OFDM SIGNAL AND NOISE ESTIMATION

Abstract

A signal estimator for an OFDM radio receiver is configured to generate a signal power estimate for a reference signal received on a subcarrier from a plurality of OFDM subcarriers. The signal estimator generates a first channel estimate as a first function of a first set of one or more unfiltered reference-signal channel estimates, where the first set includes an unfiltered reference-signal channel estimate. It generates a second channel estimate as a second function of a second set of one or more unfiltered reference-signal channel estimates, where the second set has no unfiltered reference-signal channel estimate in common with the first set. The signal estimator then generates the signal power estimate by multiplying the first channel estimate with the second channel estimate, such that the generated signal power estimate does not increase with the absolute square of any of the unfiltered reference-signal channel estimates in the first and second sets.

Claims

1.-25. (canceled)

26. A method of generating a noise power estimate for a particular reference signal received on a particular subcarrier, from among a plurality of OFDM subcarriers, the method comprising generating the noise power estimate as an absolute square of a difference divided by a constant factor, wherein: the difference is between i) an unfiltered channel estimate for the particular reference signal and ii) a filtered channel estimate for the particular reference signal; the filtered channel estimate for the particular reference signal is a sum of the products of i) unfiltered reference-signal channel estimates for a filter set of reference signals with ii) respective reference-signal coefficients from a filter set of reference-signal coefficients; the filter set includes the particular reference signal; the respective reference-signal coefficients sum to one; and the constant factor is equal to one minus the respective reference-signal coefficient for the particular reference signal.

27. The method of claim 26, wherein the filter set of reference signals includes reference signals received on at least two different respective subcarriers from the plurality of OFDM subcarriers.

28. The method of claim 26, wherein generating the noise power estimate comprises: calculating said difference; dividing said difference by the constant factor; and calculating the absolute square of the difference divided by the constant factor.

29. The method of claim 26, wherein generating the noise power estimate comprises: calculating a modified filtered channel estimate that is equal to the filtered channel estimate minus a product of the unfiltered reference-signal channel estimate for the particular reference signal with the respective reference-signal coefficient for the particular reference signal; dividing the modified filtered channel estimate by the constant factor to determine a quotient; and calculating, as the noise power estimate, an absolute square of a difference between the unfiltered reference-signal channel estimate for the particular reference signal and said quotient.

30. The method of claim 29, further comprising using the modified filtered channel estimate to generate a signal power estimate for the particular reference signal, wherein generating the signal power estimate comprises multiplying the unfiltered reference-signal channel estimate for the particular reference signal by the modified filtered channel estimate, or by a complex conjugate of the modified filtered channel estimate, such that the generated signal power estimate does not increase with an absolute square of any of the unfiltered reference-signal channel estimates.

31. The method of claim 26, wherein the particular subcarrier is a radio-frequency subcarrier.

32. The method of claim 26, wherein the particular reference signal and the filter set of reference signals are Long Term Evolution (LTE) Cell-Specific Reference Signals (CRS) resource elements (RE).

33. The method of claim 26, further comprising receiving and demodulating the particular reference signal.

34. A noise estimator for an OFDM radio receiver, comprising a hardware module and/or a processor and memory storing software for execution by the processor configured to generate a noise power estimate for a particular reference signal received on a particular subcarrier, from among a plurality of OFDM subcarriers, as an absolute square of a difference divided by a constant factor, wherein: the difference is between i) an unfiltered channel estimate for the particular reference signal and ii) a filtered channel estimate for the particular reference signal; the filtered channel estimate for the particular reference signal is a sum of products of i) unfiltered reference-signal channel estimates for a filter set of reference signals with ii) respective reference-signal coefficients from a filter set of reference-signal coefficients; the filter set includes the particular reference signal; the respective reference-signal coefficients sum to one; and the constant factor is equal to one minus the respective reference-signal coefficient for the particular reference signal.

