METHOD FOR FREQUENCY- AND TIME-SELECTIVE INTERFERENCE SUPPRESSION FOR A COMMUNICATION SYSTEM BASED ON OFDM, AND RECEIVER THEREFOR

Abstract

A method for frequency- and time-selective interference suppression for a communication system based on OFDM, and a receiver therefor. To achieve a much lower bit error rate at the output of the receiver or to permit greater interference or a lower signal-to-noise ratio (in a prior art L-DACS1 receiver, at least 45 nautical miles) for the same transmission power, the invention provides: a filter bank pulse blanking method FBPB in which the sampled received signal is applied to a blanking unit for frequency-selective pulse blanking, which blanking unit consists of an analysis filter bank having M sub-bands; a module for frequency-selective pulse blanking of the sub-band signals; and a synthesis filter bank, which reassembles the signal. The analysis filter bank, which breaks down the received signal into multiple sub-bands on a frequency-selective basis, is used before OFDM windowing, such that the sub-band breakdown applies pulse blanking on a sub-band-selective basis.

Claims

1. A method for reducing the interfering effects of pulse-shaped interference signals in an OFDM-based data transmission in a modulated data, which is assigned by a receiver, with multiple carrier frequencies, and superimposed pulse-shaped interfering signals, wherein: a) the pulse-shaped interfering signals are detected in the modulated OFDM-based signal, b) for the suppression of a pulse-shaped interference signal in the reception signal, this is multiplied by a window-function, c) the window function isconsidered in the time domain as a continuous functiondifferentiated, d) the transmission signal multiplied by the window-function is decoded after a transmission channel estimation and signal equalization, e) in the case of a transmission channel estimation of the data which are assigned to the individual carrier frequencies, a reliability value is assigned which describes how credible the received or estimated data is, and f) the reliability value for those data associated with the carrier frequencies affected by a pulse-shaped interfering signal is set to zero before the decoding in the receiver, wherein a filter bank pulse blanking method FBPB is provided, in which: a sampled received signal (r) is fed to a blanking unit for frequency-selective pulse-blanking, which comprises an analysis filter bank with M sub-bands, a module for frequency-selective pulse blanking of the sub-band signals and a synthesis filter bank, which reassembles the signal, and the analysis filter bank, which divides the receiving signal into several sub-bands in a frequency-selective manner, in front of a OFDM-windowing in such a manner that the sub-band decomposition is used to apply pulse-blanking sub-band-selectively.

2. The method according to claim 1, wherein the detection of a disturbance in a detection unit in the sub-bands takes place sub-band-selectively.

3. The method according to claim 1, wherein a blanking mitigation unit for adaptation to interfered interferences by pulse-blanking and an ICI cancellation unit for eliminating the introduced interference by pulse blanking are provided and whereby: the output of the blanking mitigation unit is provided to a module for channel estimation based on pilot values, the output of the blanking mitigation unit is provided to a module of the ICI cancellation unit for the classification of symbols, in which a high ICI disturbance was estimated as unreliable, and the output of the blanking mitigation unit is provided to a blanking equalization module for equalizing the values after the OFDM-windowing.

4. A method according to claim 1, wherein a block-based-frequency interference mitigation method BBFIM is provided, whereby a fast Fourier transformation FFT of length M is applied to the blocks of length M in the time domain, a Distance Measuring Equipment DME then suppressing disturbance in the frequency range, and finally the time signal is retrieved by an inverse fast Fourier transformation IFFT using a Hann-windowing or another Nyquist-window with a soft edge is used and the interference suppression in the frequency domain is carried in such a way that a spectral analysis is combined with the interference suppression and time-variant filtering takes place in the frequency range.

5. The method according to claim 4, wherein a filtered and sampled received signal is split into overlapping blocks with index b and length M, whereby the number of overlapping samples being at M/2:
r.sub.b[n]=r[n+b.Math.M/2](35) with b{0, 1, 2, . . . } and n{0, 1, 2, . . . , M1} and in that the blocks are then windowed with a Hann-window:
r.sub.b.sup.w[n]=r.sub.b[n].Math.w.sub.Hann[n](36)
with $\begin{array}{cc}{}_{\mathrm{Hann}}\left[n^{}\right]=\{\begin{array}{cc}\frac{1}{2}.Math.\left(1-\cos \left(\frac{2.Math..Math.}{M}.Math.n^{}\right)\right)& \mathrm{if}.Math..Math.0n^{}<M\\ 0& \mathrm{else}\end{array}& \left(37\right)\end{array}$ and wherein when a different Nyquist window is selected, the number of overlapping scanners is selected such that the sum of the time-shifted Nyquist-windows is summing up to the value 1.

6. A receiver for carrying out the method according to claim 1, wherein the sampled reception signal is fed to a blanking unit for frequency-selective pulse-blanking, which is composed of an analysis filter bank with M sub-bands, a module for frequency-selective pulse-blanking of the sub-band signals and a synthesis filter bank, which re-assembles the signal, and in that for the detection of a disturbance in the sub-bands the blanking unit is connected to a detection unit and for adapting to interfered disturbances by pulse-blanking the blanking unit is connected to a blanking mitigation unit.

7. The receiver according to claim 6, wherein the blanking mitigation unit is connected to an ICI cancellation unit, and that for the classification of symbols as unreliable, for which a high ICI disturbance is estimated, the ICI cancellation unit, a module for ICI estimation, a module for channel multiplication and a module for channel coding are provided, whereby the output signal of a DFT-module of the blanking mitigation unit is connected to the module of the ICI cancellation unit, a module for SNR estimation, which for channel estimation on the basis of pilot values is connected to a module for channel estimation and a blanking equalization module of the blanking mitigation unit for equalization of the values after the DFT.

