Mobile speed and doppler frequency estimation using cyclostationarity

Embodiments of the invention exploit cyclostationarity of linearly modulated signals, transmitted through fading channels, to provide robust blind and data-aided mobile speed estimators. Embodiments of the invention utilize at least two methods of cyclic-correlation- and cyclic-spectrum-based methods and extension to space-time speed estimation at the base station in macrocells. In comparison with background art methods, the new estimators of the embodiments of the invention can be used without any need for pilot tones, and are robust to additive stationary noise or interference of any color or distribution. In addition, embodiments of the invention can also be implemented blindly, which can increase the data throughput. Performance results of the estimators of the embodiments of the invention are illustrated via extensive Monte Carlo simulation results.

FIELD OF THE INVENTION

Embodiments of the invention may generally relate to mobile communication systems. More specifically, embodiments of the invention are used for the estimation of the speed of the mobile units in mobile communication systems.

BACKGROUND OF THE INVENTION

Speed of a mobile unit in a communications network may relate to the rate of wireless mobile channel variations. Consequently, one may wish to be able to obtain estimates of the speed of a mobile unit, in order to aid such functions as, for example, handoff, adaptive modulation, adaptive equalization, power control, etc.

Speed estimation may be done based on signals received at the mobile unit and/or at a base station or other fixed station of a network. However, received signals are generally corrupted by noise, fading, and the like.

Speed estimation, or equivalently, Doppler frequency estimation (i.e., because Doppler frequency is proportional to speed) may employ, for example, crossing-based methods or covariance-based methods. However, the accuracy of such estimates may tend to drop with increasing amounts of noise, interference, fading, etc. Furthermore, such estimators tend to be complex to implement and generally require the use of pilot symbols and/or signals.

Accurate estimation of the mobile speed which reflects the rate of wireless mobile channel variations is important for many applications such as handoff, adaptive modulation and equalization, power control, etc. Almost all background art methods for speed estimation are based on transmitted pilot tones.

SUMMARY OF THE INVENTION

One embodiment of the invention is a method of estimating a Doppler frequency corresponding to a mobile station in a communication system, comprising correlating one or more received signals that contain no pilot symbols, the signals being correlated with themselves and/or with one another.

Another embodiment of the invention is a method of estimating a Doppler frequency corresponding to a mobile station in a communication system, comprising: receiving a signal from one or more mobile stations; differentiating the received signal; correlating the received signal; correlating the differentiated received signal; processing the correlated received signal and the correlated differentiated received signal; and generating the estimate of the Doppler frequency from the processed signals.

Yet another embodiment of the invention is a method of estimating a Doppler frequency corresponding to a mobile station in a communication system, comprising: receiving a signal from one or more mobile stations; correlating the received signal; windowing and discrete time Fourier transform (DTFT) processing the correlated received signal; processing the windowed and (DTFT) processed correlated received signal; and generating the estimate of the Doppler frequency from the processed signals.

Another embodiment of the invention is a method of estimating a Doppler frequency corresponding to a mobile station in a communication system, comprising: receiving signals at multiple antennas from one or more mobile stations; cross-correlating the multiple received signals; computing phase for the cross-correlated multiple received signals; processing the computed phase for the cross-correlated multiple received signals; windowing and discrete time Fourier transform (DTFT) processing the cross-correlated multiple received signals; computing arg max of a magnitude of the windowed and DTFT processed multiple received signals; summing the computed arg max of the magnitude of the windowed and DTFT processed multiple received signals; and generating the estimate of the Doppler frequency from the summed computed arg max of the magnitude of the windowed and DTFT processed multiple received signals.

Yet another embodiment of the invention is a processor-readable medium containing processor-executable code that, when executed by a processor, causes the processor to implement a method of estimating a Doppler frequency of a received signal corresponding to one or more mobile stations in a communication system, comprising: receiving a signal from one or more mobile stations; differentiating the received signal; correlating the received signal; correlating the differentiated received signal; processing the correlated received signal and the correlated differentiated received signal; and generating the estimate of the Doppler frequency from the processed signals.

DETAILED DESCRIPTION

Various embodiments of the invention may estimate mobile station speed based on a blind cyclostationary estimation technique. This may be implemented in hardware, software, and/or firmware, and/or it may be incorporated into mobile and/or fixed stations of a network.

