阅读说明：本技术 用于说明rf通信中的多径反射现象的处理信号 (Processed signal for accounting for multipath reflection phenomenon in RF communication ) 是由 厄兹京·帕凯尔 阿里·海尔特·科内利斯·科佩拉尔 于 2021-05-19 设计创作，主要内容包括：本公开的方面可涉及射频接收器的使用,以及在此接收器中跟踪对应于OFDM多径传输信道的多径反射的多径增益和延迟。所述增益和延迟是基于信道脉冲响应的时域演进。搜索多径反射,然后使用所述多径反射来计算信道相关信息以提供信道估计,从而帮助减轻或消除接收到的信号的失真。(Aspects of the disclosure may relate to the use of a radio frequency receiver, and tracking multipath gain and delay corresponding to multipath reflections of an OFDM multipath transmission channel in such a receiver. The gain and delay are based on a time domain evolution of a channel impulse response. Multipath reflections are searched and then used to calculate channel related information to provide a channel estimate, thereby helping to mitigate or eliminate distortion of the received signal.)

1. A method, comprising:

in a Radio Frequency (RF) receiver, tracking a multipath gain and a delay corresponding to at least one of a plurality of multipath reflections of an Orthogonal Frequency Division Multiplexed (OFDM) signal received via a multipath transmission channel based on a time domain evolution of channel impulse response data associated with the transmission channel; and

in response, the multipath reflections are searched to calculate channel related information or a correlation function, and a channel estimate is provided to mitigate or eliminate distortion of the received signal.

2. The method of claim 1, further comprising tracking an evolution of the channel impulse response over time to establish information associated with at least one existing multipath reflection of a plurality of multipath reflections, and applying a matched filter to further concentrate energy associated with multipath components.

3. The method of claim 1, further comprising identifying the presence of the multipath reflection based on a calculated relationship between a convolution output and a slope detection associated with a peak corresponding to the multipath reflection.

4. The method of claim 1, additionally comprising identifying or determining the presence of the multipath reflection based on a convolved output from a filter and a derivative calculated with respect to time in order to find a peak corresponding to a slope associated with the multipath reflection, wherein the multipath reflection is determined to be present if a positive slope is followed by a negative slope in the multipath reflection and the distance between these slopes is equal to the length of the filter used to smooth the multipath reflection.

5. An apparatus, comprising:

a Radio Frequency (RF) receiver to track a multipath gain and a delay corresponding to at least one of a plurality of multipath reflections of an Orthogonal Frequency Division Multiplexed (OFDM) signal received via a multipath transmission channel based on a time domain evolution of channel impulse response data associated with the transmission channel; and

logic circuitry to, in response to the indications of gain and delay, search for multipath reflections and calculate channel correlation information or a correlation function to provide a channel estimate to mitigate or eliminate distortion of the received signal.

6. The apparatus of claim 5, further comprising computing an optimal frequency domain interpolation for channel correlation by using coefficients corresponding to gain and delay for each of the plurality of multipath reflections embodied by the OFDM signal.

7. An apparatus as claimed in claim 5, wherein the OFDM signal carries data in OFDM symbols, and the apparatus further comprises tracking the multipath reflections over time, and in response, providing the covariance matrix calculation from the OFDM symbols of the received signal using an optimal set of interpolation coefficients in the frequency direction associated with channel covariance matrix calculation.

8. The apparatus of claim 5, further comprising tracking an evolution of the at least one of the plurality of multipath reflections over time and filtering by extracting an impulse response and by correlating the impulse response of a current OFDM symbol with a complex conjugate version of a previous OFDM symbol.

9. The apparatus of claim 5, further comprising tracking an evolution of the channel impulse response over time and establishing information associated with an existing one of the at least one of a plurality of multipath reflections.

10. The apparatus of claim 5, wherein the logic circuit is further configured to identify or determine the presence of the multipath reflection based on a relationship between a convolution output and a slope detection associated with the multipath reflection, wherein the presence of a multipath reflection is determined in response to discerning from a slope of a signal associated with the multipath reflection, and wherein a magnitude or gain of any particular multipath reflection does not mitigate the determination.

