CN108259399B - Time domain equalizer and control method thereof - Google Patents
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Abstract
The invention provides a time domain equalizer for eliminating an echo signal in a received signal. The received signal comprises an original signal and the echo signal. The time domain equalizer comprises a time delay amount estimator, an amplitude magnification ratio estimator and a phase offset estimator. The time delay estimator finds a delay amount that maximizes a cost function as an estimated delay amount of the echo signal relative to the original signal. The amplitude magnification estimator determines an estimated amplitude magnification of the echo signal relative to the original signal according to the estimated delay amount. The phase offset estimator determines an estimated phase offset of the echo signal relative to the original signal according to the estimated delay amount.
Description
Technical Field
The present invention relates to time domain equalizers, and more particularly to the manner in which parameters are determined in a time domain equalizer.
Background
Orthogonal Frequency Division Multiplexing (OFDM) technology has the advantages of high spectrum utilization rate and simple hardware architecture, and is widely used in communication systems in recent years. The ofdm signal is composed of a plurality of symbols (symbols). In order to avoid inter-symbol interference (ISI) caused by multipath (multipath), a guard interval (guard interval) is provided at the front end of each symbol. However, in a more complex communication environment, propagation delay exceeding the guard interval length may still occur, thereby causing intersymbol interference and resulting in a decrease in the overall performance of the system. This problem cannot be solved by the frequency domain equalization technique, but a time domain equalizer must be additionally provided before the frequency domain equalizer at the receiving end. The time domain equalizer is configured to effectively eliminate or reduce the interference of echo signals (echo signals) with respect to the original signal as much as possible by correctly estimating the arrival time delay, amplitude amplification and phase offset of each echo signal with respect to the original signal in the multiple propagation paths.
Disclosure of Invention
The invention provides a time domain equalizer and a control method thereof. By defining a proper cost function (cost function) as the evaluation basis, the time domain equalizer and the control method according to the present invention can estimate the time delay of an echo signal relative to the original signal. Further, based on the estimated delay amount, the amplitude magnification and phase shift of the echo signal relative to the original signal can also be determined.
According to an embodiment of the present invention, a time-domain equalizer is used for canceling an echo signal in a received signal. The received signal comprises an original signal and the echo signal. The time domain equalizer comprises a time delay amount estimator, an amplitude magnification ratio estimator and a phase offset estimator. The time delay estimator first finds a delay amount that maximizes a cost function as an estimated delay amount of the echo signal relative to the original signal. The amplitude magnification estimator determines an estimated amplitude magnification of the echo signal relative to the original signal according to the estimated delay amount. The phase offset estimator determines an estimated phase offset of the echo signal relative to the original signal according to the estimated delay amount. The cost function is:
wherein the symbol y represents the received signal, k represents a sampling index, and the signal y [ k + T]Representing a delayed signal, y, generated by the received signal after a time delay of length tau*[k+τ]Representing the conjugate of the delayed signal.
Another embodiment according to the present invention is a control method for a time-domain equalizer. The time domain equalizer is used for eliminating an echo signal in a received signal. The received signal comprises an original signal and the echo signal. First, a delay amount that maximizes a cost function is found as an estimated delay amount of the echo signal relative to the original signal. Based on the estimated delay amount, an estimated amplitude magnification and an estimated phase offset of the echo signal relative to the original signal are determined. The estimated delay, the estimated amplitude amplification and the estimated phase offset are then used to set a filtering condition to be applied by the time domain equalizer to the received signal. The cost function is:
wherein the symbol y represents the received signal, k represents a sampling indexSignal y [ k + T ]]Representing a delayed signal, y, generated by the received signal after a time delay of length tau*[k+τ]Representing the conjugate of the delayed signal.
Drawings
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below, wherein:
fig. 1 is a functional block diagram of a time-domain equalizer according to an embodiment of the present invention.
Fig. 2 is a flowchart of a time-domain equalizer control method according to an embodiment of the invention.
It is noted that the drawings of the present invention include functional block diagrams that represent various functional devices that can be associated with one another. These drawings are not detailed circuit diagrams, and the connecting lines are only used to indicate signal flows. The various interactions between functional elements and/or processes need not be through direct electrical connections. In addition, the functions of the individual elements do not have to be distributed as shown in the drawings, and the distributed blocks do not have to be implemented by distributed electronic elements.