Embodiments of the invention provide speed estimators that exploit the cyclostationarity of linearly modulated signals. The new estimators can be applied blindly, without using training symbols, which increase the data throughput. On the other hand, for the case where pilot symbols are available, embodiments of the invention are estimators which provide more accurate estimates, compared to blind methods. Essentially, cyclostationary-based estimators are not sensitive to additive stationary noise or interference of any color or distribution, which are known to affect pilot-tone-based approaches. The robustness of the new estimators to non-isotropic scattering and the variations of line-of-sight (LOS) is also investigated. Extensive Monte Carlo simulations are conducted to illustrate the performance of the new estimators.

The following paragraphs provide detailed descriptions of the signal, channel and noise models used in embodiments of the invention. In particular, the received lowpass complex envelope of a linearly modulated signal, transmitted through a frequency-flat fading channel, can be expressed as Equation (1) below:
z(t)=h(t)s(t)+ν(t),  (1)
where s(t)=Σmw(m)g(t−mT), and we have the following definitions w(m)h(t) fading channel,w(m) stationary random sequence of transmitted symbols chosen from a finite-alphabet complex constellation,g(t) convolution of the transmitter's signaling pulse and the receiver filter which, without loss of generality, is a raised cosine with rolloff factor βε[0,1],ν(t) a complex stationary process which represents the summation of noise and interference, independent of h(t) and w(m),T symbol period.
z(t)=h(t)s(t)+ν(t)  (1)
where s(t)=Σmw(m)g(t−mT), and we have the following definitions:h(t) fading channel,w(m) stationary random sequence of transmitted symbols chosen from a finite-alphabet complex constellation,g(t) convolution of the transmitter's signaling pulse and the receiver filter which, without loss of generality, is a raised cosine with rolloff factor βε[0,1], andν(t) a complex stationary process which represents the summation of noise and interference, independent of h(t) and w(m), T symbol period.

The unit-power fading process h(t) includes the random diffuse component hd(t) and the deterministic LOS component, as shown in Equation (2) below:

h⁡(t)=1K+1⁢hd⁡(t)+KK+1⁢ⅇ-j2π⁢⁢fD⁢t⁢⁢cos⁢⁢α0+jϕ0.(2)
In Equation (2), hd(t) is a zero-mean unit-variance stationary complex Gaussian process and the Rician factor K is the ratio of the LOS power to the diffuse power. In the LOS component we have fD=ν/λ=νfc/c as the maximum Doppler frequency in Hz, ν is the mobile speed, λ is the wavelength, fcis the carrier frequency, and c is the speed of light. Furthermore, j2=−1, and α0and φ0stand for the angle-of-arrival (AOA) and the phase of the LOS component at the receiver, respectively.

With von Mises distribution for the AOA, the autocorrelation function of h(t), defined by rh(τ)=E[h(t)h*(t+τ)], where E[.] and * denote mathematical expectation and complex conjugate, respectively, is given by Equation (3):

rh⁡(τ)=KK+1⁢exp⁡(j2π⁢⁢fD⁢τ⁢⁢cos⁢⁢α0)+1K+1×I0⁡(κ2-4⁢π⁢⁢fD2⁢τ2+j4π⁢⁢κ⁢⁢fD⁢τ⁢⁢cos⁢⁢α)I0⁡(κ),(3)
where αε[−π,π) is the mean AOA of the diffuse component, κ≧0 controls the width of the diffuse component AOA, and I0(.) is the zero-order modified Bessel function of the first kind. Equation (3) is an empirically-verified extension of the well-known Clarkes' model.

The following paragraphs provide detailed descriptions of the cyclostationarity of the received signal used in embodiments of the invention. In particular, the time-varying autocorrelation of the received signal z(t), defined by rz(t;τ)=rz(t,u)=E[z(t)z*(u)] with u=t+τ, can be shown in Equation (4) to be

rz⁡(t;τ)=rh⁡(τ)⁢rs⁡(t;τ)+rv⁡(τ),⁢where(4)rs⁡(t;τ)=∑m⁢∑n⁢r~w⁡(n-m)⁢g⁡(t-mT)⁢g*(t+τ-nT),(5)
in which {tilde over (r)}w(n−m)=E{w(m)w*(n)}. It is well known that s(t) is a cyclostationary random process since rs(t;τ) is periodic in t, with period T. Consequently we have rz(t+kT;τ)=rz(t;τ),t,τ, which indicates that z(t) is cyclostationary as well, with the same period T.