Description

BRIEF DESCRIPTION OF THE DRAWING FIGURES

[0031] The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

[0032] Further advantages and details can be found in the following description of a preferred embodiment of the invention with reference to the drawing. In the drawings:

[0033] FIG. 1 shows the block diagram of a receiver according to the invention for frequency- and time-selective interference suppression,

[0034] FIG. 2 shows a block diagram of an L-DACS1 transmitter according to the state of the art,

[0035] FIG. 3 is a graph showing the unfiltered L-DACS 1 and DME signal with a frequency offset of 500 kHz and +500 kHz according to the prior art,

[0036] FIG. 4 shows a graph with unfiltered L-DACS 1 and DME signal at the L-DACS 1 receiver in the time domain according to the prior art,

[0037] FIG. 5 is a block diagram for a receiver with pulse-blanking and combination unit according to the DFT according to the prior art,

[0038] FIG. 6 is a block diagram for a receiver, in which the order of DME suppression and OFDM windowing is changed,

[0039] FIG. 7 is a flow diagram for a block-based-frequency-interference-mitigation method BBFIM according to the invention,

[0040] FIG. 8 is a graph for a non-windowed, a rectangle-windowed, and a Hann-windowed DME signal in the time domain,

[0041] FIG. 9 shows a graph for the power density spectrum of the DME signals of FIG. 8,

[0042] FIG. 10 is a graph for packet error rate (PER) and for varying number of samples at an E.sub.b/N.sub.0-value of 6.0 dB,

[0043] FIG. 11 is a graph for the packet error rate (PER) and for varying E.sub.b/N.sub.0-values at worst-case,

[0044] FIG. 12 is a flow chart for a filter bank pulse-blanking method FBPB before the OFDM-windowing according to the invention,

[0045] FIG. 13 is a graph for the bit error rate (BER) before decoding and for varying number of TACAN/DME stations at different number of sub-bands,

[0046] FIG. 14 is a graph for the bit error rate (BER) before decoding and for varying number of TACAN/DME stations at different block sizes,

[0047] FIG. 15 shows a graph for the bit error rate (BER) before decoding and for varying the number of TACAN/DME stations at different threshold values ,

[0048] FIG. 16 is a graph for the packet error rate (PER) and for various E.sub.b/N.sub.0-values at different thresholds and without DME interference,

[0049] FIG. 17 is a graph for the packet error rate (PER) and for various E.sub.b/N.sub.0-values at different thresholds and moderate DME interference,

[0050] FIG. 18 is a graph for the packet error rate (PER) and for various E.sub.b/N.sub.0-values at different thresholds and strong DME interference,

[0051] FIG. 19 is a graph for the bit error rate (BER) before decoding and for varying the number of TACAN/DME stations at different threshold values ,

[0052] FIG. 20 is a graph for packet error rate (PER) and for varying number of TACAN/DME stations at different thresholds and strong DME interference, and

[0053] FIG. 21 is a graph for the packet error rate (PER) and for various E.sub.b/N.sub.0-values at the threshold value =10 for FBPB and =12 for BBFIM and for different DME interference according to the invention.

DETAILED DESCRIPTION OF THE INVENTION

[0054] The receiver structure of a frequency and time-selective interference suppression according to the invention for a communication system based on OFDM using a filter bank is shown in FIG. 1. Inventive constituents of the receiver E are a blanking unit BU for a frequency-selective pulse-blanking with the aid of a filter bank, a detection unit DU for the frequency-selective detection of the interference, a blanking mitigation unit BMU for adaptation to interfered disturbances introduced by pulse-blanking and an ICI cancellation unit ICU for eliminating the interference introduced by pulse blanking

[0055] In Q. Zhang, Y. Zheng, S. Wilson, Excision of Distance Measuring Equipment Interferences from Radio Astronomy Signals, The astronomic journal, pp. 2933-2939, 2005, the suppression of DME-signals in broadband astronomy signals is examined with the aid of a filter bank. This idea is now transferred to an OFDM-system. The blanking unit BU according to the invention consists of the analysis filter bank AFB with M sub-bands, the module for the frequency-selective pulse-blanking of the sub-band signals PBS (comparable to a switch per spectral range, which extends or suppresses the signal, in particular outputting the spectral components Signal for DME-detection via line BS and outputting the control information of the pulse blanking, i.e. quasi the switch positions per spectral range over the time or per block via line BC) and a synthesis-filter-bank SFB, which reproduces the signal (via BS). The analysis filter bank AFB, which divides frequency-selectively the receive signal SRS into several sub-bands, is used before the OFDM-windowing. The polyphase structure according to the invention can be used during the implementation. Pulse-blanking can be applied sub-band-selectively by the sub-band decomposition. That is, sub-bands that are severely affected by interference can be more suppressed than sub-bands that are less affected. After being subdivided into different sub-bands with the analysis filter bank AFB, the blanking process can be applied separately in each sub-band. As a result, the useful signal is less strongly attacked than with pure pulse-blanking. The number of sub-bands is M. In Q. Zhang, Y. Zheng, S. Wilson, Excision of Distance Measuring Equipment Interferences from Radio Astronomy Signals, reference as above, a filter bank is generally proposed (i.e., not OFDM-specific) for suppressing narrow-band interference in a broadband system.

[0056] The detection of the disturbance in the detection unit DU (in particular in the module DME detection DD) is simplified by the sub-band decomposition because sub-bands are present which are strongly affected by the disturbance. Detection of existing DME impulses occurs over time or per block and for each spectral component, whereby the information about other spectral components can be used to decide whether a disturbance is present in a spectral range. Thus, interference-detection can be applied to improve the decision to suppress the pulse. If this is not known, pulse-blanking with power detection, see S. Brandes, S. Gligorevic, M. Ehammer, T. Grupl, R. Dittrich, Expected B-AMC System Performance, reference as above, can also be used here, but only sub-band-selective.

[0057] The introduced ICI is greatly reduced by the sub-band selective suppression. The remaining disturbance is estimated using the blanking mitigation unit BMU. This information is now used three times as follows: [0058] 1. For channel estimation in module CE, pilot values SP are used. If it is known how strongly which pilot is affected by ICI, this can be taken into account in the channel estimation. [0059] 2. The ICI estimate in the IE module is also used to calculate the reliability information for channel decoding in the CD module. In this case, symbols where a high ICI disturbance has been estimated are classified as unreliable. [0060] 3. In the module blanking equalization BE the signal energy loss is counteracted by pulse-blanking. This equalization works optimally.

[0061] The iterative estimation and extinction of introduced ICI in OFDM is often described in the literature. For example, in S. Brandes, U. Epple, M. Schnell, Compensation of the Impact of Interference Mitigation by Pulse Blanking on OFDM Systems, reference as above, an implementation thereof in the case of pulse-blanking and OFDM is described. According to the invention, the method is extended in the ICI cancellation unit ICU, since ICI is now sub-band-selective and needs to be estimated differently.

