The present invention provides a system and method for estimating and reducing the effect of antenna coupling in on-frequency repeaters. In a preferred embodiment, an internal feedback path is used to estimate the coupling, by dithering a forward gain, and measuring a change in the power spectrum of a signal in the signal path in response to the dithering. The internal feedback path may also be used to compensate for the external coupling between antennas based on the estimated coupling, allowing the forward gain of the repeater to be increased if required. Thus, the present invention also provides an improved base station repeater.
An on-frequency repeater in accordance with embodiments of the invention is shown in
The block diagram shown in
The main components of the repeater as shown in
As known to those skilled in the art, additional components may be included in the repeater 10. For example, first and second image reject filters may be included and located, e.g., between the LNA 23 and the down-converting mixer 24, and between the up-converting mixer 28 and the power amplifier 29, respectively. A first duplexer 11 is often found between the antenna 21 and LNA 23. A circulator and a second duplexer may be located, e.g., between the PA 29 and the output antenna 22. Additional gain stages may be present at various locations within the RF path 280 and the IF path 240.
The input signal, e.g., the in-coming signal without the effects of feedback, is denoted by x(t). The Fourier transform of x(t) is denoted by X(ω). The output signal and its Fourier transform are denoted by y(t) and Y(ω), respectively. The input signal X(ω), although used in the following for modeling, usually cannot be directly measured because it is difficult to separate X(ω) from the output signal Y(ω) through the coupling path H. What can be measured usually is a signal v(t) within a signal path of the repeater, using measuring means 200, which may also measure the power spectrum of the signal v(t).
Within
The signal v(t), whose Fourier transform is denoted by V(ω), is a measurement made prior to the variable gain C. V(ω) includes the effect of the feedback coupling H, but does not include the direct effect of the variable gain C. The signal v(t) may be filtered by a linear filter operation whose frequency response is L{ω}. The external feedback coupling is modeled as
where an are complex coefficients, and Tn are loop delays. An estimate of the feedback coupling has the same form:
where bn are complex coefficients. In
In the following analysis, the IF filter 25 shown in
The transfer function of the repeater, using the measurement signal v(t), may be written as
The input signal X(ω) usually cannot be measured because the input antenna 21 sums both X(ω) and the coupled signal from the output antenna 22, H(ω)Y(ω). Statistical properties of the measured signal, v(t), may be used to estimate the feedback coupling H. In the present approach, the power spectrum of v(t) is used. The real and imaginary components of the forward gain are dithered to assist in the estimation and subsequent iterative search for the feedback coefficients, bn.
The power spectrum of the measured signal, Sv(ω), written as a function of the input power spectrum, Sx(ω), is
where ΔH=H−Hest and is referred to herein as the “residual feedback coupling.” The partial derivative of the measured power spectrum with respect to the real component of C is:
(Eq. 5) can be rewritten as
Using (Eq. 4), Sx(ω) can be removed from (Eq. 7), resulting in
The partial derivative with respect to the imaginary component of the gain is
From (Eq. 8) and (Eq. 10), it can be seen that dithering either the real or imaginary component of the forward gain, C, induces fractional changes in the measured power spectrum, Sv(ω), which is used later to obtain information regarding the antenna coupling H. Note that only one direction of the gain can be dithered at a given time. Adjusting both the real and imaginary components of C simultaneously will still only measure one dimension of the gain (at 45 degrees to the coordinate axes).
From (Eq. 8) and (Eq. 10), it can be seen that the real and imaginary components of ΔH(A)−1 are
respectively. The real and imaginary components of ΔH(A)−1 from (Eq. 11) and (Eq. 12) can be combined as a quantity M(ω):
From (Eq. 13), the estimate of the residual feedback coupling becomes
The estimate of the residual feedback coefficients, bn−an, is obtained by performing an inverse discrete Fourier transform on (Eq. 14) (the digital form is discussed later, see (Eq. 25)). Alternatively, an inverse fast Fourier transform (IFFT) can be applied to ΔH, which provides coefficient estimates for all delay taps.