The cyclic correlations which are the Fourier coefficients of rz(t;τ) for cyclic frequencies k/T=0, ±1/T, ±2/T, . . . , are given by Equation (6)

Ωs⁡(k;f)=1T⁢G⁡(f)⁢G*(f-kT)⁢Ω~w⁡(f),(7)
where G(f ) is the Fourier transform of g(t) and {tilde over (Ω)}w(f) is the power spectrum of the sequence of transmitted symbols {w(m)}, which is also the Fourier transform of {tilde over (r)}w(n−m)

The following paragraphs provide detailed descriptions of the cyclostationary-based estimators used in embodiments of the invention. In particular, for an arbitrary proper complex process z(t), it is known that rż(t;τ)=rż(t,u)=∂2rż(t;u)/∂t∂u, where dot denotes differentiation with respect to time t. According to Equation (4) we have

It is easy to show that rs{dot over (s)}(t;τ), r{dot over (s)}s(t;τ) and r{dot over (s)}(t,τ) are periodic w.r.t. t with period T. Therefore ż(t) is cyclostationary as well, with the same period T. With the assumption of isotropic scattering and no LOS, i.e., rh(τ)=J0(2πfDτ) where J0(.) is the zero-order Bessel function of the first kind, one obtains rh{dot over (h)}(0)=r{dot over (h)}h(0)=0 and r{dot over (h)}(0)=−rh(τ)|Σ=0=2π2fD2, where prime denotes differentiation with respect to τ. Therefore, the cyclic correlation of ż(t) at τ=0 can be obtained by calculating the k-th Fourier coefficients of Equation (8) w.r.t. t is:
Rż(k;0)=2π2fDRs(k;0)+R{dot over (s)}(k;0)+r{dot over (ν)}(0)δk,  (10)
where Rs(k; 0) and R{dot over (s)}(k; 0) are the k-th Fourier coefficients of Equation (5) and Equation (9), respectively. To obtain a noise free estimator for fD, we choose k≠0 and divide Rż(k;0) in (10) by Rz(k;0) in (6), which after rearranging the terms gives us

The cyclic correlations of z(t) can be estimated from the discrete-time-version signal of z(t), oversampled at a rate of P/T and represented by {z[n]}n=0N−1in Equation (12) as:

R^z.⁡(k;P⁢⁢τd/T)=1N⁢∑n=0N-τd-1⁢z.⁡[n]⁢z.*[n+τd]⁢ⅇ-j2π⁢⁢kn/P.(13)
Note that Rs(k;0) and R{dot over (s)}(k;0) in Equation (11) depend on the statistics of the symbols {w(m)}, as well as the pulse shape.

Assuming the transmitted data symbol sequence {w(m)} is white and zero-mean, Equation (7) simplifies to:

Ωs⁡(k;f)=σw2T⁢G⁡(f)⁢G*(f-kT),(14)
where σw2=E[|w(m)|2] is the average power of the sequence. It is easy to see that Ωs(k;f)=0,|k|≧2, when g(t) is a raised cosine. By taking the inverse Fourier transform of Equation (14), one can show that

Rs⁡(k;τ)=σw2T⁢ⅇjπ⁢⁢k⁢⁢τ/T⁢∫-∞∞⁢G⁡(f+k2⁢T)×G*(f-k2⁢T)⁢ⅇ-j2π⁢⁢f⁢⁢τ⁢ⅆf,(15)
which results in

Based on Equation (9) and Equation (14), we have:
Ω{dot over (s)}(k;f)=σw2T−1{hacek over (G)}*(f){hacek over (G)}*(f−k/T),
where {hacek over (G)}(f)=j2πfG(f). Similar to Equation (15), one obtains Equation (17) as:

Rs.⁡(k;τ)=σw2T⁢ⅇjπ⁢⁢k⁢⁢τ/T⁢∫-∞∞⁢G⋓⁡(f+k2⁢T)×G⋓*(f-k2⁢T)⁢ⅇ-j2π⁢⁢f⁢⁢τ⁢ⅆf,(17)
which gives us Equation (18) as:

Rs.⁡(1;τ)=∫-β/(2⁢T)β/(2⁢T)⁢(f2-14⁢T2)⁢cos2⁡(π⁢⁢fTβ)⁢ⅇ-j2π⁢⁢f⁢⁢τ⁢ⅆf×σw2⁢T⁢⁢π2⁢ⅇjπτ/T.(18)
By substituting Equation (16) and Equation (18) into Equation (11), the blind speed estimator can be written in Equation (19) as:

If instead we choose the fixed training sequence w(m)=(−1)mσw, then it can be shown in Equation (21) and Equation (22) that for the Data-Aided Speed Estimator:

Rs⁡(1;τ)=σw2⁢T4⁢exp⁢{jπτ/T},(21)Rs.⁡(1;τ)=-π2⁢σw24⁢T⁢exp⁢{jπτ/T},(22)
which interestingly do not depend on the rolloff factor β. Following the same approach that resulted in Equation (19) and Equation (20), the data-aided speed estimator can be derived in Equation (23) as:

By taking the Fourier transform of Equation (6) w.r.t. τ, for k≠0, we obtain in Equation (24):
Ωz(k;f)=Ωh(f)Ωs(k;f), k≠0  (24)
wheredenotes convolution. Note that by choosing k≠0, the effect of noise is disappeared. Now the idea is to obtain fDfrom the estimate of Ωz(k;f). The consistent cyclic spectrum estimate can be obtained by windowing {circumflex over (R)}z(k;Pτd/T) in Equation (12) with the window W(2Lg+1)(τd), defined over [−Lg,Lg] and gives Equation (25) as:

For the Data-Aided Speed Estimator, based on Equation (21), Ωs(1;f) is an impulse at f=1/(2T). Therefore Ωz(1;f) is simply the Doppler spectrum Ωh(f) shifted from f=0 to f=1/(2T). Hence, we can use the same technique to estimate fDi.e., as shown in Equation (26):

In this section, embodiments of the invention are extended to a system for a multi-antenna cyclostationary-based estimator to improve the performance. Consider a uniform linear antenna array at an elevated base station (BS) of a marcocell, composed of L omnidirectional unit-gain elements, with element spacing d. The BS experiences no local scattering, whereas the single-antenna mobile station (MS) is surrounded by local scatters. Let the received signals at the l-th element be: zl(t)=hl(t) s(t)+νl(t), l=1, 2, . . . , L, which is similar to Equation (1).

Then the time-varying space-time crosscorrelation function between Za(t) and zb(t), 1≦a≦b≦L, defined by rz((b−a)Δ,(t;τ))=E[za(t)zb*(t+τ)] such that Δ=d/λ, is given in Equation (27) as:
rz((b−a)Δ,(t;τ))=rh((b−a)Δ,τ)rs(t;τ)+rν(τ)δb−a,  (27)
where the space-time channel crosscorrelation, defined by:
rh((b−a)Δ,τ)=E[ha(t)hb*(t+τ)],
is given in Equation (28) as:

Note that in Equation (29), α0=α is assumed, due to the small angle spread at the BS. With τ=0 and a≠b in Equation (27), the time-varying spatial cross-correlation function in Equation (27) can be written in Equation (30) as:
rz((b−a)Δ,(t;0))=rh((b−a)Δ,0)rs(t;0),  (30)
where rh((b−a)Δ, 0) for macrocells is given in (29) and rs(t; 0) can be obtained from Equation (5). Since noise components of different elements are independent, the effect of noise has not shown up in Equation (30) as a≠b. As we will see later in Equation (31), cos α can be estimated by looking at the phase of rz((b−a)A, (t;0)) in Equation (30), due to the special form of rh((b−a)Δ, 0) in Equation (29) and also because rs(t; 0) in Equation (30) is real and positive.

When the BS experiences such heavy nonisotropic scattering κ≧14.6, it is straightforward to verify that there is a strong peak in the power spectrum of each branch Ωhl(f), at fDcos α, even when there is no LOS. On the other hand, based on Equation (14), it can be shown that Ωs(1;f), for a zero-mean i.i.d. sequence {w(m)}, is a uni-modal spectrum centered at f=1/(2T), with a bandwidth of β/T. In addition, for the training sequence w(m)=(−1)mσw, one can see from Equation (21) that Ωhl(f) is an impulse at f=1/(2T) as well. Therefore, according to Equation (24) and due to the impulsive shape of Ωhl(f) when κ is large, we conclude that the peak of Ωzl(1;f) for each branch happens at f=fDcos α+1/(2T). Now relying upon both cyclic spectrum and the spatial information provided by multiple antennas, we propose the following space-time estimator.

