WO2009059390A1

WO2009059390A1 - Method and system for digitally correcting sampling effects

Info

Publication number: WO2009059390A1
Application number: PCT/CA2007/001992
Authority: WO
Inventors: René JANICEK; Jean-Pierre Baudens; Jonathan Labs
Original assignee: Wavesat Inc.
Priority date: 2007-11-06
Filing date: 2007-11-06
Publication date: 2009-05-14

Abstract

The present invention relates to a method and a system for digitally correcting sampling offset of a signal. The method proceeds with measuring a sampling offset, and introducing a phase correction corresponding to the measured sampling offset on symbols of the signal. The system includes a receiving unit for receiving the signal, and a measuring unit for measuring the sampling offset. The system also includes a correction module for introducing a phase correction corresponding to the measured sampling offset on samples of the signal.

Description

METHOD AND SYSTEM FOR DIGITALLY CORRECTING SAMPLING

EFFECTS

FIELD OF THE INVENTION

The present invention relates to a method and system for correcting sampling effects, and more particularly to a method and system for digitally correcting sampling effects caused by free running oscillators.

BACKGROUND OF THE INVENTION

In today's wireless networks, subscriber stations communicate with base stations, which enable them to access various types of networks. The signals between the subscriber stations and the base stations are exchanged over the air. The signals contain data that has first been digitalized, if not already in that format. Afterwards, depending on the type of modulation and protocol used by the subscriber stations and base stations, the data has been encoded, and mixed with a carrier wave. Upon receipt of the signal, the recipient (either one of the subscriber stations or base stations) removes the carrier wave, demodulates the signal, and attempts to revert it to its original format.

Multiple factors may hinder the quality of the exchange of signals between the subscriber stations and base stations. One such factor is intrinsic to the design of the subscriber stations and base stations: frequency offset. Both subscriber stations and base stations rely on a local oscillator for sampling the data and generating the carrier wave. To obtain the best quality of signal between the subscriber station and the base station, it is necessary that their respective local oscillators be in synchronicity, i.e. at a same frequency, and in phase. However, as each subscriber station and each base station is equipped with its own oscillator, and typically the subscriber station may communicate with hundreds of base stations, while the base station may communicate with thousands of subscriber stations, it is necessary to provide a mechanism in the subscriber station to alleviate frequency offset. Such mechanism is rendered even more essential as prices for good oscillators, and varying oscillators, such as Voltage Controlled Temperature Controlled Oscillators (VCTCXO), is quite high, and causes a strong impact on an ultimate design cost of the subscriber station. Thus in order to remain competitive, manufacturers of subscriber stations and wireless communication chips need a mechanism to overcome frequency offset that does not rely on using VCTCXOs.

Furthermore, as in many designs the same local oscillator is used for generating the carrier wave, and for digitizing the data, a frequency offset between communicating subscriber station and base station may further cause a sampling offset. The effects of sampling offset may result in important degradation of the data, and thus needs to be addressed.

Some standards, such as IEEE 802.16, recognize the importance of limited sampling offset between communicating subscriber station and base station, and define a required accuracy sampling rate. More specifically for IEEE 802.16, the required accuracy has been defined at 5ppm, which for a sampling rate of 40MHz, means that the local oscillators of the communicating subscriber station and base station needs to be within ± 200 Hz. Such required accuracy creates an added burden on subscriber station manufacturers and wireless communication chips manufacturers.

There is therefore a need for a method and a system for digitally correcting sampling effects with a relatively high accuracy.

SUMMARY OF THE INVENTION The present invention provides a method and system for correcting the effects of sampling offset of a signal. More particularly, the present invention describes a method and a system for digitally correcting the sampling offset with relatively high accuracy.

For doing so, an aspect of the present invention relates to a method for digitally correcting sampling offset of a signal, that includes steps of measuring a frequency offset and introducing a phase correction corresponding to the measured frequency offset on symbols of the signal.

In another aspect, the present invention is directed to a system for digitally correcting sampling offset of a signal. The system includes a receiving unit, a measuring unit and a correction module. The receiving unit is adapted for receiving the signal. Then the measuring unit measures the sampling offset, and the correction module introduces a phase correction corresponding to the measured sampling offset on symbols of the signal.