Drawings

The various exemplary embodiments may be more completely understood in consideration of the following detailed description in connection with the accompanying drawings, in which:

fig. 1 is a system level diagram including multipath searching, channel correlation, and distortion calculation illustrating an example of an RF receiver according to the present disclosure;

fig. 2 is a frequency versus time graph illustrating an exemplary positioning of pilot tones within a subcarrier and an interpolated position according to the present disclosure;

FIG. 3 is a frequency versus time graph illustrating sub-channel interpolation positions according to the present disclosure;

FIG. 4 is a system level diagram illustrating an example of an optimal frequency interpolation based channel estimation method according to the present disclosure;

FIG. 5 is a system level diagram illustrating an example of a multipath tracking method according to the present disclosure;

FIG. 6 is a time domain diagram illustrating an example of multipath reflections viewed in an IFFT in accordance with the present disclosure;

fig. 7 is an exemplary graph illustrating instantaneous Channel Impulse Response (CIR) according to the present disclosure;

fig. 8 is an exemplary graph illustrating aspects associated with a Channel Impulse Response (CIR) and an averaging window in accordance with the present disclosure; and is

Fig. 9 is an exemplary plot of multipath reflections with various delays according to the present disclosure.

While the various embodiments discussed herein are capable of various modifications and alternative forms, various aspects of the embodiments have been shown by way of example in the drawings and will be described in detail. It should be understood, however, that the intention is not to limit the disclosure to the particular embodiments described. On the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the scope of the disclosure, including aspects defined in the claims. In addition, the term "example" as used throughout this application is for illustration only, and not for limitation.

Detailed Description

Aspects of the present disclosure are believed to be applicable to a number of different types of devices, systems, and methods involving RF (radio frequency) Orthogonal Frequency Division Multiplexing (OFDM) -based receiver systems. In certain embodiments, aspects of the present disclosure have been shown to be particularly beneficial in the context of use in OFDM receivers that are susceptible to damage from multipath reflections, and in which channel state information is provided, for example, transmitted over known pilots on a known frequency grid via configuration of a system transmitter. Although the present disclosure is not necessarily limited to such aspects, an understanding of the specific examples in the following description may be understood from a discussion in such specific contexts.

Thus, in the following description, numerous specific details are set forth to describe specific examples presented herein. It should be apparent, however, to one skilled in the art that one or more other examples and/or variations of these examples may be practiced without all of the specific details given below. In other instances, well-known features have not been described in detail so as not to obscure the description of the examples herein. For purposes of illustration, the same reference numbers may be used in different drawings to identify the same elements or additional examples of the same elements. Also, while aspects and features may in some cases be described in separate figures, it should be appreciated that features from one figure or embodiment may be combined with features of another figure or embodiment, even if the combination is not explicitly shown or explicitly described as a combination.

Certain specific examples of the present disclosure are directed to aspects directed to frequency interpolation methods suitable for OFDM receivers in which channel state information is provided via pilots that may be associated with a frequency grid. As applied, for example, in connection with OFDM-based radio and video broadcast systems that may use such pilot-based transmission, an exemplary aspect is to track individual gains and delays for each multipath reflection, including channel impulse responses, and calculate one or more channel covariance matrices from the OFDM symbols to derive optimal interpolation coefficients. These coefficients may then be used to improve the suppression of noise due to multipath interference. In this context, pilots may include pilots present in a received OFDM symbol and/or pilots that are temporally interpolated from future and past OFDM symbols (e.g., via Wiener-Hopf techniques for interpolating a channel at a subcarrier from pilots present in an OFDM symbol and time-domain interpolated pilots).

In a more specific embodiment, such noise suppression improvement is associated with channel covariance, as may be used in systems such as DRM/CDR (world digital broadcasting/china digital broadcasting) and DVB-T/T2 (digital terrestrial video broadcasting), which does not strictly assume a fixed (model-based) function, and filtering is adaptive according to the present disclosure to allow for an increase in noise suppression level, such as a 1.2dB improvement for long echo channels in the DRM case.

In such a specific example, the interpolation coefficient filter may depend only on the implementation of the gain and delay of the multipath components, and thus optimally achieves noise suppression between the multipath components. In yet other related embodiments, additional significant improvements may be achieved in CDR and DVB-T/T2 similar long echo channels (single frequency network use case) as well as other system types that address multipath interference via less than ideal methods.