Based on Equation (30), we can estimate cos α via
côs α≈∠{circumflex over (R)}z(Δ,(0;0))/(−2πΔ),  (31)
where ∠ denotes the phase of a complex number and {circumflex over (R)}z(Δ, (0; 0)) is the estimate of

R^z⁡(Δ,(0;0))=(L-1)-1⁢∑l=1L-1⁢R^zl⁡(Δ,(0;0))whereR^zl⁡(Δ,(0;0))=N-1/2⁢∑n=0N-1⁢zl⁡(n)⁢zl+1*⁡(n),⁢l∈[1,L-1],
is the l-th adjacent-antenna-pair estimate of Rz(Δ, (0; 0)). It is worth emphasizing that if noise components νl(t), l=1, 2, . . . , L are spatially correlated, we need replace {circumflex over (R)}z(Δ, (0; 0)) in (31) with {circumflex over (R)}z(Δ, (1; 0)) in order to have a noise-free estimate of côs α. Finally, fDcan be estimated via Equation (32) as:

f^D=Pcos⁢⁢α⁢⁢LT⁢∑l=1L⁢-12⁢T+arg⁢⁢f⁢⁢max⁢Ω^zl⁡(1;f),(32)
where {circumflex over (Ω)}zl(1;f) can be obtained via Equation (25). Note that the cyclic-spectrum-based estimator in Equation (32) can be applied either blindly or with the aid of the training sequence w(m)=(−1)mσw.

In this section, we first evaluate the performance of the proposed single antenna estimators using Monte Carlo simulation and next investigate the effect of noise, nonisotropic scattering, and LOS. Then we present the performance of our space-time estimator. The fading channel is generated using a spectral method from the background art. The bandlimited Gaussian noise ν(t), with the autocorrelation σ2νg(τ), is simulated via the same method. It is worth noting that our algorithm does not put any constraint on the distribution of both the fading process and the noise, although only for simulation purposes we generate them as complex Gaussian processes. We define signal-to-noise ratio SNR=σ2w=σ2ν. The performance of the estimator is measured by using the root mean squared error (RMSE) criterion E {[(fD−fD)2]}1/2.

In all the simulations we have, the roll-off factor β=0.5, oversampling rate P=8, and the symbol duration T=0:001 second. Each data-aided estimation uses M=256 symbols and 200 Monte Carlo simulations, whereas blind algorithms use M=512 4-QAM i.i.d. symbols 400 Monte Carlo simulations. The abbreviations DA, NDA, CC, and CS in the figures refer to data aided, non-data aided (blind), cyclic correlation, and cyclic spectrum, respectively. For example, DA-CC in a legend box represents a data-aided cyclic correlation based speed estimator.

We first investigate the performance of single antenna estimators, illustrated fromFIG. 1-FIG.6.FIG. 1shows the performance of three estimators DA-CC, NDA-CC, and DACS when the channel is isotropic, κ=0, Rayleigh fading with SNR=10 dB. Obviously, the DA-CS is the best, and DA-CC and NDA-CC have comparable estimation errors at small Dopplers, while DA-CC performs better than NDA-CC at large Dopplers. The robustness of these estimators against noise is shown inFIG. 2in isotropic Rayleigh fading, for a fixed fDT=0.1. Again, the DA-CS exhibits the best performance.FIG. 3andFIG. 4demonstrate the effect of nonisotropic scattering parameters κ and α0. As one can see, the CS-based method is less sensitive to than the CC-based techniques but more sensitive to α. Based onFIG. 5andFIG. 6, we have similar observation regarding the effect of the LOS parameters K and α0. Note that for all the curves inFIG. 3-FIG.6, we have fDT=0.1 and SNR=10 dB.

Now we evaluate the performance of the space-time CS-based estimator in Equation (32). In the simulation, L=4 spacetime correlated complex Gaussian processes for the macrocell scattering scenario of K=0, K=100, and α=60° are generated, with Δ=½. For each branch, the noise power is the same as the single antenna case, with SNR=10 dB per branch.

FIG. 7illustrates the estimation error, for both DA and NDA approaches. As we see, the DA-CS method provides excellent performance over a wide range of Dopplers. The curve for the DA-CS method for L=1 is also shown inFIG. 7, which clearly shows the advantage of using more than one antenna. Apparently, the presence of LOS will further improve the performance.