35. The noise estimator of claim 34, wherein the hardware module and/or the processor is configured to generate the filtered channel estimate by multiplying each of the unfiltered reference-signal channel estimates for the filter set by the respective reference-signal coefficient to generate a set of products, and summing products in the set of products.

36. The noise estimator of claim 34, wherein the filter set of reference signals includes reference signals received on at least two different respective subcarriers from the plurality of OFDM subcarriers.

37. The noise estimator of claim 34, wherein the hardware module and/or the processor is configured to generate the noise power estimate by: calculating said difference; dividing said difference by the constant factor; and calculating an absolute square of the difference divided by the constant factor.

38. The noise estimator of claim 34, wherein the hardware module and/or the processor is configured to generate the noise power estimate by: calculating a modified filtered channel estimate that is equal to the filtered channel estimate minus a product of the unfiltered reference-signal channel estimate for the particular reference signal with the respective reference-signal coefficient for the particular reference signal; dividing the modified filtered channel estimate by the constant factor to determine a quotient; and calculating, as the noise power estimate, an absolute square of a difference between the unfiltered reference-signal channel estimate for the particular reference signal and said quotient.

39. The noise estimator of 38, wherein the hardware module and/or the processor is further configured to use the modified filtered channel estimate to generate a signal power estimate for the particular reference signal, wherein generating the signal power estimate comprises multiplying the unfiltered reference-signal channel estimate for the particular reference signal by the modified filtered channel estimate, or by a complex conjugate of the modified filtered channel estimate, such that the generated signal power estimate does not increase with the absolute square of any of an unfiltered reference-signal channel estimates.

40. (canceled)

41. A signal estimator for an OFDM radio receiver, comprising a hardware module and/or a processor and memory storing software for execution by the processor configured to generate a signal power estimate for a particular reference signal received on a particular subcarrier, from among a plurality of OFDM subcarriers, by: generating a first channel estimate as a first function of a first set of one or more unfiltered reference-signal channel estimates, the first set including an unfiltered reference-signal channel estimate for the particular reference signal; generating a second channel estimate as a second function of a second set of one or more unfiltered reference-signal channel estimates, wherein the second set of unfiltered reference-signal channel estimates has no unfiltered reference-signal channel estimate in common with the first set of unfiltered reference-signal channel estimates; and generating the signal power estimate, wherein generating the signal power estimate comprises multiplying the first channel estimate by the second channel estimate, such that the generated signal power estimate does not increase with an absolute square of any of the unfiltered reference-signal channel estimates in the first and second sets of unfiltered reference-signal channel estimates.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Certain preferred embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0066] FIG. 1 is a schematic diagram of signal-to-noise-ratio (SNR) estimator embodying the invention;

[0067] FIG. 2 is graph showing the performance of the SNR estimator relative to a prior-art approach and a theoretical optimum;

[0068] FIG. 3 is graph showing the performance of the SNR estimator relative to a prior-art approach;

[0069] FIG. 4 is an NB-IoT resource grid showing two sets of reference symbols which are used for estimating signal power for a first reference symbol in a method embodying the invention; and

[0070] FIG. 5 is the same NB-IoT grid showing two different sets of the reference symbols which are used for estimating signal power for a second reference symbol.

DETAILED DESCRIPTION

[0071] FIG. 1 shows the key functional blocks in an SNR estimator 1 embodying the invention. It incorporates a signal estimator and a noise estimator, each embodying other aspects of the invention.

[0072] The SNR estimator 1 may be implemented in software executing on a DSP, although in other embodiments some or all of its functions could be hardwired (e.g., as digital logic on an integrated-circuit chip), or performed by an FPGA, or implemented in software executing on one or more general-purpose processors.