Such adaptive processing according to aspects of the present disclosure thus permits significant improvements in multipath-related noise suppression, and in certain specific examples, optimal results for any given channel profile may be achieved due to the adaptive (multipath tracking) nature of the processing. Such improvements may be even more pronounced in certain other embodiments where such adaptive multipath tracking aspects are used in combination with time-based interpolation methods/filters (as discussed below).

In a more particular example, radio and/or video broadcast systems (e.g., DRM/CDR and DVB-T/T2) are implemented with such pilot-based OFDM transmissions. In some embodiments, the example method tracks the individual gain and delay of each multipath reflection, including the channel impulse response, and computes the channel covariance matrix from the OFDM symbols and derives the optimal wiener interpolation coefficients, which allows the missing subchannels to be recovered by interpolation. As indicated above, the systems and methods are examples and are not necessarily intended to limit the disclosure or the manner in which various aspects may be used in accordance with the disclosure.

In other particular examples related to and in some cases constructed on the foregoing aspects, embodiments of the disclosure relate to an RF (radio frequency) receiver that tracks multipath gain and delay corresponding to multipath reflections of an OFDM transmitted signal. In this context, one particular method involves searching for multipath reflections to calculate channel-related information, and using information gleaned from the time-domain evolution of the channel impulse response data, providing channel estimates with reduced or eliminated distortion of the received signal. Since this distortion may cause bit channel omission, the identification and elimination of the distortion may be important.

In yet other particular examples related to the above aspects, such adaptive tracking of multipath signals facilitates recovery of the missing sub-channels by computing an optimal frequency domain interpolation of the channel correlation and by using coefficients corresponding to the gain and delay of each of the multipath reflections embodied by the OFDM signal. Additionally, where the OFDM signal carries data in OFDM symbols and these symbols are subject to multipath reflections as they are received, this approach may additionally be implemented to track multipath reflections over time or via evolution-based multipath reflection tracking. This may allow for another step in which the channel covariance matrix of the received signal is calculated using the optimal set of interpolation coefficients in the frequency direction associated with the covariance matrix calculation. Additionally, with such evolution-based multipath reflection tracking, information associated with existing multipath reflections can be readily established. This tracked information may then be filtered by extracting the impulse response and by correlating the impulse response of the current OFDM symbol with the complex conjugated version of the previous OFDM symbol.

In one particular example according to the present disclosure, tracking multipath reflections may involve convolving a Channel Impulse Response (CIR) with a matched filter (or averaging filter) to additionally concentrate the energy of the multipath components before identifying existing multipath reflections. Such filtering may be advantageous because such processing (e.g., IFFT) and bandwidth limitations may smear multipath components (smear) in time. Additionally, such convolution may include adaptively calculating a correlation model for a frequency direction for at least one OFDM symbol in the received OFDM signal. In this example, a derivative of the convolved data is then obtained, and it is determined based on this derivative that a multipath reflection is present under certain conditions. Based on this derivative, a multipath reflection is determined to be present if a positive slope is followed by a negative slope in the multipath reflection and the distance between these slopes is equal to the length of the filter used to smooth the multipath reflection.

The results of the above example provide an indication of the gain and delay of all multipath reflections. This allows the true autocorrelation function of the correlation lag (the "lag" refers to the distance from the interpolated point to the nearest pilot position) to be estimated.

The above example may be part of an RF OFDM receiver comprising an RF OFDM transmitter forming a radio system for transmitting and receiving signals using OFDM data and pilot symbols for the transmission of digital data.

Turning now to the drawings and in relation to the aspects and embodiments disclosed above, fig. 1 shows an example illustrating a portion of an RF pilot based OFDM receiver. The antenna 110 may receive multiple transmissions, including a desired channel. The desired channel signal may include one or more multipath signals along with the direct transmission. The receiver front end 120, along with various processing tasks, creates a demodulated signal of the desired channel. This signal is passed to a multipath searching block 130, which multipath searching block 130 searches for and tracks any received multipath signals included with the desired channel. The information found in the multipath searching block 130 (e.g., gain and delay) is passed to a channel correlation calculation block 140, which channel correlation calculation block 140 generates the parameters/information needed to mitigate or eliminate multipath distortion. The parameters/information generated by the correlation computation block 140 are passed to a distortion computation block 150, which distortion computation block 150 performs multipath distortion correction on the received signal, thereby improving the signal.