BRIEF DESCRIPTION OF THE DRAWINGS

In the following description, the following drawings are used to describe and exemplify the present invention in which like references denote like parts:

Figure 1a is a flowchart of a method for digitally correcting sampling effects in a transmitter in accordance with an aspect of the present invention; Figure 1b is a flowchart of a method for digitally correcting sampling effects in a receiver in accordance with an aspect of the present invention;

Figure 2 is a schematic block diagram of a system for digitally correcting sampling effects in accordance with an aspect of the invention;

Figure 3 is a schematic block diagram of a transceiver for digitally correcting sampling effects with yet another embodiment of the present invention;

Figure 4a is a graphical representation of a simulation demonstrating the effects of sampling offset of an OFDM signal;

Figure 4b is a graphical representation of signal to noise ratio of the simulation of Figure 4a; Figure 5 is a graphical representation of a simulation demonstrating the effects of another sampling offset of the OFDM signal;

Figure 6 is a graphical representation of a correction performed on the signal of Figure 4a by a subscriber station; - A -

Figure 7 is a graphical representation of a signal to noise ratio measured by a base station upon receipt of the signal of Figure 6;

Figure 8 is a graphical representation of another simulation demonstrating the effects of sampling offset; Figure 9a is a graphical representation of a variable slope used to digitally correct the sampling offsets; and

Figure 9b is a graphical representation of another variable slope used to digitally correct sampling offsets.

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to a method and system for digitally correcting sampling offsets. As specifications set for sampling offsets in standards like IEEE 802.16 are relatively low, it is very important to precisely measure the sampling offset present between a base station and a communicating subscriber station. To remedy the situation, the present invention provides in a first aspect a method and a system in the subscriber station that measures the frequency offset, then derives there from the sampling offset with a communicating base station, and which introduces a phase correction on symbols of the signal to be transmitted to the base station. The introduced phase correction is composed of a constant phase correction and a phase slope correction. In a general manner, the constant phase correction and the phase slope correction are initialized at the beginning of a new symbol, and incremented with each sample of the symbol. In another aspect, the present invention provides a method and a system for correcting sampling offsets of received signals in the subscriber station.

Reference is now made to Figure 1a, which depicts a flowchart of a method for digitally correcting sampling effects in a transmitter in accordance with an aspect of the present invention. The method 100 starts with a step of receiving a signal from the base station, in step 110. Then the method continues with deriving or measuring a sampling offset in step 120. Alternatively, and without departing from the present invention, the sampling offset could be derived or measured at period instant, and instead of every time a signal to be transmitted is received. In the context of the present invention, both measurement and derivation of the sampling offset are contemplated as alternate methods of obtaining a value for the sampling offset. For simplification however, throughout the following Description, reference will be made to measuring the sampling offset, but such measuring should be understood as directly measuring the sampling offset, or indirectly deriving the sampling offset. Various methods exist in the art to measure the sampling offset in step 120. One such method consists of measuring a phase of pilot tones of the OFDM symbols. Given equally spaced pilot tones, a linear phase slope can be measured throughout one symbol. Another method for measuring the sampling offset consists of using a least squares fit. In the particular case of IEEE 802.16, a requirement on the use of a local oscillator at a base station and for both an Intermediate Frequency (IF) and a sampling clock however facilitates the measuring of the sampling offset when the same requirement is imposed on the subscriber station, as demonstrated in the following equation:

f ooffff -- J f±sooffff

where: f_Off is a total frequency offset between the base station and the subscriber station; fsoff is the sampling offset; fRF is the radio frequency; and f_s is the sampling rate. Another method that can be used to measure the sampling offset of step 120, consists of measuring the frequency offset with a Digitally Automatic Frequency Control (DAFC) and deriving there from the sampling offset. The DAFC will provide values of an integer frequency offset (IFO) and a fractional frequency offset (FFO), provided by two different PHY algorithms. The following equation can then be used: f_off = - \mean{FF0 + 2 - π - IFO)

To reduce error estimation, the DAFC may average the measurements obtained from a preamble of the signal over 128 frames.