[0073] The SNR estimator 1 will initially be described in the context of an LTE Category M1 (LTE-M) radio receiver chip, which is a low-power specification of LTE, intended for Internet-of-Things (IoT) data exchange over cellular networks. It operates in a channel having a bandwidth of 1.4 MHz, which is divided into 72 orthogonal subcarriers. Data is transmitted using OFDM. Predefined CRS resource elements (RE) are transmitted on every third subcarrier, at known times for each subcarrier. The radio receiver receives 48 CRS elements every 1 millisecond (corresponding to one subframe). These allow the radio receiver to generate unfiltered channel estimates for each of the CRS-bearing subcarriers for particular instants in time corresponding to the CRS elements. A filtered channel estimate can be obtained by calculating a weighted average over a set of subcarriers (i.e., averaging over frequency) and over a number of time instants (e.g., averaging over time). These filtering processes reduce noise in the channel estimates.

[0074] Using the terminology introduced previously, a filtered channel estimate for a particular CRS resource element i (which is an example of a particular reference signal, as described above) can be expressed as:

[00003]${\hat{h}}_{\mathrm{filt}}\left(i\right)=\left({}_{-.Math.\frac{K}{2}.Math.}.Math.{\hat{h}}_{C.Math.R.Math.S}\left(i-.Math.\frac{K}{2}.Math.\right)+\mathrm{.Math.}+{}_{-1}.Math.{\hat{h}}_{\mathrm{CRS}}\left(i-1\right)+{}_0.Math.{\hat{h}}_{\mathrm{CRS}}\left(i\right)+\mathrm{.Math.}+{}_{.Math.\frac{K}{2}.Math.}.Math.{\hat{h}}_{\mathrm{CRS}}\left(i+.Math.\frac{K}{2}.Math.\right)\right),$

where .sub.j.sub.j=1, for a filter set of reference-signal coefficients, .sub.j, and where K+1 is the size of the filter (in time and frequency).

[0075] For example, for LTE-M, K+1 might equal thirty-two, with the filter window spanning sixteen CRS-bearing subcarriers in frequency and one millisecond in time.

[0076] In the frequency axis (i.e., ignoring time), the weights .sub.j may slope up linearly from .sub.K/2 to a mid-point at .sub.0 and then slope down linearly to .sub.K/2. However, other filter shapes are possible, and the radio receiver may tune the weights dynamically in response to changing conditions. Moreover, different weights may be used for different resource elements, in order to prevent the filter extending beyond the relevant channel or channels in the frequency axis.

[0077] The SNR estimator 1 contains a set of filtered channel estimators 2a, 2b, 2c, corresponding to different respective CRS resource elements for difference subcarriers. For simplicity, only three filtered channel estimators 2a, 2b, 2c are shown in FIG. 1, but it will be appreciated that the SNR estimator 1 will typically contain more than this. These filtered channel estimators 2a, 2b, 2c access unfiltered channel estimates, .sub.CRS(i), and calculate .sub.filt(i) values as shown above for respective resource elements.

[0078] Each filtered channel estimator 2a, 2b, 2c outputs successive filtered channel estimates at regular intervals. These are received by respective signal-and-power estimation blocks 3a, 3b, 3c.

[0079] Each signal-and-power estimation block 3a, 3b, 3c generates a signal power estimate and a noise power estimate.

[0080] The signal power estimate is calculated as:

[00004]${\hat{P}}_S\left(i\right)=\frac{1}{1-{}_0}.Math..Math.\left\{{\hat{h}}_{C.Math.R.Math.S}\left(i\right).Math..Math.{\left({\hat{h}}_{f.Math.i.Math.l.Math.t}\left(i\right)-{}_0.Math.{\hat{h}}_{C.Math.R.Math.S}\left(i\right)\right)}^{*}\right\}$

[0081] where * denotes the complex conjugate, and { } returns the real component of the expression in the brackets. Here, the .sub.CRS(i) term is a first channel estimate, as described above, and the (.sub.filt(i).sub.0.sub.CRS(i))* is a second channel estimate, as described above.

[0082] As can be seen more clearly from the following two equivalent expressions, this has the effect of removing the .sub.CRS(i) term from the middle of the filtered channel estimate, such that the signal power estimate is based on a modified filtered channel estimate that has no .sub.CRS(i) term in it.