[0062] In the filter bank pulse-blanking method FBPB according to the invention, the order of DME suppression and OFDM-windowing are exchanged, see FIG. 6 as well as in detail below. Because of the frequency-selective character of DME, the suppression in the frequency range should take place whereas the impulsive characteristic should not be ignored.

[0063] An analysis of the thresholds for power detection according to the invention is described in detail below. Before the OFDM-demodulation, the processed sub-bands are reassembled in the synthesis step. There is a target conflict between the resolution in time and frequency range. The number of sub-bands and the filter type determine this target conflict. A low-pass filter on the receiver can be omitted since the DME-signals are suppressed by frequency selection. The implementation according to the invention with the aid of a polyphase structure is described in detail below.

[0064] In each sub-band in, the sampled receive signal r [n] is filtered with a finite impulse response (FIR) h.sub.m[n] of length K, where in ={0, . . . , M1}. The sub-band filters are generated by modulating a low-pass filter h.sub.0[n]:

h.sub.m[n]=h.sub.0[n].Math.w.sub.M.sup.mn(6)

where w.sub.M=e.sup.2/M. To reduce the complexity, according to the invention, the synthesis filter bank can be brought into a polyphase structure:

[00004]$\begin{array}{cc}{r}_m\left[n\right]=r\left[n\right]*h_m\left[n\right]=\underset{k=-K/2}{\overset{K/2-1}{.Math.}}.Math..Math.r\left[n-k\right].Math.h_0\left[k\right].Math.{}_M^{-\mathrm{mk}}& \left(7\right)\\ =\underset{=0}{\overset{M-1}{.Math.}}.Math.{}_M^{-m.Math..Math.}.Math.\underset{=-K/2.Math.M}{\overset{K/2.Math.M-1}{.Math.}}.Math.r\left[n-.Math..Math.M-\right].Math.h_0[.Math..Math..Math.M+],& \left(8\right)\end{array}$

wherein the second sum in (6) corresponds to the windowed and periodically expanded input signal. The window corresponds to the impulse response of the prototype filter. For each output value n, a Fast Fourier Transform FFT of length M is applied. The block diagram of this implementation is shown in FIG. 12.

[0065] A comparison with respect to complexity and performance with other pulse-blanking methods with the assumption of a perfect DME detection is made below. Firstly, however, power detection for DME detection is shown and analyzed for different threshold values.

[0066] After subdivision into different sub-bands, the blanking process can be applied in each sub-band. Pulse-blanking with power detection is a very simple procedure. The signal r.sub.m[n] in the sub-band in (m{0, 1, . . . , M1}) is set to zero at position n if the instantaneous power of the receiving signal in the m-th subband |r.sub.m[n]|.sup.2 exceeds the threshold value .Math.P.sub.m[n]:

[00005]$\begin{array}{cc}{r}_m^{\mathrm{IM}}\left[n\right]=\{\begin{array}{cc}{r}_m\left[n\right],& \mathrm{if}.Math..Math.{.Math.r_m\left[n\right].Math.}^2<.Math.P_m\\ 0,& \mathrm{else}\end{array}& \left(9\right)\end{array}$

P.sub.m is the average received power of the L-DACS1 signal in the sub-band in, and is the power-detection parameter. Before the OFDM-demodulation, the sub-bands are summed up in the synthesis filter bank.

[0067] The adjusted threshold value is a design parameter. An intuitive choice is =1, which is a good compromise between interference suppression and ICI formation. Instead of making the decision to blank the sub-band signals hard if a certain threshold value is reached, a soft decision can also be made if the average power of the useful signal P.sub.m, the disturbance variance N.sub.m.sup.awgn and the instantaneous power of the pulse interference P.sub.m.sup.pulse[n] is available on all sub-bands:

[00006]$\begin{array}{cc}{r}_m^{\mathrm{MMSE}}\left[n\right]=r_m\left[n\right].Math.c_m\left[n\right]& \left(10\right)\\ \mathrm{with}& \\ c_m\left[n\right]=\frac{P_m^{\mathrm{useful}}}{P_m^{\mathrm{useful}}+N_m^{\mathrm{awgn}}+P_m^{\mathrm{pulse}}\left[n\right]}& \left(11\right)\end{array}$

[0068] The adaptation of the OFDM receiver components to the influence by pulse suppression is taken into account by the SINR after filter bank pulse suppression (in the SINR estimation module SE of the blanking unit BU, which estimates the signal quality for the OFDM subcarriers according to the residual distortions and the DME disturbances still present, in order to take them into further normal processing; i.e. carriers with residual interference are e.g. weighted less in the channel decoding, this is realized by appropriate scaling during LLR calculation), the equalization pulse suppression, the adaptation of the channel estimation (estimation in the channel module CE), the adaptation of the LLR calculation (in the LLR-calculation module LLR) and the ICI extinction (in the ICI cancellation unit ICI), as described below.

[0069] The SINR on the subcarriers k of an OFDM-symbol can be written as

[00007]$\begin{array}{cc}\mathrm{SINR}\left(k\right)=\frac{E^{{\mathrm{used}}^{}}\left(k\right)}{E^{{\mathrm{awgn}}^{}}\left(k\right)+E^{\mathrm{ICI}}\left(k\right)+E^{{\mathrm{pulse}}^{}}\left(k\right)}& \left(12\right)\end{array}$

where E.sup.used(k), E.sup.awgn(k), E.sup.ICI(k) and E.sup.pulse(k) represent the energies of the useful signal, noise, ICI and pulse interference after the pulse blanking on the subcarrier k. The following formulas are derived below.

[0070] The frequency response from the subcarrier k in the subband in is H.sub.m.sup.FBPB(k). The residual energy of the useful signal is then

[00008]$\begin{array}{cc}{E}^{{\mathrm{used}}^{}}\left(k\right)=\underset{m=0}{\overset{M-1}{.Math.}}.Math..Math.H_m^{\mathrm{FBPB}}\left(k\right).Math.{\left(\frac{1}{N}.Math.\underset{n}{.Math.}.Math..Math.c_m\left[n\right]\right)}^2.Math.E^{\mathrm{useful}}& \left(13\right)\end{array}$

[0071] The summing according to equation (13) takes place in practice for the run index n from 0 to K1. The expectation of the noise power is

[00009]$\begin{array}{cc}E.Math.\left\{E^{{\mathrm{awgn}}^{}}\left(\right)\right\}=E^{\mathrm{awgn}}.Math.\underset{k=0}{\overset{K-1}{.Math.}}.Math.{.Math.\underset{m=0}{\overset{M-1}{.Math.}}.Math.H_m^{\mathrm{FBPB}}\left(k\right).Math.C_m\left(-k\right).Math.}^2& \left(14\right)\end{array}$

where Cm(k) is the DFT transformation of the blanking window/Fade-out window cm[n].