Thus in the context of standards such as IEEE 802.16, which include a requirement on the use of one oscillator for the sampling clock and the IF, a sampling offset will manifest itself as a frequency offset. However, the present invention is not limited to such standards, though the measuring of the sampling offset is greatly facilitated in standards including such a requirement.

The method then pursues with the determination of a required phase correction in step 122, and continues with the application of a phase correction in step 124, corresponding to the measured sampling offset, on symbols of the signal. In a preferred manner, the phase correction is introduced in a frequency domain, and for example just before the Inverse Discrete Fourier Transform module. Such introduction is mathematically represented as follows: y_k - x_k - e-"^> - e-*^«~^> Where: k = -( ^subcamers | J l^earn^ers I _ ]

Xk is an I/Q modulation of subcarrier k;

Nsubcarπers is a total number of subcarriers in the OFDM symbol including guard subcarriers; ψj is the constant phase correction for the OFDM symbol j; and qpsiopej is the phase slope correction in frequency for the OFDM symbol. The application of the phase correction is performed in steps 130-170. The phase correction comprises a constant phase correction and a phase slope correction. The constant phase correction and the phase slope correction are initialized to zero at a beginning of each frame of the signal, and subsequently incremented for each subsequent OFDM symbol. For doing so, the method, in step 130, verifies whether the OFDM symbol to be corrected is the beginning of a new frame. When the OFDM symbol does not correspond to the beginning of a new frame, the method continues in step 140, where verification is made on the value of the measured sampling offset. If the value of the measured sampling offset is smaller than Vz the duration of a sample, the method continues with incrementing the constant phase correction and the phase slope correction in step 150 in the following manner.

The constant phase correction φ j+i is calculated using the following equation:

, (1 + CP)

where: f_son is the sampling offset; f_s is the sampling rate f_Off is the measured frequency offset; CP is a fractional size of a cyclic prefix of the signal; and fRF is a measured radio frequency for the signal measured in GHz.

The phase slope correction φ _siopej+i is calculated on a frame by frame basis, for one symbol, using the following equation: Ψ slope.] +1 = Ψslope.j ⁺ Φ slope ^₁ • where:

_Φ^_mc, = ~AJ^CP)f and where: Δf is a subcarrier spacing of the signal, expressed in GHz. As a sampling offset will cause a small intrinsic frequency offset in standards with a requirement on oscillator such as IEEE 802.16, a second order effect in the phase correction may be corrected using instead the following equation:

T slope, j+l ~ T slope, j τ slope_mc] τ slope_mc2 where:

- 1 φ*_* Ψ^emc2 = Ψslc Ψ, ^eιnc\ 32 -π -f, RΓ

In the event that the sampling offset value is greater than Vz the duration of a sample as verified in step 140, the method then continues with a step 160 of adapting the symbol and modifying accordingly the phase slope correction. In the case of larger sampling offsets, the adding or dropping of a sample is necessary to allow proper demodulating of the signal. For doing so, a sample is added or dropped in the time domain. In a preferred manner, the adding or dropping of a sample is done where a cyclic prefix is pre-pended to the symbol. Thus, instead of adding the number of redundant cyclic prefix sample, i.e. N_cp copied from the last samples of the OFDM symbol, only N_cp-i are pre-pended when a sample needs to be dropped. Alternatively, when a sample needs to be added, an extra zero is inserted before the cyclic prefix. In the instance that adapting requires inserting a sample, the latter is performed in the time domain, and the phase slope correction is modified using the following equation:

2π τ slope,j+l T slope, j τ slope_ιnc\ T slope _ιn ^! _ι ^c2 /V

Similarly, in the instance where the adapting consists of dropping one sample, the phase slope correction is then modified using the following equation:

x r

In the circumstance where adding or dropping of a sample is required during a silent part of the frame, it is also possible to adjust a starting point of a following data burst. However, in such a case, special care should be given to the signs of the different variables, as they directly carry the information on which direction the sampling offset is going.