Fig. 2 provides an example illustrating pilot-based OFDM transmission presented in symbol number (or time) in the vertical axis and in frequency in the horizontal axis. The illustration includes a so-called gain reference or pilot 220, which gain reference or pilot 220 is a known symbol and is transmitted with a certain periodicity in both the time and frequency domains, as shown. An example of temporal interpolation is also shown. Consider a four-tap filter that combines pilot and wiener filter coefficients, which are calculated as: the time-variance of the channel due to doppler spread. The squares labeled as interpolation entries 230 are each interpolated with an associated pilot 220 having a coefficient set of (0, 1, 2, 3). The pilot consistent with symbol 10 and coefficient set 4 is the existing pilot improved by recalculating the entry with the associated 4 pilots. It should be noted that the channel need not be estimated for all subcarriers that do not have pilots.

The frequency interpolation task after the time interpolation step is shown in fig. 3, which computes/interpolates (in the frequency direction) the missing sub-carriers for a particular OFDM symbol and filters the already interpolated sub-carriers after the time interpolation.

Part of an example system may be a method of computing optimal frequency domain interpolation coefficients. In order to derive the optimal interpolation coefficients, channel covariance matrix calculation is required. For this purpose, it may be necessary to measure the frequency selectivity due to the multipath properties of the wireless channel. This is captured in the autocorrelation function in the frequency direction and given by:

in equation (3), H_fRepresenting the frequency domain channel transfer function. Equation (3) uses the availability of the channel transfer function for all subcarriers in the frequency domain. Therefore, this function cannot be calculated directly from the available gain references (pilots) after time interpolation due to subcarrier omission. Other methods may be found that allow equation (3) to be calculated in other ways.

As another example of an aspect of the present disclosure, fig. 4 illustrates one manner in which channel estimation may be performed. In fig. 4, after selecting the proper time synchronization for the proper FFT window, the above method begins by extracting the gain references in the time direction and interpolating the missing gain references in the time direction for the particular OFDM symbol as shown in fig. 2 (block 410). It should be noted that the symbol 10 has been interpolated, as identified by the interpolation entry 230. See also interpolated entry 320 shown in fig. 3. This step may be replaced with other temporal interpolation schemes.

Other portions of the example method may include a block 420 for providing or calculating a power delay profile in terms of delay and gain via multipath tracking. The power delay profile is related to the correlation function via fourier transform and, therefore, data characterizing the power delay profile or a model of the power delay profile is input to block 430. The power delay profile of block 420 may be configured to estimate the power delay profile by averaging the time domain channel impulse response obtained from the time domain interpolation gain reference.

By tracking the time-domain evolution of the channel impulse response (e.g., multipath reflections of the wireless channel), equation (3) can be bypassed to compute the true autocorrelation function and hence the true channel covariance matrix. If the gain and relative position of the multipath reflection are known, it is possible to calculate the true autocorrelation function or channel covariance matrix in correlation function 430. Using the data from the autocorrelation function, it is possible to also create a channel covariance matrix in the frequency domain and solve the wiener-hopplev equation to obtain the optimal frequency interpolation coefficients, for wiener-hopplev calculation block 440. In convolution block 450, the calculated interpolation coefficients derived in 440 may be used to optimally estimate the channel (e.g., estimate the missing subcarriers) for a particular OFDM symbol in the presence of noise.

Multipath tracking block 420 is an example of a method that allows multipath reflections to be found, thereby permitting the gain and delay and/or position of multipath components to be identified. Once these multipath reflections are found, those values can be used to calculate the true autocorrelation function or adaptive brick wall filtering at the location of the multipath component. Exemplary steps for producing efficient tracking of multipath reflections are shown in fig. 5.