[0072] The expected value of ICI energy is

[00010]$\begin{array}{cc}E.Math.\left\{E^{\mathrm{ICI}}\left(\right)\right\}=\underset{k}{\underset{k=0}{\overset{K-1}{.Math.}}}.Math.E^{\mathrm{LDACS}}\left(k\right).Math.{.Math.\underset{m=0}{\overset{M-1}{.Math.}}.Math.H_m^{\mathrm{FBPB}}\left(k\right).Math.C_m\left(-k\right).Math.}^2& \left(15\right)\end{array}$

[0073] In U. Epple, D. Shutin, M. Schnell, Mitigation of Impulsive Frequency-Selective Interference in OFDM Based Systems, IEEE Wireless Communications Letters, reference as above, an approximation of the ICI energy is described, which is only valid if the fading coefficients are independent but equally probable. However, this is not the case if pulse interference lasts longer than one sample value.

[0074] The energy of the soft-suppressed impulse noise cannot be calculated directly because it passes through channel deformation, reception filtering, filter-bank filtering, and sub-band selective soft pulse blanking. If a pulse occurs, however, it is suppressed and therefore the ICI is crucial for that actual SINR.

[0075] The pulse suppression leads to energy reduction on the data carriers and to ICI (see U. Epple, K. Shibli, M. Schnell, Investigation of Blanking Nonlinearity in OFDM Systems, reference as above). The energy reduction can be calculated by

[00011]$C\left(0\right)=\frac{1}{\sqrt{\sqrt{N}}}.Math.\underset{n=0}{\overset{N-1}{.Math.}}.Math.c\left[n\right]$

for SPB and CPB, as well as calculated by

[00012]$R^{{\mathrm{ICI}}^{}}\left(k\right)=\underset{k}{\underset{=0}{\overset{K-1}{.Math.}}}.Math.S\left(\right).Math.H\left(\right).Math.C\left(k-\right)$

for FBPB. After this, the values after the DFT (which converts the control information for the pulse suppression into the frequency range, from which the distortions introduced by the pulse suppression into the useful signal can then be derived) can be equalized with the help of the Pulse suppression equalization unit BE in the blanking mitigation unit BMU, i.e. these distortions in the useful signal are partially compensated before this is fed to the normal OFDM demodulation.

[00013]$\begin{array}{cc}{R}^{}\left(k\right)=\frac{R^{}\left(k\right)}{V_{\mathrm{LDACS}}\left(k\right)}& \left(16\right)\end{array}$

[0076] The argument k of V.sub.LDACS(k) can be used for Simple Pulse Blanking SPB and Combination Pulse Blanking CPB are omitted because all subcarriers are equally affected. Of course, the ICI energy also increases through this process. This must be considered.

[0077] If pilot-based channel estimation is used, the knowledge of the SINR value on each pilot is advantageous to improve the accuracy of the channel estimation. For this purpose, the SINR value of each pilot is calculated by equation (12) and passed to the channel estimation unit CE. Then MMSE-based channel estimation can be adapted to the SINR values (see U. Epple, K. Shibli, M. Schnell, Investigation of Blanking Nonlinearity in OFDM Systems, reference as above).

[0078] If we have an estimate of the sending symbols S (k), the ICI can be calculated by

[00014]$C\left(0\right)=\frac{1}{\sqrt{\sqrt{N}}}.Math.\underset{n=0}{\overset{N-1}{.Math.}}.Math.c\left[n\right]$

using the estimated channel frequency response (k) and the DFT of the cancellation coefficients C(k).

[0079] If a filter bank is used, the ICI can be calculated by equation (15) with the frequency response of the sub-band filter H.sub.m.sup.FBPB(k). The DFT values of the extinction coefficients C.sub.m(k) are then frequency-selective.

[0080] The derivation of the above equations is as follows:

[0081] For the analysis of the blanking effects, the sampled receive signal of an OFDM symbol after pulse blanking can be written as:

[00015]$\begin{array}{cc}\begin{array}{c}{r}^{}\left[n\right]=.Math.c\left[n\right].Math.r\left[n\right]\\ =.Math.c\left[n\right].Math.\left(s\left[n\right]*h\left[n\right]+n^{\mathrm{awgn}}\left[n\right]+i^{\mathrm{pulse}}\left[n\right]\right)\end{array}& \left(17\right)\end{array}$

[0082] The DFT is

[00016]$\begin{array}{cc}\begin{array}{c}{R}^{}\left(k\right)=.Math.C\left(k\right)*R\left(k\right)\\ =.Math.C\left(k\right)*\left(S\left(k\right).Math.H\left(k\right)+N^{\mathrm{awgn}}\left(k\right)+I^{\mathrm{pulse}}\left(k\right)\right)\end{array}& \left(18\right)\end{array}$

[0083] Equation (17) can be divided: the deformed useful signal, the deformed AWGN noise signal and the partially suppressed impulse noise. The deformed useful signal consists of the energy-reduced signal on all subcarriers and the inputted ICI.

[0084] The calculation of the energy reduction factor of the useful signal and the calculation of the exact ICI values after the pulse suppression, as well as the estimation thereof, are described below. In particular, the estimation of the reduced noise variance is described, assuming that the residual interference of the impulse interference after the suppression is negligible.