Returning now to Figure 1a, when the step of determining whether the symbol is the beginning of a new frame, the method proceeds with step 170 of reinitializing the constant phase correction and the phase slope correction. The method of Figure 1a can proceed with the correction of the sample offset on a symbol-by-symbol basis, or in a frame-by-frame basis for each symbol. Reference is now made to Figure 1b, which depicts a method 180 for digitally correcting sampling effects in a receiver in accordance with an aspect of the present invention. In the case of the receiver in the subscriber station, the digital correction of the sampling offset is simpler, as some modules already handle phase correction. However, to provide quality results, it is necessary to verify whether the sampling offset value is greater than ^ΛA the duration of a sample, and to add or drop a sample when necessary. The method 180 thus starts in step 110 by receiving the signal, and step 120 of measuring the sampling offset. Any method, as previously described, can be used to perform such measurement. The method then determines the phase correction in step 122, and applying phase correction in step 124. The method then continues with step 140 of verifying whether the value of the sampling offset is greater than ^ΛA the duration of a sample. In the case where the sampling offset value is greater than Vz sample duration, the method moves to step 160 and adapts the symbol by adding or dropping a sample, as needed and in a manner similar to previously discussed. In the case where the sampling offset value is smaller than 14 the duration of a sample, the method proceeds with receiving the next symbol of the signal.

Reference is now made to Figure 2, which depicts a schematic block diagram of a system for digitally correcting sampling effects in accordance with an aspect of the invention. The system 200 may be incorporated within a transmitter, a receiver, or a transceiver. The system 200 includes a receiving unit 210, a measuring unit 220, a correction module 230 and an adaptation module 240. Each of these components may be independently incorporated within a transmitter, a receiver, or a transceiver. Alternatively, the receiving unit 210, the measuring unit 220, the correction module 230 and the adaptation module 240 may consist of additional functionalities to existing components of the transmitter, receiver or transceiver. The receiving unit 210, measuring unit 220, the correction module 230 and the adaptation module 240 may independently or concurrently be hard coded or consist of software.

The receiving unit 210 is adapted for receiving the signal 205. The received signal is sent directly or ultimately to the measuring unit 220. The measuring unit 220 is adapted for measuring the sampling offset present in the signal. The sampling offset may be measured using any of the previously described methods. When the sampling offset has been measured, the signal is provided to the correction module 230, which is adapted for introducing a phase correction corresponding to the measured sampling offset on symbols of the signal. As mentioned before, the phase correction includes a constant phase correction and a phase slope correction. The constant phase correction and phase slope correction are calculated by methods and equations as previously described. The correction module 230 is further adapted to initialize the constant phase correction and the phase slope correction at a preamble of each frame of the signal, and subsequently increment those values for each symbol. Finally, the adaptation module is adapted for determining whether the measured sampling offset is greater than half the duration of a sample. In the case where the sampling offset is greater than half the duration of a sample, the adaptation module 240 adds or drops a sample, and when implemented in a transmitter, further modifies the phase slope correction.

Reference is now made to Figure 3, which represents a schematic block diagram of a transceiver for digitally correcting sampling effects in accordance with another embodiment of the present invention. The transceiver 300 is composed of a transmitter path (Tx Path) 305 and a receiver path (Rx Path) 310. The transmitter path 305 and the receiver path 310 both use Media Access Control (MAC) 315 and an oscillator 320. In addition, the transmitter path 305 further includes a Forward Error Controller (FEC) 325, a mapper 330, a Digital Automatic Phase Control (DAPC) 335, an Inverse Fast Fourier Transform (IFFT) 340, a Cyclic Prefix (CP) insertion module 345, a Digital Automatic Frequency Control (DAFC) 350, a digital Intermediate Frequency (IF) module 355 and a Digital-to-Analog Converter (DAC) 360. In this implementation of the transmitter, the MAC 315 is performing the tasks of the receiving unit 310. The DAPC 335 performs the measuring of the sampling offset, and the tasks of the correction module, while the adaptation module is taken over by the CP insertion 345. The receiver path 310 includes an ADC 410, a Digital IF 405, a DAFC 400, a synchronizer 395, a frequency offset unit 390, a Discrete Fourier Transform DFT) 385, an equalizer 380, a phase corrector module 375, a demapper 370 and a FEC 365. In the receiver path 310, the receiving of the signal is performed by the ADC 410. Then, the measuring of the sampling offset is handled by the frequency offset unit 390 and the phase corrector 375, while the correction of the sampling offset is taken over by the phase corrector 375, and the adaptation task is performed by the frequency offset unit 390, along with the phase corrector 375.