[00005]$\begin{array}{c}{\hat{P}}_S\left(i\right)=.Math.\frac{1}{1-{}_0}.Math..Math.\{{\hat{h}}_{C.Math.R.Math.S}\left(i\right).Math.({}_{-.Math.\frac{K}{2}.Math.}.Math.{\hat{h}}_{C.Math.R.Math.S}\left(i-.Math.\frac{K}{2}.Math.\right)+\mathrm{.Math.}.Math..Math.{}_{-1}.Math.{\hat{h}}_{C.Math.R.Math.S}\left(i-1\right)+\\ {.Math.{}_1.Math.{\hat{h}}_{C.Math.R.Math.S}\left(i+1\right)+\mathrm{.Math.}+{}_{.Math.\frac{K}{2}.Math.}.Math.{\hat{h}}_{C.Math.R.Math.S}\left(i+.Math.\frac{K}{2}.Math.\right))}^{*}\}\\ =.Math.\frac{1}{1-{}_0}.Math..Math.\left\{{\hat{h}}_{C.Math.R.Math.S}\left(i\right).Math..Math.{\left(\underset{k0}{.Math.}.Math.{}_k.Math.{\hat{h}}_{C.Math.R.Math.S}\left(i+k\right)\right)}^{*}\right\}\end{array}$

[0083] This means that the signal power estimate does not contain a squared .sub.CRS (i) term. The benefits of this are explained below.

[0084] In some other embodiments, additional terms may be absent from the filtered channel estimate and present in the .sub.CRS (i) term, so that calculating the signal power estimate includes multiplying the sum of a first plurality of unfiltered channel estimates, including h.sub.CRS(i) (defining a first channel estimate), by the conjugate of the sum of second set of one or more unfiltered channel estimates (defining a second channel estimate), where the second set does not include any of the first plurality of unfiltered channel estimates.

[0085] The noise power estimate is calculated as:

[00006]${\hat{P}}_N\left(i\right)={.Math.{\hat{h}}_{C.Math.R.Math.S}\left(i\right)-\frac{1}{1-{}_0}.Math.\left({\hat{h}}_{f.Math.i.Math.l.Math.t}\left(i\right)-{}_0.Math.{\hat{h}}_{C.Math.R.Math.S}\left(i\right)\right).Math.}^2$

[0086] Again, the .sub.CRS(i) term is removed from the middle of the filtered channel estimate.

[0087] This can be expressed in terms of the modified filtered channel estimate, as:

[00007]${\hat{P}}_N\left(i\right)={.Math.{\hat{h}}_{C.Math.R.Math.S}\left(i\right)-\frac{1}{1-{}_0}.Math.\left(\underset{k0}{.Math.}.Math.{}_k.Math.{\hat{h}}_{C.Math.R.Math.S}\left(i+k\right)\right).Math.}^2$

[0088] The signal-and-power estimation block may calculate this value by any mathematically-equivalent set of operations. It may calculate the modified filtered channel estimate and store this value in memory as an intermediate result, although this is not essential.

[0089] If the original filtered channel estimate is retained in the expression, the noise power estimate can also be written as:

[00008]$\begin{array}{c}{\hat{P}}_N\left(i\right)=.Math.{.Math.\frac{1}{1-{}_0}.Math.\left\{\left(1-{}_0\right).Math.{\hat{h}}_{C.Math.R.Math.S}\left(i\right)-{\hat{h}}_{f.Math.i.Math.l.Math.t}\left(i\right)+{}_0.Math.{\hat{h}}_{C.Math.R.Math.S}\left(i\right)\right\}.Math.}^2\\ =.Math.{.Math.\frac{1}{\left(1-{}_0\right)}.Math.\left({\hat{h}}_{C.Math.R.Math.S}\left(i\right)-{\hat{h}}_{f.Math.i.Math.l.Math.t}\left(i\right)\right).Math.}^2\\ =.Math.{.Math.\frac{1}{{.Math.}_{k0}.Math.{}_k}.Math.\left({\hat{h}}_{C.Math.R.Math.S}\left(i\right)-{\hat{h}}_{f.Math.i.Math.l.Math.t}\left(i\right)\right).Math.}^2\\ =.Math.\frac{1}{{\left(1-{}_0\right)}^2}.Math.{.Math.\left({\hat{h}}_{C.Math.R.Math.S}\left(i\right)-{\hat{h}}_{f.Math.i.Math.l.Math.t}\left(i\right)\right).Math.}^2\end{array}$