[00017]$\begin{array}{cc}{R}^{\mathrm{useful}+{\mathrm{ICI}}^{}}\left(k\right)=\left(S\left(k\right).Math.H\left(k\right)\right)*C\left(k\right)& \left(19\right)\\ R^{\mathrm{useful}+{\mathrm{ICI}}^{}}\left(k\right)=\underset{=0}{\overset{K-1}{.Math.}}.Math..Math.(S\left(\right).Math.H\left(\right).Math.C\left(k-\right)& \left(20\right)\end{array}$

where C(k)=C(k)*. This means that the windowing corresponds to a convolution of the spectrum without pulse suppression S(k) H(k) with the DFT transformation C(k) of the window coefficients of the pulse suppression c[n]. This sum can be divided into two parts. The first part contains the energy reduction of the useful signal on each subcarrier:

R.sup.useful(k)=S(k)H(k)C(0).(21)

with

[00018]$\begin{array}{cc}C\left(0\right)=\frac{1}{\sqrt{\sqrt{N}}}.Math.\underset{n=0}{\overset{N-1}{.Math.}}.Math..Math.c\left[n\right]& \left(22\right)\end{array}$

[0085] The energy reduction factor on the subcarrier k is

[00019]$\begin{array}{cc}V\left(k\right)={C\left(0\right)}^2={\left(\frac{1}{\sqrt{N}}.Math.\underset{n=0}{\overset{N-1}{.Math.}}.Math.c\left[n\right]\right)}^2& \left(23\right)\end{array}$

[0086] The second part consists of the ICI values

[00020]$\begin{array}{cc}{R}^{{\mathrm{ICI}}^{}}\left(k\right)=\underset{k}{\underset{=0}{\overset{K-1}{.Math.}}}.Math..Math.S\left(\right).Math.H\left(\right).Math.C\left(k-\right)& \left(24\right)\end{array}$

[0087] The exact ICI value can now be calculated if an estimation of the transmission values S(k) is present, see ICI cancellation unit. The ICI energy on the subcarrier k can be calculated via

[00021]$\begin{array}{cc}{E}^{\mathrm{ICI}}\left(k\right)={.Math.\underset{k}{\underset{=0}{\overset{K-1}{.Math.}}}.Math.\underset{\mathrm{zero}-\mathrm{mean},i.i.d.}{\underset{}{S\left(\right).Math.C\left(k-\right)}}.Math.}^2& \left(25\right)\end{array}$

[0088] The values for S(k) and C(k) are mean-value free and the values of S(k) are distributed independently of one another but identical, therefore the expected value

[00022]$\begin{array}{cc}E.Math.\left\{E^{\mathrm{ICI}}\left(k\right)\right\}=\underset{k}{\underset{=0}{\overset{K-1}{.Math.}}}.Math.E^{\mathrm{useful}}\left(\right).Math.{.Math.C\left(k-\right).Math.}^2& \left(26\right)\end{array}$

with E.sup.useful(k)=E{|S(k)e.sup.j.sup.k|).

[0089] If a filter-bank pulse suppression method is used, the energy reduction is subcarrier-selective. Since the frequency response of the sub-band filter H.sub.m.sup.FBPB(k) and the sub-band-selective cancellation coefficients cn[n] are known, equation (26), (equation 22) and (equation 24) can be adapted:

[00023]$\begin{array}{cc}{R}^{{\mathrm{ICI}}^{}}\left(k\right)=\underset{k}{\underset{=0}{\overset{K-1}{.Math.}}}.Math..Math.S\left(\right).Math.H\left(\right).Math.C\left(k-\right)& \left(27\right)\\ V\left(k\right)=\underset{m=0}{\overset{M-1}{.Math.}}.Math..Math.H_m^{\mathrm{FBPB}}\left(k\right).Math.{\left(\frac{1}{\sqrt{N}}.Math.\underset{n=0}{\overset{N-1}{.Math.}}.Math.c_m\left[n\right]\right)}^2.Math..Math.\mathrm{and}& \left(28\right)\\ E^{\mathrm{ICI}}\left(\right)={.Math.\underset{k}{\underset{=0}{\overset{K-1}{.Math.}}}.Math.\underset{m=0}{\overset{M-1}{.Math.}}.Math..Math.\underset{\mathrm{zero}-\mathrm{mean},i.i.d.w.r.t.k}{\underset{}{S\left(k\right).Math.H_m^{\mathrm{FBPB}}\left(k\right).Math.C_m\left(-k\right)}}.Math.}^2& \left(29\right)\end{array}$

[0090] The expected value is

[00024]$\begin{array}{cc}E.Math.\left\{E^{\mathrm{ICI}}\left(\right)\right\}=\underset{k}{\underset{=0}{\overset{K-1}{.Math.}}}.Math.E^{\mathrm{useful}}\left(k\right).Math.{.Math.\underset{m=0}{\overset{M-1}{.Math.}}.Math..Math.H_m^{\mathrm{FBPB}}\left(k\right).Math.C_m\left(-k\right).Math.}^2& \left(30\right)\end{array}$

[0091] For the estimation of the noise variance after the pulse suppression, the energy of the noise component after pulse suppression and DFT is equivalent

[00025]$\begin{array}{cc}{E}^{{\mathrm{awgn}}^{}}\left(\right)=.Math.\underset{k=0}{\overset{K-1}{.Math.}}.Math.\underset{\mathrm{zero}-\mathrm{mean},i.i.d.}{\underset{}{N\left(k\right).Math.C\left(-k\right)}}.Math.& \left(31\right)\end{array}$

[0092] The expected value is

[00026]$\begin{array}{cc}E.Math.\left\{E^{{\mathrm{awgn}}^{}}\right\}=E^{\mathrm{awgn}}.Math.\underset{k=0}{\overset{K-1}{.Math.}}.Math.{.Math.C\left(-k\right).Math.}^2& \left(32\right)\\ E.Math.\left\{E^{{\mathrm{awgn}}^{}}\right\}=E^{\mathrm{awgn}}.Math.\underset{k=0}{\overset{K-1}{.Math.}}.Math.{.Math.c\left(k\right).Math.}^2& \left(33\right)\end{array}$

[0093] If a filter bank is used, the calculation of the filter bank will change

[0094] Expected value for:

[00027]$\begin{array}{cc}E.Math.\left\{E^{{\mathrm{awgn}}^{}}\left(\right)\right\}=E^{\mathrm{awgn}}.Math.\underset{k=0}{\overset{K-1}{.Math.}}.Math.{.Math.\underset{m=0}{\overset{M-1}{.Math.}}.Math..Math.H_m^{\mathrm{FBPB}}\left(k\right).Math.C_m\left(-k\right).Math.}^2& \left(34\right)\end{array}$

[0095] The filter bank pulse-blanking method FBPB according to the invention comprises the following points: [0096] Combination of a filter bank with pulse-blanking in the blanking unit BU for suppressing frequency-selective impulse interference in OFDM, [0097] Algorithm for estimating DME in the sub-bands by exploiting the spectral shape, [0098] Adjustment of OFDM-demodulation and channel decoding to intercepted interference by pulse-blanking, [0099] For further improvement of the reception quality, implementation of an ICI cancellation by an iterative feedback, which reconstructs the assumed send signal SRS from the last decoding result (via a Connecting line from the module for channel decoding CD, module for channel estimation CE and module for channel multiplication ICM), estimates the actual disturbances in the useful signal (ICI cancellation unit (ICU)) and uses this estimate to subtract the disturbances (adder A) and/or uses in the frame of the SINR estimate (connection line UD to SINR estimation SE).