There are various practical considerations when digitally implementing the system shown in
where N is the number of samples in the power spectrum, and Tsample is the temporal sampling interval of the signal v(t). To estimate the coefficients bn reliably, Δω must be smaller than 2π/Tn, preferably by some multiples. As a result, many samples are required when Tn<<Tsample. In such cases it is preferable that the sampling interval be reduced as much as the bandwidth of the input signal will allow without significant aliasing.
In digital form, the derivatives used in (Eq. 11) and (Eq. 12) are approximated by differences. For (Eq. 11), the power spectrum Sv is measured using two different forward gains, C1 and C2, where
C
1
=C
0−0.5·ΔRe{C}, (Eq. 16)
and
C
2
=C
0+0.5·ΔRe{C}. (Eq. 17)
The digital form of (Eq. 11) becomes
and λreg is a small positive constant. The ε2−1 and ε2+1 terms are included to reduce the effects of changes in the power spectrum Sv resulting from input signal variations rather than variations in the feedback coupling. Similarly for (Eq. 12), the power spectrum Sv is measured using two different forward gains, C3 and C4, where
C
3
=C
0−0.5·ΔIm{C}, (Eq. 21)
and
C
4
=C
0+0.5·ΔIm{C}. (Eq. 22)
The difference approximation for (Eq. 12) becomes
In general, the use of (Eq. 18) and (Eq. 23) tends to underestimate the magnitude of the residual coefficients (bn−an); however, this is compensated by the iterative process, discussed below, which forces |bn−an| to converge to zero after some iterations.
Within the iterative process, the update of the coefficient bn is
b
n(ti+1)=bn(ti)+γ·Δbn (Eq. 24)
where γ is a convergence constant and Δbn is the estimate of the residual coupling for the coefficient associated with loop delay Tn. The estimate of the residual coupling is
which is the inverse discrete Fourier transform of ΔH(ωk) for delay Tn. If the dominant delay taps in (Eq. 1) are known, only those coefficients need to be computed. For an unknown delay spread, all N delay taps are computed using an inverse FFT of ΔH(ωk), after which the dominant delay taps are selected.
Consider the case where the signal v(t) is filtered after being extracted from the forward signal path, as shown in
S
L{v}(ωk)=|L(ωk)|2·Sv(ωk). (Eq. 26)
Since (Eq. 18) and (Eq. 23) are the ratios of the difference and sum of two power spectra, the filtering |L(ωk)|2 does not affect the estimate of M directly, as long as the same filter is applied to both each pair of spectra (Sv(1) and Sv(2), or Sv(3) and Sv(4)). The filtering affects the relative influence of ε2−1, ε2+1, ε4−3, and ε4+3 in the estimation of M(εk): they become more significant at frequencies where the attenuation of |L(εk)| is higher. Filtering becomes useful when small offsets are added to the denominators of (Eq. 18) and (Eq. 23), which allows noisy portions of the spectrum to be discounted.
Shorter segments of data can be integrated to obtain the estimate of M(εk):
Integrating shorter sequences allows the real or imaginary parts of the variable gain, C, to be ramped up and down in smaller increments that will not affect significantly the bit error rate at the receiver of the base station or the mobile. It also makes the estimation less sensitive to dynamics in the signal statistics.
By using smaller increments in either |ΔRe{C}| or |ΔIm{C}|, the difference between neighboring spectra due to the feedback is reduced. Thus, large differences are due in part to variations in the waveform statistics. Measurements originating from such spectral pairs are removed from (Eq. 27) and (Eq. 28).
The above-mentioned approach assumes that the statistics of the input signal x(t) remains constant between two neighboring measurements of the power spectrum. This assumption of constant input signal statistics can be verified if the minimum delay through the repeater, Tmin, is known. Variations in Δbn wherein Tn<Tmin indicate changes in the input statistics over the dithering interval and that the estimate of M is corrupted. However, it is more useful to identify changes between pairs of the measurements before adding them to (Eq. 27) and (Eq. 28). Let the auto-correlation be denoted by ρt(
The delay through the repeater is usually dominated by the insertion delay of the IF filter 25. As a result, the insertion delay of the IF filter 25 may be used as a conservative lower bound on the minimum delay, Tmin, when determining if pairs of measurements should be excluded from (Eq. 27) and (Eq. 28) as outliers.