[0090] Thus, the noise power estimate may alternatively be calculated by subtracting the filtered channel estimate from the unfiltered channel estimate, for the particular reference signal, and dividing this by a constant factor equal to one minus the respective reference-signal coefficient for the particular reference signal, then taking the absolute square of this quotient.

[0091] Because both the noise power estimate and the signal power estimate can be calculated using the modified filtered channel estimate, this can efficiently be calculated once and used for both estimates. Each signal-and-power estimation block 3a, 3b, 3c receives an unfiltered channel estimate for a respective subcarrier resource element, which it multiplies by the value (.sub.0) and adds to the filtered channel estimate. The result of this sum is then multiplied by

[00009]$\frac{1}{1-{}_0}.$

The result of this multiplication is then sent to a signal power estimator block 4a and also to a noise power estimator block 5a. The other signal-and-power estimation blocks 3b, 3c have similar signal power estimator blocks and noise power estimator blocks.

[0092] The signal-power estimator block 4a takes the complex conjugate of its input, multiplies this by the unfiltered channel estimate for the respective resource element, and outputs the real component of this multiplication.

[0093] The noise-power estimator block 5a multiplies its input by minus one and adds it to the unfiltered channel estimate for the respective resource element. It then calculates the absolute square of this sum, which it outputs as a noise power estimate for the particular resource element. This can serve as a noise power estimate for the corresponding subcarrier, over a given time window.

[0094] The outputs of the noise-power estimator blocks 5a for the respective signal-and-power estimation blocks 3a, 3b, 3c are all input to a linear averaging block 6, which calculates a linear average (i.e., arithmetic mean) value across the subcarriers. This gives an average noise power estimate for the whole channel.

[0095] The output of each signal-power estimator block 4a enters a respective SNR estimator block 7a, 7b, 7c, which also receives the average noise power estimate from the linear averaging block 6. Each SNR estimator block 7a, 7b, 7c divides the subcarrier-specific signal power estimate by the average noise power estimate to generate an SNR estimate for the respective subcarrier.

[0096] The SNR estimates are output from the respective SNR estimator blocks 7a, 7b, 7c to a common linear or non-linear filtering block 8, which can perform optional linear or non-linear filtering over time and/or frequency. The degree of filtering that is appropriate at this stage may vary depending on the application requirements.

[0097] The improved performance of the new approaches to signal power estimation, disclosed herein, can be more fully appreciated from the following analysis.

[0098] An unfiltered channel estimate, .sub.CRC(i), is composed of a true channel coefficient and additive noise, .sub.CRS (i)=h(i)+n(i), where h(i) and n(i) denote a true channel coefficient and a noise sample, respectively.

[0099] Assume, for simplicity, that the channel is constant over the frequency and time resources that are used to generate the filtered channel estimatesi.e., h(i)=h(j), ji. Assume also that the receiver noise is additive white Gaussian noisei.e. the noise samples are uncorrelated, so E[n(i)n(j)*]=E[n(i)]E[n(j)*], ij.