After a sine (sine) window 510 is applied to the time-interpolated gain references to obtain the channel impulse response in the time domain, an inverse FFT520 is performed on these time-interpolated gain references. These gain references 310 as seen in FIG. 3 are at a particular ratio N_fResampling is performed on all frequency bins (frequency bins). This periodicity is a design parameter for the network operator/broadcaster and may be desirable to coverIs determined as a function of the maximum delay spread tau of the particular worst case channel profile_mmaxAnd a system sampling period T_sAnd is given as N_f＜T_s/τ_mmax. The minimum IFFT size for obtaining an unaliased replica of the impulse response in the time domain is N_f·B_w. Here, B_wRefers to the number of carriers used (bandwidth). In one example, as seen in FIG. 5, a system sample rate of 48kHz is selected for DRM car radios that meet this criteria. For a simplified implementation, the size of the IFFT may be selected to be the smallest power of two that meets the minimum size specification.

Performing an IFFT has the effect of convolving the wireless channel impulse response associated with the multipath reflection in the time domain similar to the sine function (similar to the characteristics of Dirac) because the IFFT size is larger than the bandwidth used. (Note that the brick-wall filter is assumed in the frequency domain to be the same size as the bandwidth used, which is multiplied point-by-point with the channel transfer function in the frequency domain. the inverse FFT of this brick-wall filter is a sine function. since the inverse Fourier transform of the point-by-point multiplication is equivalent to convolution, this sine function will be convolved with multipath reflections_w). This convolution spreads the reflected energy in the time domain. It is desirable to see dirac-like characteristics in the time domain to focus the reflected energy into a position and gain that can easily identify the reflection and limit the interference therebetween due to convolution. It should be noted that the sine function, which performs a point-by-point multiplication with the channel transfer function in the frequency domain, is equivalent to a convolution of the multipath reflections with a brick-wall filter in the time domain. It is possible to minimize the width of this brick-wall filter to 1/IFFTsize (equal to the length of 1 sample duration in the time domain). This step is represented by block 510. Therefore, the window function coefficient in the frequency domain may be calculated using equation (4).

In (4), K_minAnd K_maxRefers to the minimum and maximum indices of the carriers used.

After the time domain impulse response is computed using IFFT, the result has N due to the upsampling of the gain reference at the same rate_fAnd (4) a copy. After time interpolation, there is one interpolation gain reference available in the frequency domain every Nf subcarriers. After that, the interpolated gain reference can be regarded as N for all subcarriers_fAnd (5) performing double down sampling. Now by a factor of N by inserting zeros in the frequency domain_fThese interpolated gain references are upsampled and this zero insertion produces a replica of the Channel Impulse Response (CIR) in the time domain. In an alternative example embodiment, one may choose to have the circuitry perform an IFFT only on the time domain interpolated gain reference and not on the inserted zeros representing the missing subcarriers; in this case, a smaller IFFT size may be used and no copy of the CIR is obtained and the window function (equation 4) may be applied to the corresponding location of the time-domain interpolation gain reference.

FIG. 6 shows the resampling ratio N_fFor the 4 example, there are therefore four copies of the channel impulse response, and this may also apply to the previous alternative example embodiment. The original "spectrum" (required CIR610) around time 0 is considered to be the "original" spectrum when the rest is only a replica of the same impulse response. Time-domain response of the required CIR in h_t，τWhere t denotes a time index (or OFDM symbol index) and τ denotes a delay of a multipath reflection for each OFDM symbol. The multipath reflections appear as a sine function 620 with lobes that have a width based on the ratio of the IFFT size to the bandwidth used.

Since the evolution of the multipath reflections needs to be tracked over time, the extracted impulse response may be filtered. For this purpose, the impulse response of the current OFDM symbol is correlated with the complex-conjugated version of the previous OFDM symbol in the following way.