[0100] Through the receiver structure according to the invention, the bit error and packet error rate is lowered or with the same bit error/packet error rate a lower transmission power can be used or with the same transmission power, stronger disturbances or a smaller signal-to-noise ratio (in the case of the prior art, at least 45 nm (nautical mile)) can be permitted.

[0101] The filter bank pulse-blanking method FBPB according to the invention suffers from a high complexity because the filter operations must be applied M times. Even with an efficient polyphase structure, the complexity remains high.

[0102] In order to reduce the complexity of the interference suppression, a block-based method can be used for the frequency-selective division instead of the filter bank pulse blanking method FBPB, which transforms overlapping, Hann-windowed time blocks into the frequency range with the aid of a fast Fourier transformation FFT affected to frequency components. An adaptation of the OFDM components is not possible, since the integrated ICI cannot be calculated analytically so easily.

[0103] In order to avoid the spectral deformation of the impulse disturbance, the following describes a novel method according to the invention using a Hann-windowing and the interference suppression in the frequency range with the aid of a complexity-reduced block structure. This is hereinafter referred to as block-based frequency interference mitigation Method BBFIM. According to the invention, an FFT of length M is applied to the blocks of length M in the time domain, the DME interference is then suppressed in the frequency domain, and finally the time signal is recovered by an inverse Fast Fourier Transform (IFFT). The determination of M represents a target conflict between frequency selectivity and time selectivity.

[0104] Instead of the inflexible OFDM-window having a length of an OFDM-symbol as a block, the length of the window is reduced according to the invention and the DME suppression is advanced as shown in FIG. 7. The suppression process is applied in the frequency domain. In K. Kammeyer, K. Kroschel, Digital Signal Processing, Vieweg+Teubner Verlag, 7. Edition, 2009, a similar structure is used for the application of efficient filtering with a weighted overlap-add method. Instead of the FFT of a finite impulse response, BBFIM combines a spectral analysis with the interference suppression. This can be understood as time-variant filtering in the frequency domain.

[0105] Firstly, the filtered and sampled receive signal is split into overlapping blocks with index b and length M, the number of overlapping samples being at M/2:

r.sub.b[n]=r[n+b.Math.M/2](35)

with b{0, 1, 2, . . . } and n{0, 1, 2, . . . , M1}.

[0106] The blocks are then windowed with a Hann-window:

r.sub.b.sup.w[n]=r.sub.b[n].Math.w.sub.Hann[n](36)

with

[00028]$\begin{array}{cc}{}_{\mathrm{Hann}}\left[n^{}\right]=\{\begin{array}{cc}\frac{1}{2}.Math.\left(1-\cos \left(\frac{2.Math..Math.}{M}.Math.n^{}\right)\right)& \mathrm{if}.Math..Math.0n^{}<M\\ 0& \mathrm{else}\end{array}& \left(37\right)\end{array}$

[0107] If the degree of overlap is set to 50%, a Hann-window satisfies the characteristic that the sum of the windowed parts is the original signal. If other overlapping degrees are selected, a modified window can be used.

[0108] In this windowing according to the invention, the spectral form of the DME pulses is only slightly changed. FIG. 8 shows a non-windowed, a rectangular-windowed, and a Hann-windowed version of a DME signal. The DME double pulse is cut off by the rectangle-window. On the other hand, the Hann-window does not destroy the Gaussian form of the DME impulse.

[0109] FIG. 9 shows the power density spectrum of these signals. It is also apparent that all frequencies are disturbed by DME when a rectangle-window is used. The Hann-windowed signal, however, does not suffer from the cut-off of the DME pulse. Therefore, the frequency-selective interference suppression is improved by the use of a Hann-window. After the windowing, each block is transformed by means of FFT of length M into the frequency domain.

R.sub.b[k]=FFT.sub.M{r.sub.b.sup.w[n]}(38)

[0110] Now the pulse-like frequency-selective is suppressed by zeroing the FFT output values at the points where the DME interference (interference) has been detected. A simple implementation is again the power detection, where the values are set to zero whose energies at the output of the FFT exceed a certain value:

[00029]$\begin{array}{cc}{R}_b^{\mathrm{IM}}\left[k\right]=\{\begin{array}{cc}{R}_b\left[k\right],& \mathrm{if}.Math..Math.R_b\left[k\right]<.Math.\stackrel{\_}{P}\left[k\right]\\ 0,& \mathrm{else}\end{array}& \left(39\right)\end{array}$

[0111] The threshold value is again the determining parameter and P[k] represents the expected value of the L-DACS1 signal energy at the frequency position k. An investigation of a choice for is described below. Thereafter, an IFFT is applied to retrieve the time signal for each block:

r.sub.b.sup.IM[n]=IFFT.sub.M{R.sub.b.sup.IM[k]}(40)

[0112] Since the blocks overlap, the values in the time domain must also be summed overlapping:

[00030]$\begin{array}{cc}{r\left[n\right]}^{\mathrm{IM}}=\underset{b=-}{\overset{}{.Math.}}.Math..Math.r_b^{\mathrm{IM}}\left[n-b.Math.M/2\right]& \left(41\right)\end{array}$

[0113] In practice, by the 50% overlap of the blocks (see FIG. 7) the predecessor block and the successor block are considered in the sum formation according to equation (41), (see also equation (35)). The combination of Hann-windowing and FFT-block processing, is the key of the solution according to the invention to realize interference suppression at L-DACS1 with a limited complexity. A low-pass filter can also be omitted since the DME interference is frequency-selective suppressed. The target conflict between the resolution in time and time frequency range is achieved by selecting a suitable window size M.

[0114] To investigate computational complexity, the number of complex multiplications (CM) per OFDM symbol is examined. The signals are received in a frequency band of 2.5 MHz, where L-DACS1 is in the center of the spectrum, see FIG. 8. An FFT of length 256 is used for OFDM demodulation. Since the guard interval contains 44 additional values, 300 values must be processed per OFDM symbol. M/2.Math.log.sub.2(M/2) CM are necessary to calculate an FFT of length M, see K. Kammeyer, K. Kroschel, Digital Signal Processing, reference as above, ICI suppression is not considered here.