[0100] Then the signal power estimate {circumflex over (P)}.sub.s(i) can be written as:

[00010]${\hat{P}}_S\left(i\right)={.Math.h\left(i\right).Math.}^2+.Math.\left\{\underset{k0}{.Math.}.Math.{}_k.Math.n\left(i\right).Math.{n\left(i+k\right)}^{*}\right\}$

[0101] This contrasts with the known approach of estimating signal power as the absolute square of the filtered channel estimate, which, under the above assumptions, results in

[00011]$\begin{array}{c}{\hat{P}}_S\left(i\right)=.Math.{.Math.{\hat{h}}_{f.Math.i.Math.l.Math.t}\left(i\right).Math.}^2\\ =.Math.{.Math.h\left(i\right).Math.}^2+{.Math.}_k.Math.{.Math.{}_k.Math.}^2.Math.{.Math.n\left(i+k\right).Math.}^2+\underset{k,lk}{.Math.}.Math.{}_k.Math.{}_l.Math.n\left(i+k\right).Math.{n\left(i+l\right)}^{*}+.Math.\\ .Math.\underset{k,lk}{.Math.}.Math.{}_k.Math.{}_l.Math.{n\left(i+k\right)}^{*}.Math.n\left(i+1\right)\end{array}$

[0102] The |h(i)|.sup.2 term of this last equation is desired. The last two noise cross-correlation terms vanish to zero as the number of resource elements, i, in the filter increases. Also post-processing averaging can decrease these last two terms further. The second term, .sub.k|.sub.k|.sup.2|n(i+k)|.sup.2, however, has been found to cause very large errors for signal estimation when SNR<<0 dB. This term does not appear in the signal power estimates generated by embodiments of the invention, which only has cross-correlation terms and no squared noise terms.

[0103] Under the same assumptions as above, the noise power estimate for a CRS RE i, on a particular subcarrier, can then be written as:

[00012]$\begin{array}{c}{\hat{P}}_N\left(i\right)=.Math.{.Math.n\left(i\right)-\underset{k0}{.Math.}.Math.\frac{{}_k}{1-{}_0}.Math.n\left(i+k\right).Math.}^2\\ .Math.{.Math.n\left(i\right).Math.}^2\end{array}$

[0104] The summand term is undesired, but tends to zero as the number of resource elements in the filter increases.

[0105] This contrasts with the known approach of estimating noise power as the absolute square of the difference between a filtered channel estimate and an unfiltered channel estimate, which, under the above assumptions, results in:

[00013]$\begin{array}{c}{\hat{P}}_N\left(i\right)=.Math.{.Math.\left(1-{}_0\right).Math.n\left(i\right)-\underset{k0}{.Math.}.Math.{}_k.Math.n\left(i+k\right).Math.}^2\\ .Math.{\left(1-{}_0\right)}^2.Math.{.Math.n\left(i\right).Math.}^2\end{array}$

[0106] The applicant has found that this (1.sub.0).sup.2 coefficient can scale down the sample noise power estimate and thus can cause a constant, small error in the estimate. This problem is overcome in the noise power estimates generated by embodiments of the invention.

[0107] When a signal power estimate, generated as described herein, is divided by an average noise power estimate, generated as described herein, the SNR estimate asymptotically approaches the true SNR value:

[00014]${\hat{}}_i.fwdarw.\frac{{.Math.h\left(i\right).Math.}^2}{{.Math.n\left(i\right).Math.}^2},$

[0108] as the number of CRS resource elements is increased.

[0109] This contrasts with a known SNR estimator, described earlier, which asymptotically approaches the value of:

[00015]${\hat{}}_i=\frac{{\hat{P}}_S\left(i\right)}{{\hat{P}}_N\left(i\right)}.fwdarw.\frac{{.Math.h\left(i\right).Math.}^2+{}_k.Math.{}_k^2.Math.{.Math.n\left(i+k\right).Math.}^2}{{\left(1-{}_0\right)}^2.Math.{.Math.n\left(i\right).Math.}^2},$

[0110] as the number of CRS resource elements is increased.

[0111] When true SNR>>0 dB, the error term .sub.k .sub.k.sup.2|n(i+k)|.sup.2<<|h(i)|.sup.2, and the known SNR estimator gives accurate enough results.