Although many additional components have been shown and depicted in Figure 3, such components are not essential for the present invention, and are only representative of components generally found in OFDM transceivers.

Reference is now made concurrently to Figure 4a and Figure 4b, which respectively show a graphical representation of a simulation demonstrating the effects of sampling offset of an OFDM signal, and a graphical representation of signal to noise ratio of the simulation of Figure 4a. This simulation has been performed using a bandwidth of 7 MHz, a cyclic prefix of ¹/4, a sampling offset of 400 Hz, and a FFT size of 256. The three graphs shown on Figure 4a demonstrate the response of a base station, when no correction is performed by the transmitter of the subscriber station. As can be seen, from symbol 390, the transmission is off by 1 sample. This sampling offset causes a severe signal to noise ratio, as depicted on Figure 4b. Such results are not desirable, and thus demonstrate the importance of correcting the sampling offset at the transmitter of the subscriber station, prior to sending to the base station.

Reference is now made to Figure 5, which is a graphical representation of a simulation demonstrating the effects of another sampling offset of the OFDM signal. For this simulation, a bandwidth of 7 MHz was used, with a cyclic prefix of %, and a sampling offset of 800Hz. The three graphs depicted on

Figure 5 demonstrate the response of the base station, when a correction of a

1^st order is applied to the signal by the transmitter of the subscriber station. Using only the 1^st order correction, a small residual frequency offset still remains, as well as a residual phase slope.

Reference is now made to Figure 6, which is a graphical representation of a simulation of a correction performed on the signal of Figure 5, but with a 2^nd order correction. As can be seen on the 3 graphs, the 2^nd order correction allows a quasi flat phase slope, thus confirming that the 2^nd order correction aligns the sampling clock of the subscriber station to the sampling clock of the base station, and provides signals within the required threshold of standards such as IEEE 802.16.

Reference is now made to Figure 7, which is a graphical representation of a signal to noise ratio measured by a base station upon receipt of the signal of

Figure 6. As can be appreciated, the correction applied by the system of the present invention has allowed, even in the presence of a sampling offset between the oscillators of the subscriber station and the base station, to correct the signal prior to its transmission to the base station, and thus produce a signal with very good signal to noise ratio.

Reference is made to Figure 8, which is a graphical representation of another simulation demonstrating the effects of sampling offset. For this simulation, a bandwidth of 7MHz was used, with a cyclic prefix of %, and a sampling offset of -800Hz. In this simulation, the 2^nd order correction was used by the system of the present invention on the transmitter path of the subscriber station, and an extra sample was added in the data flow. Reference is now made concurrently to Figures 9a and 9b, which respectively show a graphical representation of the constant phase correction for compensating a sampling offset of 800Hz and -800Hz. Both simulations were performed for a bandwidth of 7MHz, and a cyclic prefix of %. The present invention has been described by way of preferred embodiments. It should be clear to those skilled in the art that the described preferred embodiments are for exemplary purposes only, and should not be interpreted to limit the scope of the present invention. The method and system as described in the description of preferred embodiments can be modified without departing from the scope of the present invention. The scope of the present invention should be defined by reference to the appended claims, which clearly delimit the protection sought.

Claims

CLAIMS:

1. Method for digitally correcting sampling offset of a signal, the method comprising steps of: a) measuring a sampling offset; and b) introducing a phase correction corresponding to the measured sampling offset on samples of the signal.

2. The method of claim 1 , wherein the phase correction corresponding to the measured sampling offset comprises a constant phase correction and a phase slope correction.

3. The method of claim 2, wherein the constant phase correction and the phase slope correction are initialized to zero at a preamble symbol of each frame of the signal, and subsequently incremented for each symbol.

4. The method of claim 3, wherein a sampling clock used to generate the signal and an oscillator for receiving the signal are derived from a same reference.