FIG. 8shows an exemplary conceptual block diagram corresponding to an embodiment of the invention. In particular,FIG. 8discloses an antenna providing a receiver81that outputs a received time-domain signal z(t). The received time-domain signal z(t) is fed to a differentiator82that outputs a differentiated version of the received time domain signal ż(t). As shown inFIG. 8, both z(t) and ż(t) are sampled to produce z[n] and ż[n], respectively. The sampled versions of the signals z[n] and ż[n] are fed to correlator83and correlator84, respectively. The outputs of the correlators83,84are fed to a divider85and the output of the divider85is fed to a summer86where an additional factor is added to the result. A square root function87is applied to the output of the summer85and the result is fed to a multiplier88where an additional factor is applied. The output of the multiplier provides an estimate of the Doppler frequency, {circumflex over (f)}D, using the technique suggested by Equation (23) above. Note that the receivers in thisFIG. 8, as well as those shown inFIG. 9AandFIG. 9B, may be used to obtain low-pass complex envelopes of received signals.

FIG. 9Ashows an exemplary conceptual block diagram corresponding to a portion of another embodiment of the invention. In particular,FIG. 9Adiscloses In particular, an antenna providing a receiver90that outputs a received time-domain signal z(t). The received time-domain signal z(t) is sampled to produce z[n] which is fed to correlator92. The outputs of the correlator92is fed to a Windowing discrete time Fourier transform (DTFT)93. The maximum value of the magnitude of the Windowing DTFT93is determined by the function block94. The output of function block94is fed to a summer86where a factor (e.g., ½T) is added to the result. A magnitude function block96is applied to the output of the summer and the result is fed to a multiplier98where an additional factor (e.g., P/T) is applied. This portion of the embodiment may be used to compute individual components of an estimator, where the individual components correspond to signals received by multiple antennas.

FIG. 9Bshows an exemplary conceptual block diagram that may incorporate the block diagram shown inFIG. 9A. As noted above, multiple antennas may be used to provide an estimate of the Doppler frequency, {circumflex over (f)}D. As an example,FIG. 9Bshows two antennas feeding two receivers91A,91B. However, the invention is not thus limited. In this embodiment, which may be used to compute the estimate as suggested by Equation (32), each individual signal (or low-pass complex envelope) may pass through an apparatus that may compute individual components, as described in Equation (25), and which may be implemented, for example, as inFIG. 9A.

Additionally, at least two of the signals (z1(t) and z2(t) as shown inFIG. 9B(but the invention is not thus limited) may be pairwise correlated in correlator93and further processed (i.e., by phase angle function97, inversion function99, multipliers and adders) to obtain an estimate of a factor for a multiplier used to multiply a sum of individual components that may be computed using the apparatus ofFIG. 9Ato obtain an estimate of the Doppler frequency, {circumflex over (f)}D.

FIG. 10shows an exemplary flowchart that incorporates the various methods indicated by the equations discussed above. The following paragraphs discuss how the various methods ofFIG. 10may be combined to produce to implement the embodiments of the invention shown inFIGS. 8,9A and9B. Moreover, most of the various methods shown inFIG. 10may be implemented via a processor-readable medium containing processor-executable code that, when executed by a processor, causes the processor to implement the various methods.

In a non-limiting example, the conceptual block diagram ofFIG. 8can be implemented by the following method steps shown inFIG. 10. In step100ofFIG. 10, a signal(s) is received at the receiver81ofFIG. 8. The received signal(s) is differentiated in step101and correlators83,84perform correlations on sampled versions of both the received signal and the differentiated received signal in step102. The two correlations of the received signal and the differentiated received signal are fed to a divider85in step104. In step107ofFIG. 10: (1) a sum value is computed by adding a factor to the divided correlations; (2) a square root87of the sum value is computed and the resulting square root is multiplied88by an additional factor in order to generate an estimate of the Doppler frequency {circumflex over (f)}D.

In another non-limiting example, the conceptual block diagram ofFIG. 9Acan be implemented by the following method steps shown inFIG. 10. In step100ofFIG. 10, a signal(s) is received at receiver90ofFIG. 9A. The received signal is sampled and correlations are performed by correlator92on the sampled version of the received signal in step102. A windowed, discrete time Fourier transform (DTFT) is performed on the correlated signal at step105. Step108computes an output that is the argument of the maximum of the magnitude of the windowed DTFT. In step110ofFIG. 10: (1) a sum value is computed by adding a factor to the output in a summing function; (2) a magnitude value is computed by a magnitude function96; and the resulting magnitude value is multiplied by a second factor in a multiplier98.