The element numbers in the figures are illustrated as follows:
100: time domain equalizer 11: circuit for generating candidate delay amount
12: the time delay amount estimator 14: amplitude magnification estimator
16: phase offset estimator 18: filter with a filter element having a plurality of filter elements
S22-S26: procedure step
Detailed Description
In the signal model adopted in the present invention, the original signal sent by the transmitting end is represented as symbol x, and the received signal received by the receiving end is represented as symbol y. Without considering the symbol time offset (symbol timing offset) and the frequency offset (frequency offset), the received signal y after multiple propagation paths can be represented as follows:
wherein k represents a sampling indicator, and P represents the total number of echo signals caused by multiple propagation paths of the transmission channel from the transmitting end to the receiving end. As can be seen from equation one, the received signal y is the sum of the original signal x and the P echo signals. Symbol ap、θp,k、(Mp+Δp) Respectively representing the amplitude amplification factor, the phase offset and the arrival time delay of the P-th echo signal relative to the original signal x (P is a positive integer, and P is an integer index ranging from 1 to P). n [ k ]]Representing a noise signal. Amount of time delay of arrival (M)p+Δp) Comprising two components, the symbol MpThe approximate delay amount of the p-th echo signal is known to the receiving end by the inverse fast Fourier transform, but the fine delay amount ΔpAre difficult to measure.
According to equation one, the transfer function between the original signal x and the received signal y received at the receiving end can be defined as:
the design goal of the time-domain equalizer provided by the invention is to eliminate the echo signal in the signal y as much as possible, that is, the conversion function Z/X between the output signal Z of the time-domain equalizer and the original signal X is close to 1. Thus, it can be deduced that the ideal transfer function Z/Y should be:
correspondingly, the ideal output signal z of the time-domain equalizer is:
fig. 1 is a functional block diagram of a time-domain equalizer according to an embodiment of the present invention. The time domain equalizer 100 estimates the delay of the arrival time, the amplitude amplification factor and the phase offset of each echo signal with respect to the original signal x, and thus it becomes the basis for adjusting the received signal y. As shown in fig. 1, the time domain equalizer 100 includes a candidate delay amount generating circuit 11, a time delay amount estimator 12, an amplitude amplification factor estimator 14, a phase offset estimator 16, and a filter 18; the operation of each circuit is as follows.
For an echo signal, the time delay estimator 12 first finds an arrival time delay that maximizes a cost function (costfunction) as an estimated delay of the echo signal with respect to the original signal x
The cost function is:
where k represents a sample index, y k]Is the kth sample of the received signal y. The signal y [ k + T [ ]]Representative signal y [ k [ ]]A delayed signal, y, generated after a time delay of length tau*[k+τ]Then it represents the delayed signal y k + tau]The conjugate signal of (2). Delayed signal y [ k + T [ ]]From the signal y k by the time delay estimator 12]Generating; the delay amount τ is a variable that is controllable by the time delay amount estimator 12. The operation in equation five can be considered as calculating the signal y k]And its delayed signal y [ k + T]And accumulating the correlation results over a period of time. Theoretically, the closer the delay τ used by the time delay estimator 12 is to the actual delay of the echo signal, the more the signal y k]And its delayed signal y [ k + T]The higher the correlation, the larger the calculation result of equation five. In view of this, the time delay estimator 12 is designed to find the delay τ that maximizes the cost function C (τ) as the estimated delay of the echo signal with respect to the original signal x
The candidate delay amount generation circuit 11 can pre-select or determine a plurality of candidates in real timeThe delay amount and is supplied to the time delay amount estimator 12. As described above, the approximate delay amount M of the pth echo signalpIs known to the receiving end through the inverse fast fourier transform, but with a fine delay deltapAre difficult to measure. For each echo signal, the delay amount candidate generating circuit 11 can find the approximate delay amount and select the delay amount candidate from the range adjacent to the approximate delay amount. For example, assume that the proximity is known to be (M)p-τmin)～(Mp+τmax) And it is desirable to select ten candidate delay amounts tau0～τ9Then let the candidate delay amount τ0Is equal to (M)p-τmin) Let the candidate delay amount τ9Is equal to (M)p+τmax) And at the candidate delay amount tau0And τ9Interpolation between them to generate other eight candidate delay tau with equal interval from small to large1～τ8。
In practice, the time delay estimator 12 has many possibilities to find the delay τ that maximizes the cost function C (τ); the following examples are given by way of illustration only, and the scope of the present invention is not limited thereto.
