active Expired - Fee Related
- 2002-09-16 EP EP02256376A patent/EP1401163B1/en not_active Expired - Lifetime
-
2003
- 2003-09-15 US US10/527,783 patent/US7839956B1/en not_active Expired - Fee Related
- 2003-09-15 AU AU2003273880A patent/AU2003273880A1/en not_active Abandoned
- 2003-09-15 KR KR1020057004360A patent/KR100978703B1/en active IP Right Grant
- 2003-09-15 WO PCT/EP2003/010245 patent/WO2004034661A1/en active Application Filing
Patent Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US6967992B1 (en) * | 1997-11-19 | 2005-11-22 | Interuniversitair Micro-Elektronica Centrum (Imec) | Method and apparatus for receiving GPS/GLONASS signals |
US6571090B1 (en) * | 1999-10-06 | 2003-05-27 | Fujitsu Limited | Radio receiver and diversity receiver |
Also Published As
Publication number | Publication date |
---|---|
ATE416544T1 (en) | 2008-12-15 |
EP1401163A1 (en) | 2004-03-24 |
US7839956B1 (en) | 2010-11-23 |
WO2004034661A1 (en) | 2004-04-22 |
KR100978703B1 (en) | 2010-08-30 |
KR20050057326A (en) | 2005-06-16 |
EP1401163B1 (en) | 2008-12-03 |
AU2003273880A1 (en) | 2004-05-04 |
DE60230141D1 (en) | 2009-01-15 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
US7180965B2 (en) | Phase estimation and compensation in orthogonal frequency division multiplex (OFDM) systems | |
EP1171983B1 (en) | Multicarrier receiver with channel estimator | |
KR100619460B1 (en) | Method and apparatus for signal reception, and medium | |
EP2611088B1 (en) | Digital communications receiver | |
US6628926B1 (en) | Method for automatic frequency control | |
US20090163143A1 (en) | Method for determining and compensating transceiver non-idealities | |
US8433007B2 (en) | Receiver and method for receiving digital signal | |
EP1875697B1 (en) | Initial parameter estimation in ofdm systems | |
US20100098146A1 (en) | Channel estimation method and device in wireless communication system | |
US20110211653A1 (en) | Device and Method for the Optimal Estimation of Distortion of a Transmission Medium, Comprising the Sequential Emission of Pairs of Quadrature Complementary Sequences | |
US20050180534A1 (en) | Iterative estimation and equalization of asymmetries between inphase and quadrature branches in multicarrier transmission systems | |
CN1595919B (en) | Method for compensating convey channel frequency shift and phase change according to time, and receiving unit | |
US20050286661A1 (en) | Symbol timing error detector that uses a channel profile of a digital receiver and a method of detecting a symbol timing error | |
US10461790B2 (en) | Method for compensation of phase noise effect on data transmission in radio channel | |
US7729434B2 (en) | System and method for improved channel estimation for wireless OFDM systems | |
US7839956B1 (en) | Method and apparatus for DC offset compensation in a digital communication system | |
US8804804B1 (en) | Estimation and compensation for carrier frequency offset and sampling clock offset in a communication system | |
US6731710B1 (en) | Method for rapid carrier frequency estimation in a communication system | |
US7106811B2 (en) | Wireless communication method and apparatus for performing post-detection constellation correction | |
US7864905B2 (en) | Interference alleviation equalizing apparatus of multi-carrier communication system and method thereof | |
EP0939502B1 (en) | Channel tracking in a mobile receiver | |
JP2986261B2 (en) | Adaptive maximum likelihood sequence estimator | |
US7302016B1 (en) | Phase estimator with bias correction | |
EP1205033B1 (en) | Estimating interference in a communication system | |
US6859507B2 (en) | Method and apparatus for correcting a signal |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
STCF | Information on status: patent grant |
Free format text: PATENTED CASE |
|
CC | Certificate of correction | ||
FPAY | Fee payment |
Year of fee payment: 4 |
|
MAFP | Maintenance fee payment |
Free format text: PAYMENT OF MAINTENANCE FEE, 8TH YEAR, LARGE ENTITY (ORIGINAL EVENT CODE: M1552) Year of fee payment: 8 |
|
FEPP | Fee payment procedure |
Free format text: MAINTENANCE FEE REMINDER MAILED (ORIGINAL EVENT CODE: REM.); ENTITY STATUS OF PATENT OWNER: LARGE ENTITY |
|
LAPS | Lapse for failure to pay maintenance fees |
Free format text: PATENT EXPIRED FOR FAILURE TO PAY MAINTENANCE FEES (ORIGINAL EVENT CODE: EXP.); ENTITY STATUS OF PATENT OWNER: LARGE ENTITY |
|
STCH | Information on status: patent discontinuation |
Free format text: PATENT EXPIRED DUE TO NONPAYMENT OF MAINTENANCE FEES UNDER 37 CFR 1.362 |
|
FP | Lapsed due to failure to pay maintenance fee |
Effective date: 20221123 |