[0115] In Tab. I, the computational complexities of the four methods are shown in terms of the number of CM per OFDM symbol sorted in ascending order.

TABLE-US-00001 TABLE I Computing Complexities approach #CM additional complexity BBFIM 3600 SPB 19200 CPB 20096 combination unit FBPB 38400

[0116] A low-pass filter must be inserted before Simple Pulse-Blanking SPB and Combination Pulse-Blanking CPB. If one proceeds from a filter order of size 64, 30064=19.200 CM per OFDM symbol are necessary. The complexity of the filter is, of course, scalable. An additional FFT of length 256 for the CPB requires 256/2.Math.log 2 {256/2}=896 CM.

[0117] Subsequently, it is shown that, with respect to interference suppression, 32 subbands achieve the best result. For the selection of the number of sub-bands (FBPB) or Block size (BBFIM), an analysis is made. The bit error rate (BER) before the channel decoding is made for various DME levels with respect to effective TACAN/DME stations, whereby an effective TACAN/DME station stands for a duty cycle of 3.600 pulse pairs per second (ppps). Interferences of TACAN stations are considered in the simulations since this is the worst case. The DME double pulses are randomly distributed over time and are distributed equally to the carrier frequencies 500 kHz. The peak power of the DME pulses is 60 dBm. The highest possible TACAN pulse amplitude is used.

[0118] An E.sub.b/N.sub.0 value of 10 dB is assumed below. Assuming the link budget of L-DACS1, see also M. Sajatovic, B. Haindl, U. Epple, T. Grupl, Updated LDACS1 System Specification, reference as above, this is equivalent to an average receive level of 99.0 dBm in the en-route flight mode, i.e. in the air.

[0119] There is perfect interference detection, i.e. the signal is then set to zero when the instantaneous power of DME exceeds that of L-DACS 1. This is genius knowledge and the recipient is not known in practice, but should be sufficient for this analysis.

[0120] In FIG. 13, the performance at various values for the number of sub-bands for FBPB is shown. The worst score is 8 sub-bands. If the number of sub-bands is increased to 32, the BER decreases. A power loss is observed with more than 32 sub-bands. If the number of sub-bands is increased, the bandwidth of the sub-band filters decreases, but the pulse response in the time domain is lengthened and the DME signal is becoming increasingly smeared. In the following, 32 sub-bands are used since this provides the best results for all DME levels.

[0121] In FIG. 14 shows the performance for different block sizes at BBFIM. The best result is a block size of 64. If the block size is decreased the frequency selectivity is increased, on the other hand if the block size is increased the time selectivity increases. The following a block size of 64 is selected.

[0122] As a prototype filter, a raised cosine filter with order 64, as well as 32 sub-bands, is used with FBPB. This results in 30064=19.200 CM for windowing each sample and 30032/2log.sub.2 {32/2}=19.200 CM for the FFT. With these values, the complexity of FBPB (38.400 CM) is about twice as high as for SPB. This parameter set is also used for the performance analysis described below.

[0123] The block size at BBFIM is set to 64, since this achieves the best results. The windowing needs 2300=600 CM. An FFT and an IFFT of length 64 suggests to book with 64/2log.sub.2 {64/2}=160 CM. In an OFDM symbol, an average (2300)/64=9.375 blocks are inserted. That is, in sum, BBFIM requires 600+21.500=3.600 CM.

[0124] BBFIM has the least complexity, followed by SPB, whose complexity is about 5 times higher. The complexity of FBPB is about twice higher than SPB. CPB needs the additional combination unit; therefore, it suffers from additional complexity.

[0125] The suppression performance of all the methods set forth above is very dependent on the detection of the interference. Detection is easier for the proposed approaches because they are applied on the sub-bands (FBPB) or FFT output values (BBFIM), where are mainly DME power. This is not the case with SPB and CPB, so it can be assumed that in practical systems the performance of Simple Pulse-Blanking SPB and CPB falls even further compared to FBPB and BBFIM.

[0126] In the simulations the threshold decisions see, for example, S. Brandes, S. Gligorevic, M. Ehammer, T. Grupl, R. Dittrich, Expected B-AMC System Performance, reference as above, are replaced by the following genius-based deciding rule: Each receive value is blanked if the instantaneous power of DME on this sample is higher than the average power of L-DACS on that sample.

[0127] To apply the combining step at CPB, an estimate of the SINR values on the subcarriers in both paths is made beforehand. A combination can then be realized via maximum-ratio-combining. The simulations use genius knowledge. In practical systems, an estimation error of the SINR values results in a loss of performance.

[0128] The overall performance of the system depends only on the number of lost packets. Therefore, the packet error rate (PER) after the decoding is regarded, see M. Sajatovic, B. Haindl, U. Epple, T. Grupl, Updated LDACS1 System Specification, reference as above, whereby 728 information bits form a packet. These bits are encoded with a code rate of 0.45 and are modulated with QPSK. This is the most robust modulation and coding scheme of L-DACS1. An L-DACS 1 data frame consists of 54 OFDM symbols and carries 3 packets. The target packet error rate of L-DACS1 is 0.01. This merit number is a better choice compared to the bit error rate since the performance of the overall system depends only on the number of lost packets.

[0129] Above all the frequency diagrams of DME and L-DACS1 stations determine the influence of interferences. Instead of adopting a frequency plan, a model is used which varies only with respect to the number of DME stations, carrier frequencies, and reception powers. An overlay of many DME stations is assumed in each simulation. The simulation parameters for DME stations are shown in Tables II and III for moderate and strong DME interference.

TABLE-US-00002 TABLE II moderate DME interference center freq. duty cycle distance peak received power 500 kHz 2 .Math. 3600 ppps 26 km 60 dBm 500 kHz 2 .Math. 3600 ppps 270 km 70 dBm +500 kHz 2 .Math. 3600 ppps 26 km 60 dBm +500 kHz 2 .Math. 3600 ppps 270 km 70 dBm

[0130] The DME simulation parameters are carrier frequency relative to the L-DACS1 carrier frequency, the duty-cycle of the DME-double pulses in ppps, and the peak power of the receive level of DME in dBm.