[0112] However, when true SNR<<0 dB, the error term .sub.k .sub.k.sup.2|n(i+k)|.sup.2>>|h(i)|.sup.2, which means that the known SNR estimator saturates with

[00016]${\hat{}}_i\frac{{}_k.Math.{}_k^2.Math.{.Math.n\left(i+k\right).Math.}^2}{{\left(1-{}_0\right)}^2.Math.{.Math.n\left(i\right).Math.}^2}.$

[0113] But an SNR estimator generated by embodiments of the invention will asymptotically approach the true SNR value irrespective of the SNR region it is operating on.

[0114] FIG. 2 shows the simulated performance of a novel SNR estimator as disclosed herein, compared with a known SNR estimator that generates signal and noise estimates using the prior-art approaches described above. The graph also shows the ideal performance. As can be seen, the expected value of the novel SNR estimator is very close to the true SNR value across the whole measured SNR range, from 15 dB to +10 dB. By contrast, the expected value of the prior-art SNR estimator starts to saturate when the true SNR<5 dB. The novel SNR estimator will therefore perform well in, for example, the CQI-based link adaptation for LTE Cat-M1 when operating in CE-mode A, where the prior-art SNR estimator would not work properly.

[0115] FIG. 3 is a simulation comparison of the normalized variance of the novel SNR estimator with the normalized variance of a prior-art SNR estimator. It is based on LTE subframe-based SNR estimates which are further averaged over 16 subframes (ave16). The normalized variance of the novel SNR estimator is better (lower) than that of the prior-art SNR estimator. There are errors terms which remain in the prior-art SNR estimation approach even after post-filtering of the SNR estimates, which makes it unreliable.

[0116] FIG. 4 shows an NB-IoT resource grid. This relates to an embodiment that is similar to the embodiments described above, but which is used to receive NarrowBand-IoT signals, instead of LTE-M. The SNR estimator has the same structure as shown in

[0117] FIG. 1.

[0118] FIG. 4 illustrates the CRS resource elements that are involved in generating a signal power estimate for the resource element labelled 1. In NB-IoT downlink carrier uses one LTE physical resource block in the frequency domain, which is twelve 15 kHz subcarriers. All twelve subcarriers are shown in FIG. 4. In this example, the filter window occupies the entire NB-IoT channel in the frequency axis, and is one subframe (1 millisecond) wide in the time axis. Because it occupies the full frequency width, it slides only in the time direction. (Of course, a small filter window could be defined that moves along both the frequency and the time axes.)

[0119] The signal power estimate is generated by multiplying a first channel estimate, which is a first function of a first set of one or more unfiltered reference-signal channel estimates, with a second channel estimate, which is a second function of a second set of one or more unfiltered reference-signal channel estimates. In this case, the first set consists only of an unfiltered channel estimate for the RE labelled 1 in FIG. 4, and the first function is trivial, such that the first channel estimate is simply the unfiltered channel estimate for the resource element 1. The second set consists of unfiltered channel estimates for the remaining seven RE's in FIG. 4. The second function multiplies each of these unfiltered channel estimates by the respective weights and sums the products, as described above.

[0120] FIG. 5 shows how the identity of the first and second sets of unfiltered reference-signal channel estimates may change depending on the position of the resource element in the resource grid for which the signal power estimate is being calculated.

[0121] In this case, when calculating a signal power estimate for the RE labelled 8, the first set consists of the unfiltered channel estimate for the RE 8, while the second set consists of the unfiltered channel estimates for the seven RE's indicated in FIG. 5. The same shaped filter used for RE 1 in FIG. 4 could not be used for RE 8 because the filter would cover frequencies that lie outside the NB-IoT channel.

[0122] It is, of course, possible that the first set could contain unfiltered channel estimates for two or more resource elements, with the second set containing unfiltered channel estimates for any number of other resource elements.

[0123] It will be appreciated by those skilled in the art that the invention has been illustrated by describing one or more specific embodiments thereof, but is not limited to these embodiments; many variations and modifications are possible, within the scope of the accompanying claims.