In one embodiment, the time delay estimator 12 may estimate the candidate delay τ0～τ9Ten kinds of delayed signals of the received signal y are respectively generated, and ten cost function operation results C (tau) are generated according to the ten kinds of delayed signals and the received signal y0)～C(τ9). Subsequently, the result C (τ) is computed according to the cost function0)～(τ9) The time delay estimator 12 selects a candidate delay amount that produces a maximum cost function operation result as an estimated delay amount
For example, if C (τ)3) Operating on the result C (tau) for a cost function0)～C(τ9) The time delay estimator 12 can select the delay τ according to the operation result of the largest cost function3As an estimated delay amount
In another embodiment, a partial differential function C' (τ) generated by partially differentiating the cost function C (τ) with the delay τ as a partial derivative is provided in advance. The time delay amount estimator 12 substitutes a plurality of candidate delay amounts into the partial differential functions C '(τ), respectively, to generate a plurality of partial differential operation results, e.g., C' (τ)0)～C′(τ9). Subsequently, the time delay amount estimator 12 selects one of the candidate delay amounts that produces the partial differential operation result closest to zero as the estimated delay amount
In other words, if C' (τ)3) Is partial differential operation result C' (tau)0)～C′(τ9) The time delay estimator 12 selects the delay τ as a partial differential operation result of the nearest zero3As an estimated delay amount
In another embodiment, similarly, a partial differential function C' (τ) generated by partially differentiating the cost function C (τ) with the delay amount τ as a partial derivative is provided in advance. First, the time delay amount estimator 12 substitutes a plurality of candidate delay amounts into the cost function C (τ), respectively, to generate a plurality of cost function operation results, e.g., C (τ)0)～C(τ9). Subsequently, the result C (τ) is computed according to the cost function0)～C(τ9) The time delay estimator 12 selects a candidate delay amount that can generate a maximum cost function operation result as a preliminary estimated delay amount, and further calculates a more accurate estimated delay amount based on the preliminary estimated delay amount
(necessarily adjacent to the preliminary estimated delay amount). By a delay τ3The time delay estimator 12 will initially estimate the delay τ, which is selected as an example of the initial estimated delay3Substituting partial differential function C' (tau) to generate a first partial differential resultC′(τ3). Suppose a candidate delay amount τ0～τ9Are arranged from small to large in sequence. It can be understood that if the first partial differentiation result C' (τ) is obtained3) Above zero, the delay that maximizes the cost function C (τ) (i.e., the delay whose partial derivative is approximately zero) is likely to occur at the candidate delay τ3、τ4And the candidate delay amount τ4Corresponding partial differentiation result C' (τ)4) Possibly less than zero. In contrast, if the first partial differentiation result C' (τ)3) Less than zero, the delay that maximizes the cost function C (τ) (i.e., the delay whose partial derivative is approximately zero) is likely to occur at the candidate delay τ2、τ3And the candidate delay amount τ4Corresponding partial differentiation result C' (τ)4) Most likely greater than zero. Therefore, from the first partial differentiation result C' (τ)3) The time delay estimator 12 may derive a plurality of candidate delays τ0～τ9To select another reference delay amount. For example, if the first partial differentiation result C' (τ)3) To be greater than zero, the time delay estimator 12 may select the candidate delay τ4As another reference delay amount, and delaying the reference delay amount τ4Substituting the partial differential function C '(τ) to produce a second partial differential result C' (τ)4). Subsequently, the time delay amount estimator 12 may estimate the time delay amount based on the first partial differentiation result C' (τ)3) And a second partial differential result C' (τ)4) The interpolation produces a delay amount for making the partial differential result substantially zero as the estimated delay amount
In practical applications, the candidate delay amount does not necessarily correspond to the sampling index k of an integer, and may correspond to the sampling index k of 1.5 or k of 1.75, for example. More specifically, if a non-integer sampling index k is to be generated, the candidate delay amount used by the time delay amount estimator 12 can be generated by one-stage or multi-stage interpolation based on a plurality of delay amounts corresponding to the integer sampling index k. An example of generating candidate delay amounts by two-stage interpolation is presented below.
First, the first stage interpolation generates a plurality of preliminary interpolation results y (k + t)j). For example, using five initial delay amounts t0～t4The received signals y corresponding to each can be linearly combined to obtain five preliminary interpolation results y (k + t)j)：
Where j is an integer index ranging between 0 and 4;
as weight coefficients, each delay amount tjThe weighting coefficients are all different; mjIs a basic delay amount (and t)jIrrelevant).
Then, the second stage interpolation generates a plurality of second stage interpolation results y (k + τ)i). For example, using y (k + t) derived from equation sixj) May be interpolated again to produce eleven second stage interpolation results y (k + τ)i)：
Where i is an integer index ranging from 0 to 10,
as weight coefficients, each delay amount tjAll of the weighting coefficients are different.