[0131] An E.sub.b/N.sub.0 value of 4.6 dB applies. If the link budget of L-DACS1 is used, see M. Sajatovic, B. Haindl, U. Epple, T. Grupl, Updated LDACS1 System Specification, reference as above, then this is equivalent to a reception level of 104.4 dBm in flight mode en-route.

[0132] In FIG. 15 the BER is shown before the channel decoding for FBPB (M=32) for different values of the Power Detection Parameter for different number of effective DME stations. If a DME fault is not active, a 10 is advantageous if the number of DME stations is 10, then the best value is 8, followed by 10. Therefore, a value of =10 is a good value.

[0133] The worst interference is expected on L-DACS aircraft, so only FL is simulated. Furthermore, interference from TACAN stations with the highest possible pulse amplitude and duty cycle is assumed because this is the worst case. If we take the link budget of L-DACS as the basis, see M. Sajatovic, B. Haindl, U. Epple, T. Grupl, Updated LDACS1 System Specification, reference as above, thus, an E.sub.b/N.sub.0 value of 6.0 dB corresponds to an average reception level of 103.0 dBm in the en-route flight mode.

[0134] In FIG. 16, the packet error rate is shown for a scenario without DME interference and for various E.sub.b/N.sub.0 values. A threshold value 10 is necessary in order to limit the influence of interference suppression, if no interference is present. It is noteworthy that the PER curve of 12 falls below the curve of gen-sampled DME detection. This is because noisy interference-free sample values are set to zero, which is advantageous.

[0135] In FIG. 17, a scenario with a moderate DME disturbance is shown. The best result is to achieve thresholds of 8, 10 and 12.

[0136] In cases of severe DME disturbance, cf. FIG. 18, a threshold of 6 is the best, followed by a value of 8.

[0137] Table IV gives an overview of the loss of various thresholds if you are looking for a PER of 1%. If the focus is on reception in scenarios with little DME interference, a threshold of 10 should be selected. In the case of a severe fault, the parameter to be selected drops to 8.

TABLE-US-00003 TABLE IV Loss in dB at different thresholds compared to the best threshold PER = 1% scenario, .fwdarw. 4 6 8 10 12 14 no DME fail 0.5 0.12 0.04 0 0 moderate DME fail 0.45 0 0 0 0.1 heavy DME 1.4 0 0.15 0.5 0.7 1.0

[0138] In FIG. 19 the BER is shown before the decoding of BBFIM (M=64) for different threshold values with varying effective number of DME stations. If no DME is active, a 12 is advantageous. An effective number of 10 DME stations achieve the best result at values 10 and 12.

[0139] FIG. 20 shows the PER for strong DME interference Again, the best threshold is 10, followed by 12.2. Table V gives an overview of the loss when using different thresholds and a PER of 1%.

TABLE-US-00004 TABLE V Loss in dB at different thresholds compared to the best threshold PER = 1% scenario, .fwdarw. 4 6 8 10 12 14 no DME fail fail 0.5 0.18 0.05 0 moderate DME fail 1.0 0.3 0.1 0 0 heavy DME fail 0.9 0.15 0 0.15 0.3

[0140] A fixed threshold of 12 is a good compromise since the performance is the best in moderate DME disturbance and it is close to the optimum threshold at high DME disorder.

[0141] In FIG. 21, an overview of the PER curves for the three DME scenarios is given once again when the values =10 and =12 are used.

[0142] FIG. 10 shows the PER for varying number of ppps. The peak power of the DME receive signal is 60 dBm. The frequency offset of the DME channels are equally distributed at 0.5 MHz. The position to of the DME pulses is random. Assuming a target error rate of 0.01, FBPB does not fail under a duty cycle of 10.000 ppps, followed by BBFIM with 6.000 ppps. CPB and SPB already fail at a duty cycle of 2.500 ppps and 1.500 ppps.

[0143] A worst-case DME scenario is assumed in order to demonstrate the robustness of the procedures, see the following table III.

TABLE-US-00005 TABLE III Strong DME interference center freq. duty cycle distance peak received power 500 kHz 3.600 ppps 26 km 50 dBm 500 kHz 2 .Math. 3.600 ppps 26 km 60 dBm 500 kHz 4 .Math. 3.600 ppps 270 km 70 dBm +500 kHz 3.600 ppps 26 km 50 dBm +500 kHz 2 .Math. 3.600 ppps 84 km 60 dBm +500 kHz 4 .Math. 3.600 ppps 270 km 70 dBm

[0144] The DME simulation parameters are as follows: carrier frequencies relative to the carrier frequency of L-DACS 1, the duty-cycle of the DME-double pulses in ppps, the distance between DME ground station and LDACS receivers on the aircraft, and the peak power of the reception signals in dBm. The aviation radio channel is also valid for the DME signal. Therefore, the same en-route channel-scenario is used for DME signals, i.e. the echo paths are also received.

[0145] FIG. 11 shows the robustness for varying E.sub.b/N.sub.0 values. The loss of FBPB and BBFIM to the interference free case is for a PER of 0.01 at approximately 2 dB and 3 dB. The distance to CPB is nearly 6 dB, since CPB suffers enormously from the spectral spreading of the DME pulses. Simple Pulse-Blanking SPB fails completely because the ICI is too high.

[0146] The filter bank pulse-blanking method FBPB according to the invention with sub-band-selective pulse blanking has the best performance under all interference suppression methods considered. In particular, a filter bank with frequency-selective pulse-blanking is used in the sub-bands, whereby 32 sub-bands achieve the best result with regard to BER if an L-DACS1 receiver having a bandwidth of 2.5 MHz is used for DME interference what is equal to a sub-band distance of 78.125 kHz. In combination with pulse-blanking and power detection, a fixed power detection threshold value in the range 10-12 achieves good results for all DME pulse abundances; disadvantage is a high complexity.

[0147] The second block-based frequency-selective method according to the invention BBFIM for interference suppression offers the second best interference suppression and has the least complexity. In particular, efficient block processing is combined with a Hann-windowing. The best result is a block size of 64 if a bandwidth of 2.5 MHz is used for an L-DACS1 receiver with DME interference. It can also be combined with power detection with an optimal threshold of 12 for all DME pulse frequencies. Therefore, it is the best choice when low complexity is required.

[0148] Additional advantages and modifications will readily occur to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details and illustrative examples shown and described herein. Accordingly, various modifications may be made without departing from the spirit or scope of the general inventive concept as defined by the appended claims and their equivalents.