In equation (5), E represents the mean/desired operator, and Real means that this calculation is performed on the Real component of the correlation in the time direction. The superscript H is the complex conjugate operation. The desired operator may be implemented as a first order IIR filter by the following equation.

y_t＝α·x_t+(1-α)·y_t-1 (6)

In the case of the equation (6),is the input to the IIR filter. This filtering needs to be performed on the basis of the samples of the impulse response (in terms of τ). The range to be covered in the τ dimension should match the range/length of the required CIR. This is essentially the length of the guard interval, as OFDM systems are designed to maintain the CIR within the guard interval. Therefore, the number of required IIR filters is equal to the length of the guard interval. Note that there is an implicit synchronization specification here, since the multipath reflection of the desired CIR does not have to start with τ ═ 0. In equation (6), α is a filter coefficient that determines the corner frequency of the averaging filter. Correlating 530 the complex conjugate of the current impulse response and the previous impulse response may be considered a denoising step because the noise realizations for the current impulse response and the previous impulse response are independent. It should be noted that in the case of averaging the absolute impulse response, no noise filtering is implemented.

In this example embodiment, once the impulse response is averaged in the time direction, the next task is to identify the number of multipath reflections (only 2 in this example), their gain and delay (in the τ dimension). The width of the sine function representing a single multipath component is also known. The width is equal to round (2. IFFTsize/B)_w). To enable detection, existing multipath reflections in the time domain view, matched filtering or averaging filters (moving windows with equal coefficients) or round (2. IFFTsize/B) of a length exactly matching the main lobe (or width) of the multipath reflection may be used_w). This exemplary embodiment uses averaging windows with equal coefficients and convolves the time domain view of the impulse response to emphasize the sine function corresponding to the multipath reflectionA main lobe. This is shown as signal processing block 540.

Identifying the presence of multipath reflections may also result from an evaluation of the derivative 550 of the convolution output (e.g., at block 540). By calculating these parameters as part of the evaluation and detecting the correlation slope, an indication of the multipath reflection can be provided. For example, the evaluation may indicate that multipath reflections are present only when a positive slope is followed by a negative slope and the distance between these slopes is equal to the length of the filter. Because the slope value is not known by this check, the strength and/or gain of the multipath reflection does not affect the detection performance. The data from block 550 and the data from IFFT block 520 are used in maximum extraction block 560 to extract the required gain and delay.

Thus, these aspects associated with the example used in fig. 5 may correspond to, or provide an estimate of, the delay profile of the received signal that is based on a time average of instantaneous Channel Impulse Response (CIR) estimates where multipath reflections in the instantaneous CIR are most likely to be present (in time). The knowledge gained in the upper branch of fig. 5 is used to provide a limited search in the instantaneous CIR to locate the gain and delay of the multipath component as in the maximum extraction block 560 of fig. 5.

Continuing in this example, if a multipath reflection is detected, the actual gain and delay of this peak is searched in the instantaneous channel impulse response, rather than on the average CIR. The reason for this is that the instantaneous CIR represents the current OFDM symbol that has to be estimated and the average CIR helps to identify the number of multipath reflections and the locations where they are to be searched in the instantaneous CIR. Fig. 7 shows the instantaneous CIR of an example channel realization.

Fig. 8 shows eight multipath reflections detected by the above example method. The upper plot 810 is the mean CIR. The middle plot 820 shows the situation after convolving the upper plot 810, where the length of the moving average window is equal to the length of the main lobe of the multipath reflection, i.e., (round (2. IFFTsize/B)_w)). The bottom plot 830 shows the differentiation of the middle plot 820. A simple logical check is performed by looking at the sign of the differentiation result. Negative after a positive slope (+)Slope (-), where the distance equals round (2. IFFTsize/B)_w). This indicates the multipath reflection found.

In such cases where there are missing subcarriers, providing the calculations or estimates associated with equation (3) may be more burdensome due to subcarrier omission. However, the gain (ρ) with respect to K multipath reflections is confirmed_k) And delay (τ)_k) With such information in mind, the true autocorrelation function can be estimated as:

in equation (7), m represents the lag of the autocorrelation function. The number of lags to be calculated for the channel covariance matrix is N_taps·N_fIn which N is_tapsRefers to the number of taps of the interpolation filter, and N_fIs the gain reference periodicity after temporal interpolation. Therefore, the hysteresis range is 0 … N_taps·N_f-1. It should be noted that, due to the nature of the fourier transform, the convolution step in the frequency domain is equivalent to a point-by-point multiplication in the time domain. Thus, if the gain and position of each multipath reflection is known, then a brick-wall filter can be used for the instantaneous CIR in the time domain, as given in FIG. 9, which shows a graph with different delays (τ) in FIG. 9₁，τ₂，τ₃) Three multipath reflections. This brick-and-wall filter in the time domain is equivalent to a sine function in the frequency domain. In conjunction with this, in another particular example embodiment, the autocorrelation function may be calculated as the estimated gain (ρ) of the gain and delay from each multipath reflection_k) And delay (τ)_k) The sum of the sine functions controlled, and can be viewed as a substitute for equation (7). This formula can be given as:

the hysteresis range of m is entirely as defined above, i.e. 0 … N_taps·N_f-1

Can be used asThe optimal interpolation filter coefficients in the frequency domain are calculated or estimated by a wiener-hopplev relation or equation that is performed in a similar manner to the temporal interpolation filter calculation in equation (2). It should be noted that R is represented in the frequency domain_ffThe channel covariance matrix of (a) is available in this respect. The channel covariance matrix can be calculated as R using equation (8)_ff(k，l)＝R_f(k-l), wherein k, l ═ 0 … N_taps-1. Here, N_tapsRefers to the number of taps corresponding to the frequency interpolation filter. The equation for the optimal filter coefficients is given by:

the coefficients calculated in equation (9) can be used to interpolate the missing sub-carriers by convolution with the output of the time-interpolated channel estimate.

Impressive results have been achieved in certain experimental/more detailed examples in accordance with aspects of the present disclosure and involving at least one non-fixed channel covariance matrix. In such tests, a conventional frequency interpolation scheme relying on a fixed channel covariance matrix hypothesis (or a fixed model for the autocorrelation function in the frequency domain) may be used as a reference point; an example in this regard may be a single brick-wall filter that may, for example, capture the width of the entire CIR. In accordance with the present disclosure, tracking multipath reflections may include identifying relevant information (gain and delay) from the multipath reflections and allowing adaptive brick wall filtering as shown in fig. 9. Such channel dependent filtering achieves (optimal) noise reduction, where noise between the brick-wall filters is filtered out and performance is significantly better than the fixed correlation model. Tests have shown such performance improvements in the gain shown as much as 1.2dB, and when used with pilot-based OFDM receivers, associated performance improvements in baud rate, bit error rate, and/or general signal reception are achieved.

Those skilled in the art will recognize various terms as used herein. By way of example, the present specification describes and/or illustrates aspects by way of various circuits with reference to terms such as block, module, and/or other circuit-type depictions (e.g., reference numeral 410-450 of fig. 4 depicts a block/module as described herein). Such circuitry or circuitry may be used with other elements to illustrate how certain example embodiments may be carried out in the form or structure, steps, functions, operations, activities, and so forth. For example, in certain embodiments discussed above, as may be done in the methods shown in fig. 4 and 5, one or more of the modules are discrete logic circuits or programmable logic circuits configured and arranged to implement these operations/activities. In certain embodiments, such programmable circuitry is one or more computer circuits, including memory circuitry for storing and accessing programs to be executed as a set (or sets) of instructions (and/or to be used as configuration data to define how the programmable circuitry performs), and the programmable circuitry performs associated steps, functions, operations, activities, etc., using an algorithm, method, or process as described by fig. 4. Depending on the application, the instructions (and/or configuration data) may be configured to be implemented in logic circuitry, where the instructions (whether characterized in the form of object code, firmware, or software) are stored in and accessible from memory (circuitry). As another example, where the specification may refer to "a first [ structure type ]," a second [ structure type ], "etc., where [ structure type ] may be replaced by terms such as [" circuitry, "circuitry," etc. ], the adjectives "first" and "second" are not used to imply any description of the structure or to provide any material meaning; rather, such adjectives are merely English antecedents to distinguish one similarly named structure from another (e.g., "the first circuit configured to switch … …" is interpreted as "the circuit configured to switch … …").

Based on the foregoing discussion and description, one skilled in the art will readily recognize that various modifications and changes may be made to the various embodiments without strictly following the exemplary embodiments and applications illustrated and described herein. For example, a method as illustrated in the figures may involve steps performed in various orders, where one or more aspects of embodiments herein are maintained, or may involve fewer or more steps. Such modifications do not depart from the true spirit and scope of aspects of the present disclosure, including the aspects set forth in the claims.