Combining six and seven, the cost function C (tau) can be obtainedi) The deployment is as follows:
wherein,
from the eight and nine equations, the partial differential function C' (τ) can be derivedi)：
Wherein A isk,I、Ak,QCorresponding to the in-phase component and the quadrature-phase component of the signal, respectively. Practically, coefficient of
And
may be pre-calculated and stored in memory as reference data for use by the time delay amount estimator 12.
Generating an estimated delay amount for an echo signal at a time delay amount estimator 12
Then, the amplitude magnification estimator 14 estimates the delay amount based on the estimated delay amount
Determining an estimated amplitude magnification of the echo signal relative to the original signal x
In one embodiment, the amplitude magnification estimator 14 determines the estimated amplitude magnification according to the following operation:
wherein k ∈ GI represents the sampling result within a guard interval (guard interval) corresponding to the original signal x when calculating the estimated amplitude magnification,
representing the estimate produced by the time delay estimator 12The delay is measured and μ represents the length of the fast fourier transform applied to the received signal y by the receiving end to which the time domain equalizer 100 belongs. In practice, the numerical values in formula eleven
Which may have been generated by the time delay amount estimator 12 shortly before, may be provided directly to the amplitude magnification estimator 14 for use.
In addition, an estimated delay amount is generated for an echo signal at a time delay amount estimator 12
The phase offset estimator 16 then estimates the amount of delay based on the estimated amount of delay
Determining an estimated phase offset of the echo signal relative to the original signal x
In one embodiment, the phase offset estimator 16 finds the operation result
As the estimated phase offset
Actually, the operation result
Which has been generated by the time delay estimator 12 earlier and can be provided directly to the phase offset estimator 16 for use.
Finally, the filter 18 estimates the delay amount from each echo signal
Estimating amplitude magnification
And estimation phaseBit offset
To set the filtering condition to be applied to the received signal y. It should be noted how to estimate the delay amount based on each echo signal
Estimating amplitude magnification
And estimating the phase offset
It is known to those skilled in the art of the present invention to set appropriate filtering conditions to filter out these echo signals, and will not be described herein.
Those skilled in the art will appreciate that there are various circuit configurations and elements that can implement the candidate delay amount generating circuit 11, the time delay amount estimator 12, the amplitude magnification estimator 14, and the phase offset estimator 16, such as fixed and programmable logic circuits, e.g., programmable gate arrays, application specific integrated circuits, microcontrollers, microprocessors, digital signal processors, without departing from the spirit of the present invention. In addition, the estimators may be designed to perform their computational tasks by executing processor instructions stored in memory.
Another embodiment of the present invention is a control method for a time-domain equalizer, and a flowchart thereof is shown in fig. 2. The time domain equalizer is used for eliminating an echo signal in a received signal. The received signal comprises an original signal and the echo signal. First, in step S22, a delay amount that maximizes a cost function is found as an estimated delay amount of the echo signal relative to the original signal. In step S24, an estimated amplitude amplification and an estimated phase offset of the echo signal relative to the original signal are determined according to the estimated delay amount. Subsequently, in step S26, the estimated delay amount, the estimated amplitude multiplier and the estimated phase offset are used to set a filtering condition to be applied to the received signal by the time-domain equalizer. In step S22, the cost function is:
wherein the symbol y represents the received signal, k represents a sampling index, and the signal y [ k + T]Representing a delayed signal, y, generated by the received signal after a time delay of length tau*[k+τ]Representing the conjugate of the delayed signal.
It can be understood by those skilled in the art that various operation variations described in the introduction of the time-domain equalizer 100 can also be applied to the control method in fig. 2, and the details thereof are not repeated.
It should be noted that the mathematical expressions used herein are intended to explain the principles and logic associated with embodiments of the present invention and are not intended to limit the scope of the invention unless it is specifically indicated. Those skilled in the art will appreciate that there are many techniques for implementing the physical representations to which these equations correspond.
Although the present invention has been described with respect to the preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (8)
1. A time-domain equalizer for canceling an echo signal in a received signal, the received signal comprising an original signal and the echo signal, the time-domain equalizer comprising:
a time delay estimator for finding a delay amount by which a cost function is maximized as an estimated delay amount of the echo signal relative to the original signal;
an amplitude amplification factor estimator for determining an estimated amplitude amplification factor of the echo signal relative to the original signal according to the estimated delay amount; and
a phase offset estimator for determining an estimated phase offset of the echo signal relative to the original signal according to the estimated delay amount;
wherein the cost function is:
wherein the symbol y represents the received signal, k represents a sampling index, and the signal y [ k + T]Representing a delayed signal, y, generated by the received signal after a time delay of length tau*[k+τ]A conjugate signal representing the delayed signal;
the amplitude magnification estimator determines the estimated amplitude magnification according to the following operational formula:
wherein k ∈ GI represents the sampling results within a guard interval (guard interval) corresponding to the original signal,
represents the estimated delay amount generated by the time delay amount estimator, and mu represents the length of a fast Fourier transform;
the phase offset estimator finds out the operation result
As the estimated phase offset,
representing the estimated delay amount generated by the delay amount estimator.
