
[1]
1. The present application claims priority from U.S. Provisional Application Serial Nos. 60/087,036 filed May 28, 1998; 60/056,455 filed Aug. 21, 1997; and 60/056,228 filed Aug. 21, 1997, all of which are incorporated herein by this reference.
FIELD OF THE INVENTION

[2]
2. The present invention relates generally to a method and apparatus for acquiring wideband random and pseudorandom noise encoded waveforms and specifically to a method and apparatus for acquiring wideband signals, including deterministic signals, random signals and pseudorandom noise encoded waveforms that divides the waveform into a plurality of subbands prior to signal processing thereof.
BACKGROUND

[3]
3. Analogtodigital converters are devices that convert real world analog signals into a digital representation or code which a computer can thereafter analyze and manipulate. Analog signals represent information by means of continuously variable physical quantities while digital signals represent information by means of differing discrete physical property states. Converters divide the full range of the analog signal into a finite number of levels, called quantization levels, and assigns to each level a digital code. The total number of quantization levels used by the converter is an indication of its fidelity and is measured in terms of bits. For example, an 8bit converter uses 2^{8 }or 256 levels, while a 16bit converter uses 2^{16 }or 65536 levels.

[4]
4. During the conversion process, the converter determines the quantization level that is closest to the amplitude of the analog signal at that time and outputs the digital code that represents the selected quantization level. The rate at which the output is created indicates the speed of the converter and is measured in terms of samples per second (sps) or frequency in Hertz (Hz). As will be appreciated, a larger number of bits and therefore quantization levels equates into a finer representation of the analog signal.

[5]
5. In designing an analogtodigital converter, there are a number of considerations. In many applications for example it is desirable that the converter has not only a high rate of speed but also a large number of quantization levels or a high degree of fidelity. Such converters are difficult to build and therefore tend to be highly complex and very expensive. The key reason is that conversion errors and the consequential device layout constraints for reducing such errors, both of which can be ignored at slow speeds, can become significant at high speeds. As a result, in existing converters, high fidelity and high speed are commonly mutually exclusive; that is, the higher the converter speed the lower the converter fidelity and vice versa.
SUMMARY OF THE INVENTION

[6]
6. It is an object of the present invention to provide an analogtodigital converter that has a high fidelity and a high speed. Related objectives are to provide such an analogtodigital converter that is relatively simple and inexpensive.

[7]
7. The present invention is directed to a method and apparatus for processing signals, particularly wideband signals, including deterministic signals, random signals, and signals defined by pseudorandom waveforms with a relatively high degree of fidelity and efficiency at a high speed and at a low cost. The invention is particularly useful for processing wideband signal, including signals defined by broadband signals (i.e., signals having a bandwidth of preferably more than about 1 kHz and more preferably more than about 1 GHz).

[8]
8. The signal can be in any suitable form such as electromagnetic radiation, acoustic, electrical and optical.

[9]
9. In one embodiment, the method includes the following steps:

[10]
10. (a) decomposing the analog or digital signal into a plurality of signal segments (i.e., subband signals), each signal segment having a signal segment bandwidth that is less than the signal bandwidth;

[11]
11. (b) processing each of the signal segments to form a plurality of processed signal segments; and

[12]
12. (c) combining the processed signal segments into a composite signal that is digital when the signal is analog and analog when the signal is digital. As will be appreciated, the sum of the plurality of signal bandwidths is approximately equivalent to the signal bandwidth. The means for processing the signal segments can include any number of operations, including filtering, analogtodigital or digitaltoanalog conversion, signal modulation and/or demodulation, object tracking, RAKE processing, beamforming, null steering, correlation, interferencesuppression and matched subspace filtering.

[13]
13. In a particularly preferred application, the signal processing step (b) includes either analogtodigital or digitaltoanalog conversions. The use of signal segments rather than the entire signal for such conversions permits the use of a lower sampling rate to retain substantially all of the information present in the source signal. According to the Bandpass Sampling Theorem, the sampling frequency of the source signal should be at least twice the bandwidth of the source signal to maintain a high fidelity. The ability to use a lower sampling frequency for each of the signal segments while maintaining a high fidelity permits the use of a converter for each signal segment that is operating at a relatively slow rate. Accordingly, a plurality of relatively inexpensive and simple converters operating at relatively slow rates can be utilized to achieve the same rate of conversion as a single relatively high speed converter converting the entire signal with little, if any, compromise in fidelity.

[14]
14. The means for decomposing the signal into a number of signal segments and the means for combining the processed signal segments to form the composite signal can include any number of suitable signal decomposing or combining devices (e.g., filters, analog circuitry, computer software, digital circuitry and optical filters). Preferably, a plurality or bank of analog or digital analysis filters is used to perform signal decomposition and a plurality or bank of analog or digital synthesis filters is used to perform signal reconstruction. The analysis and synthesis filters can be implemented in any number of ways depending upon the type of signal to be filtered. Filtration can be by, for example, analog, digital, acoustic, and optical filtering methods. By way of example, the filters can be designed as simple delays or very sophisticated filters with complex amplitude and phase responses.