In yet another non-limiting example, the conceptual block diagram ofFIG. 9Bcan be implemented by the following method steps shown inFIG. 10. In step100ofFIG. 10, a signal(s) is received at the receivers91A,91B ofFIG. 9B. The received signals are sampled and cross-correlated by correlator93in step103. In step109ofFIG. 10: (1) the phase angle is computed by phase function97and multiplied by factor; (2) an inverse function99inverts the multiplied phase angle; and (3) the inverted multiplied phase angle is multiplied by another factor to provide a multiplier output. In step112, a sum of component values is computed and multiplied by the multiplier output in order to generate an estimate of the Doppler frequency {circumflex over (f)}D.

As noted above, various embodiments of the invention may comprise hardware, software, computer-readable medium and/or firmware.FIG. 11shows an exemplary system that may be used to implement various forms and/or portions of embodiments of the invention. As shown Such a computing system may include one or more processors114, which may be coupled to one or more system memories113. Such system memory113may include, for example, RAM, ROM, or other such machine-readable media, and system memory113may be used to incorporate, for example, a basic I/O system (BIOS), operating system, instructions for execution by processor114, etc.

The system may also include other memory115, such as additional RAM, ROM, hard disk drives, or other processor-readable media. Processor114may also be coupled to at least one input/output (I/O) interface116. I/O interface116may include one or more user interfaces, as well as readers for various types of storage media and/or connections to one or more communication networks (e.g., communication interfaces and/or modems), from which, for example, software code may be obtained. Such a computing system may, for example, be used as a platform on which to run translation software and/or to control, house, or interface with an emulation system. Furthermore, other devices/media may also be coupled to and/or interact with the system shown inFIG. 11.

Applicant has attempted to disclose all embodiments and applications of the disclosed subject matter that could be reasonably foreseen. However, there may be unforeseeable, insubstantial modifications that remain as equivalents. While the present invention has been described in conjunction with specific, exemplary embodiments thereof, it is evident that many alterations, modifications, and variations will be apparent to those skilled in the art in light of the foregoing description without departing from the spirit or scope of the present disclosure. Accordingly, the present disclosure is intended to embrace all such alterations, modifications, and variations of the above detailed description.

It will, of course, be understood that, although particular embodiments have just been described, the claimed subject matter is not limited in scope to a particular embodiment or implementation. For example, one embodiment may be in hardware, such as implemented to operate on a device or combination of devices, for example, whereas another embodiment may be in software. Likewise, an embodiment may be implemented in firmware, or as any combination of hardware, software, and/or firmware, for example. Likewise, although claimed subject matter is not limited in scope in this respect, one embodiment may comprise one or more articles, such as a storage medium or storage media. This storage media, such as, one or more CD-ROMs and/or disks, for example, may have stored thereon instructions, that when executed by a system, such as a computer system, computing platform, or other system, for example, may result in an embodiment of a method or apparatus in accordance with claimed subject matter being executed, such as one of the embodiments previously described, for example.

As one potential example, a computing platform may include an apparatus or means for implementing one or more processing units or processors, one or more input/output devices, such as a display, a keyboard and/or a mouse, and/or one or more memories, such as static random access memory, dynamic random access memory, flash memory, and/or a hard drive and one or more routers or firewall equipment. For example, a display may be employed to display one or more queries, such as those that may be interrelated, and or one or more tree expressions, although, again, claimed subject matter is not limited in scope to this example. Likewise, an embodiment may be implemented as a system, or as any combination of components such as computer systems and interfaces to computer systems (e.g., but not limited to: routers, firewalls, etc.), mobile and/or other types of communication systems and other well known electronic systems.

In the preceding description, various aspects of claimed subject matter have been described. For purposes of explanation, specific numbers, systems and/or configurations were set forth to provide a thorough understanding of claimed subject matter. However, it should be apparent to one skilled in the art having the benefit of this disclosure that claimed subject matter may be practiced without the specific details. In other instances, well known features were omitted and/or simplified so as not to obscure the claimed subject matter. While certain features have been illustrated and/or described herein, many modifications, substitutions, changes and/or equivalents will now occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and/or changes as fall within the true spirit of claimed subject matter.