2. The time domain equalizer of claim 1, wherein the delay estimator is configured to:
respectively substituting a plurality of candidate delay quantities into the cost function to generate a plurality of cost function operation results; and
according to the cost function operation results, a candidate delay amount capable of generating a maximum cost function operation result is selected as the estimated delay amount.
3. The time-domain equalizer of claim 1, wherein a partial differential function generated by partially differentiating the cost function with the delay τ as a partial derivative is provided in advance; the delay estimator is configured to:
respectively substituting a plurality of candidate delay quantities into the partial differential function to generate a plurality of partial differential operation results; and
based on the plurality of partial differential operation results, a candidate delay amount that can produce a partial differential operation result closest to zero is selected as the estimated delay amount.
4. The time-domain equalizer of claim 1, wherein a partial differential function generated by partially differentiating the cost function with the delay τ as a partial derivative is provided in advance; the delay estimator is configured to:
respectively substituting a plurality of candidate delay quantities into the cost function to generate a plurality of cost function operation results;
selecting a candidate delay amount capable of generating a maximum cost function operation result as a preliminary estimated delay amount according to the cost function operation results;
substituting the preliminary estimated delay amount into the partial differential function to generate a first partial differential result;
selecting a reference delay amount from the candidate delay amounts according to the sign of the first partial differential result;
substituting the reference delay amount into the partial differential function to generate a second partial differential result; and
the estimated delay amount is generated by interpolating according to the first partial differential result and the second partial differential result.
5. A control method applied to a time domain equalizer, the time domain equalizer is used for eliminating an echo signal in a received signal, the received signal comprises an original signal and the echo signal, the control method comprises:
(a) finding out a delay amount which can maximize a cost function as an estimated delay amount of the echo signal relative to the original signal;
(b) determining an estimated amplitude amplification factor and an estimated phase offset of the echo signal relative to the original signal according to the estimated delay amount; and
(c) setting a filtering condition to be applied to the received signal by the time domain equalizer according to the estimated delay amount, the estimated amplitude multiplying factor and the estimated phase offset;
wherein the cost function is:
wherein the symbol y represents the received signal, k represents a sampling index, and the signal y [ k + T]Representing a delayed signal, y, generated by the received signal after a time delay of length tau*[k+τ]A conjugate signal representing the delayed signal;
step (b) comprises determining the estimated amplitude magnification according to the following equation:
wherein k ∈ GI represents the sampling results within a guard interval (guard interval) corresponding to the original signal,
representing the estimated delay amount produced in step (a), μ representing the length of a fast fourier transform;
the step (b) comprises:
finding out operation result
As the estimated phase offset,
representing the estimated delay amount resulting from step (a).
6. The control method according to claim 5, wherein the step (a) includes:
respectively substituting a plurality of candidate delay quantities into the cost function to generate a plurality of cost function operation results; and
according to the cost function operation results, a candidate delay amount capable of generating a maximum cost function operation result is selected as the estimated delay amount.
7. The control method of claim 5, wherein a partial differential function generated by partially differentiating the cost function with the delay amount τ as a partial derivative is provided in advance, and the step (a) includes:
respectively substituting a plurality of candidate delay quantities into the partial differential function to generate a plurality of partial differential operation results; and
based on the plurality of partial differential operation results, a candidate delay amount that can produce a partial differential operation result closest to zero is selected as the estimated delay amount.
8. The control method of claim 5, wherein a partial differential function generated by partially differentiating the cost function with the delay amount τ as a partial derivative is provided in advance, and the step (a) includes:
respectively substituting a plurality of candidate delay quantities into the cost function to generate a plurality of cost function operation results;
selecting a candidate delay amount capable of generating a maximum cost function operation result as a preliminary estimated delay amount according to the cost function operation results;
substituting the preliminary estimated delay amount into the partial differential function to generate a first partial differential result;
selecting a reference delay amount from the candidate delay amounts according to the sign of the first partial differential result;
substituting the reference delay amount into the partial differential function to generate a second partial differential result; and
the estimated delay amount is generated by interpolating according to the first partial differential result and the second partial differential result.
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| WO2014076606A1 (en) * | 2012-11-15 | 2014-05-22 | Novelsat Ltd. | Echo cancellation in communication transceivers |
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