[15]
15. In a preferred configuration, a plurality or bank of analysis and/or synthesis filters, preferably designed for perfect reconstruction, is used to process the signal segments. As will be appreciated perfect reconstruction occurs when the composite signal, or output of the synthesis filter bank, is simply a delayed version of the source signal.

[16]
16. In one configuration, the analysis filters and synthesis filters are represented in a special form known as the Polyphase representation. In this form, Noble identities are can be used to losslessly move the decimators to the left of the analysis filters and the interpolators to the right of the synthesis filters.

[17]
17. In another configuration, noise components in each of the signal segments can be removed prior to signal analysis or conversion in the processing step. The removal of noise prior to analogtodigital conversion can provide significant additional reductions in computational requirements.

[18]
18. In yet another configuration, a coded signal is acquired rapidly using the abovereferenced invention. In the processing step, the signal segments are correlated with a corresponding plurality of replicated signals to provide a corresponding plurality of correlation functions defining a plurality of peaks; an amplitude, time delay, and phase delay are determined for at least a portion of the plurality of peaks; and at least a portion of the signal defined by the signal segments is realigned and scaled based on one or more of the amplitude, time delay, and phase delay for each of the plurality of peaks.

[19]
19. In another embodiment, a method is provided for reducing noise in a signal expressed by a random or pseudorandom waveform. The method includes the steps of decomposing the signal into a plurality of signal segments and removing a noise component from each of the signal segments to form a corresponding plurality of processed signal segments. The means for decomposing the signal can be any of the devices noted above, and the means for removing the noise component includes a noise reducing quantizer, noise filters and rank reduction. Signal reconstruction may or may not be used to process further the processed signal segments. This embodiment is particularly useful in acquiring analog signals.

[20]
20. In yet a further embodiment, a method is provided for combining a plurality of signal segments (which may or may not be produced by analysis filters). In the method, synthesis filtering is performed on each of the plurality of signal segments. The means for performing synthesis filtering can be any of the devices noted above.

[21]
21. A number of differing system configurations can incorporate the synthesis filtering means in this embodiment of the invention. For example, a system can include, in addition to the synthesis filtering means, means for emitting the plurality of signal segments from a plurality of signal sources (e.g., antennas); means for receiving each of the plurality of signal segments (e.g., antennas); and means for converting each of the signal segments from analog format to digital format (e.g., analogtodigital converter).

[22]
22. In another configuration, the system includes: a plurality of analysis filters to decompose a source signal into a plurality of decomposed signal segments; a plurality of digitaltoanalog conversion devices for converting the plurality of decomposed signal segments from digital into analog format to form a corresponding plurality of analog signal segments; a plurality of amplifiers to form a corresponding plurality of signal segments; a plurality of signal emitters for emitting the plurality of signal segments; and a plurality of receptors for receiving the plurality of signal segments.

[23]
23. In yet another configuration, the system includes: a plurality of analysis filters to decompose a source signal into a plurality of decomposed signal segments; a plurality of amplifiers to amplify the decomposed signal segments to form a corresponding plurality of signal segments; a plurality of signal emitters for emitting the plurality of signal segments; and a plurality of receptors for receiving the plurality of signal segments.

[24]
24. In another embodiment, a method is provided in which digital signals are decomposed, processed, and then recombined. Signal processing can include signal correlation (e.g., signal modulation or demodulation), and oblique projection filtration (e.g., as described in copending U.S. patent application Ser. No. 08/916,884 filed Aug. 22, 1997, entitled “RAKE Receiver For Spread Spectrum Signal Demodulation,” which is incorporated herein fully by reference).
BRIEF DESCRIPTION OF THE DRAWINGS

[25]
25.FIG. 1 depicts a first embodiment of the present invention;

[26]
26.FIG. 2 depicts an analog signal;

[27]
27.FIG. 3 depicts the analog signal of FIG. 2 divided up into a plurality of signal segments;

[28]
28.FIG. 4 depicts the first embodiment including decimation;

[29]
29.FIGS. 5A and 5B depict noble identities;

[30]
30.FIG. 6 depicts a polyphase filter representation;

[31]
31.FIG. 7 depicts a polyphase filter representation with noble identities;

[32]
32.FIG. 8 depicts another embodiment of the present invention;

[33]
33.FIG. 9 depicts the quantization process of the quantizers in FIG. 8;

[34]
34.FIG. 10 depicts a subband digital transmitter;