5. The method of claim 4, wherein the sampling offset f_son is derived from the following equation:

f ooffff -- J f isooffff

where: f_Off corresponds to a total frequency offset; fsoff corresponds to the sampling offset; fRF is the radio frequency of the signal; and fs is a sampling rate.

6. The method of claim 5, wherein the constant phase correction φ ,+i is calculated using:

, (1 + Cf)

*'^♦' ^{= φJ ~ s}« J-ϊ^ where: f_Off is the measured frequency offset;

CP is a fractional size of a cyclic prefix of the signal; and f_RF is a measured radio frequency for the signal measured in GHz.

7. The method of claim 5, wherein the phase slope correction φ _siope,j+i is calculated on a symbol basis using:

T slope, j+\ ~ T slope, j Ψ slope _Incι ' where:

J S and where: fsoff corresponds to the measured sampling offset;

CP is a fractional size of a cyclic prefix of the signal;

Δf is a subcarrier spacing of the signal, expressed in GHz; and f_s is the sampling frequency

8. The method of claim 5, wherein the phase slope correction is calculated on a symbol basis using:

T slope, j +1 ~ T slope, j T slope _mc\ ~ Ψ slope _mc2 where: - 1

Ψ slope _mc2 ~ Ψ slope _mc] γ^ - Jf f

and where: f_RF is a known RF frequency in GHz.

9. The method of claim 1 , wherein the frequency offset f_Off equals:

f_off = - 1 ^• mean(FF0 + 2 -π - IFO)

where:

FFO corresponds to a measured fractional frequency offset;

IFO corresponds to an integer frequency offset; and wherein the FFO and IFO are provided by two different PHY algorithms.

10. The method of claim 3 further comprising steps for: evaluating a sampling offset greater in length than half the duration of a sample; and adapting the symbol and modifying the phase slope correction.

11. A system for digitally correcting sampling offset of a signal, the system comprising: a) a receiving unit for receiving the signal; b) a measuring unit for measuring the sampling offset; and c) a correction module for introducing a phase correction corresponding to the measured sampling offset on symbols of the signal.

12. The system of claim 10, wherein the phase correction corresponding to the measured sampling offset comprises a constant phase correction and a phase slope correction.

13. The system of claim 11 , wherein the correction module initializes the constant phase correction and the phase slope correction at a preamble of each frame of the signal, and subsequently incremented for each symbol in the frame.

14. The system of claim 12, wherein the constant phase correction φ _J+i is calculated using:

. (I + CP) φ"^ι ~ ^φ' - ^f" U - IO- *² where: f_Off is the measured frequency offset; CP is a fractional size of a cyclic prefix of the signal; and f_RF is a known radio frequency for the signal in GHz.

15. The system of claim 13, wherein the phase slope correction φ _siope,j+i is calculated on a symbol basis using:

T slope, j +l i slope, j ' ^slope_ιnc\ ' where:

J ? and where: fsoff corresponds to the measured frequency offset; CP is a fractional size of a cyclic prefix of the signal;

Δf is a subcarrier spacing of the signal, expressed in GHz; and fRF is a known radio frequency in GHz.

16. The system of claim 14, wherein the phase slope correction is calculated on a symbol basis using:

_ιnc\ ~ T slope _mc2 where:

- 1

Ψτlope_mc2 ~ Ψϊlope_mc] -_jo . _ . f

3Δ Jl J _RF and where: f_RF is a known frequency in GHz.

17. The system of claim 10, wherein the measuring unit derives the sampling offset f_son using the following equation:

J off - Jsoff

where: f_Off corresponds to a total frequency offset; f_sof_f corresponds to the sampling offset; f_RF is the radio frequency of the signal; and f_s is a sampling rate.

18. The system of claim 10, wherein the measuring unit calculates the frequency offset f_Oft using the following equation:

f_off = - 1 ^• mean{FFO + 2 -π - IFO)

where:

FFO corresponds to a measured fractional frequency offset;

19. The system of claim 12 further comprising an adaptation module for determining whether the measured sampling offset is greater than half the duration of a sample, and if so, adapting the symbol and modifying the phase slope correction.