A simulation of the approach has been performed. The sampling rate of the digital signals is 65 MHz. The number of the frequency samples used in the power spectrum measurements is 4096, which provides a frequency resolution of about 15.9 kHz. The input signal, x(t), is a random noise band-limited to 15 MHz. It is intended to simulate three 5 MHz Wideband CDMA (WCDMA) carriers of equal power. The signal is filtered further to simulate multipath fading from the base station to the repeater. The three multipath delays are 0.23 μs, 0.28 μs, and 0.6 μs, respectively. The auto-correlation of the input signal, including multipath, is shown in
In the simulation, the dominant delay taps are [T1 T2 T3 T4]=[74 75 90 91], and the respective coefficients are [a1 a2 a3 a4]=[j0.01 j0.01 0.015 0.015]. The nominal forward gain, C0, is set to 10 (with G0=1). The real component of the variable gain, Re{C}, is swept from 0.85 C0 to 1.15 C0 and back to 0.85 C0 in increments of 0.0375 C0. The imaginary component, Im{C}, is swept from (1−j0.15) C0 to (1+j0.15) and back in increments of j 0.0375 C0. The measurement, M(ωk), obtained using (Eq. 27) and (Eq. 28), is shown in
The frequency response of the residual feedback, ΔH(ω), is computed from M(ω) using (Eq. 14), where G0C=C0. The residual coupling is computed using (Eq. 25) for Tn=0 to 4095 (using the IFFT function). The residual coupling is shown in
It is interesting to compare the auto-correlation of the input signal with multipath fading (see
The above example shows the estimate of the residual feedback coefficients for the first iteration. With this estimate, the model of the feedback, Hest, is formed. Initially, all of the coefficients of Hest are set to zero. The estimate of the residual coefficients is used in (Eq. 24) to update the model; however, only the dominant delay taps are updated to reduce the effects of input signal spectrum variation. In subsequent iterations, new dominant delay taps may be identified. In such cases, the dominant delay taps identified in the first and subsequent iterations are updated. However, as the iterative process converges, the estimated residual feedback decreases due to the compensation provided by Hest, reducing the probability to finding new dominant delay taps.
The update process, as described above, can only increase the number of dominant modes. However, to reduce the computational burden on the DSP, it is desirable to limit the number of dominant delay taps. If the number of dominant delay taps becomes larger than desired, the coefficient bn with the smallest magnitude may be removed from the model Hest (which effectively sets the coefficient to zero).
The flow of the algorithm is shown in
The computation of the real component of M(ωk) in step 70 is shown in detail in
In the exemplary case shown in
If the value of C has reached its upper limit as judged in step 85, a negative, −|ΔRe{C}|, is set in step 86 for the next change of C. If, on the other hand, C has reached its lower limit as judged in step 87, the value of Re{M(ωk)} is obtained using ΣA/ΣB. Otherwise, Sv(1) is given the value of Sv(2) in step 89, and steps 81-84 are repeated.
The computation of the imaginary component of M(ωk) (not shown) is substantially the same as the real component, except that Im{C} is ramped up and down instead of Re{C}. The average values of C should be C0, as in the case of the real component computation.
Some other embodiments of the invention are shown in
In
It will be appreciated by those skilled in the art that the foregoing embodiments are purely illustrative and not limiting in nature. A variety of modifications are possible while remaining within the scope of the present invention.
The present invention has been described in relation to a presently preferred embodiment, however, it will be appreciated by those skilled in the art that a variety of modifications, too numerous to describe, may be made while remaining within the scope of the present invention. Accordingly, the above detailed description should be viewed as illustrative only and not limiting in nature.
The present application claims priority under 35 USC section 119(e) to provisional application Ser. No. 60/793,873 filed on Apr. 21, 2006, the disclosure of which is incorporated herein by reference in its entirety.
Number | Date | Country | |
---|---|---|---|
60793873 | Apr 2006 | US |