[35]
35.FIG. 11 depicts a subband analog transmitter;

[36]
36.FIG. 12 depicts a subband receiver;

[37]
37.FIG. 13 depicts rank reduction for noise filtering;

[38]
38.FIG. 14 depicts another embodiment of the present invention;

[39]
39.FIG. 15 depicts another embodiment of the present invention;

[40]
40.FIG. 16 depicts RAKE processing;

[41]
41.FIG. 17 depicts a multiplexed radar transmitter architecture;

[42]
42.FIG. 18 depicts a radar receiver architecture;

[43]
43.FIG. 19 depicts a digital communications example of a recursive, adaptive Wiener filter;

[44]
44.FIG. 20 depicts an alternative RAKE processing methodology; and

[45]
45.FIG. 21 depicts a least squares, multiple input multiple output filter design problem.
DETAILED DESCRIPTION

[46]
46. Referring to FIG. 1, an embodiment of the present invention is illustrated. As can be seen from FIGS. 1 and 2, a wideband, pseudorandom or random signal 40 (shown in FIG. 2) is passed to a bank or plurality of analysis filters 44 an. The signal 40 has a frequency band or domain, F_{s}, having frequency bounds, f_{o }(lower) and f_{n }(upper), and therefore a bandwidth of f_{o}f_{n }(FIG. 2). The bandwidth commonly is at least about 1 kHz, more commonly at least about 1 GHz. Each of the analysis filters 44 an pass only a portion of the frequency band of the signal to form a plurality of subband signals 48 an, or time frequency components, characterized by discrete portions of the frequency band, F_{s}, of the signal 40 (FIG. 3). As will be appreciated, the summation of the individual frequency bandwidths of all of the subband signals 48 an is substantially the same as the bandwidth of the signal 40 (FIG. 3). The various subband signals 48 an are processed 52 an independently as described below to form a corresponding plurality of processed signal segments 56 an. The processed signal segments 56 an are passed to a bank or plurality of synthesis filters 60 an and combined to form a composite signal 64. Generally, the signal 40 is analog or digital and, when the signal 40 is analog, the composite signal 64 is digital, and, when the signal 40 is digital, the composite signal 64 is analog.

[47]
47. The analysis and synthesis filters 44 an and 60 an can be in any of a number of configurations provided that the filters pass only discrete, or at most only slightly overlapping, portions of the frequency domain of the signal 40. It is preferred that the frequency bands of the subband signals overlap as little as possible. Preferably, no more than about 5% and more preferably no more than about 1% of the frequency bands of adjacent subband signals overlap.

[48]
48. The filters can be analog or digital depending on the type of signal 40 or the processed signal segments 56 an. Examples of suitable analog analysis and synthesis filters include a suitably configured bandpass filter formed by one or more low pass filters, one or more high pass filters, a combination of band reject and low pass filters, a combination of band reject and high pass filters, or one or more band reject filters. Digital analysis and synthesis filters are typically defined by software architecture that provides the desired filter response.

[49]
49. In a preferred configuration shown in FIG. 4, the signal 40 is decomposed by the analysis filter bank 46 (which includes analog or digital analysis filters H_{k}(Z) 44 an) into subband signals which are each sampled by a downsampler 64 an performing an Mfold decimation (i.e., taking every M^{th }sample), and the sampled subband signals are further sampled after signal processing by an upsampler 68 an (and/or expander (which fills in L1 zeros in between each sample)) and the further sampled subband signals are combined by a synthesis filter bank 62 (that includes analog or digital synthesis filters G_{k}(z) 60 an). The sampled subband signals, denoted by x_{o}(n), x_{1}(n), . . . x_{m−1}(n), are the outputs of the Nband analysis filter bank and the inputs to the Nband synthesis filter bank. As a result of decimation, the subband signals are 1/N the rate of the input rate of the signal 40.

[50]
50. Preferably, the analysis and synthesis filters are perfect reconstruction filters such that the composite signal 64 is a delayed version of the signal 40 (i.e., y(n)=u(n−L) where y(n) is the composite signal, u(n) is the signal, and L is time of delay). Using perfect reconstruction filters, the subband signals 48 an can be downsampled without any loss in fidelity of the output signal. This downsampling is permissible because the subband signals are of narrow bandwidth and the consequence of the downsampling is that any processing application 52 an that is embedded in the subbands can run at significantly reduced rates.

[51]
51. As will be appreciated, a perfect reconstruction filter system can be formed by a number of different methods, including quadrature mirror filter techniques. A preferred technique for designing a filter bank is known as a least squares multiple input multiple output filter design notation. According to this technique, which is illustrated in FIG. 21, a rational transfer matrix defining one of the filter banks is known, i.e., either H(z) or G^{T}(z), along with a rational transfer matrix F(z) defining the ideal output of the filter banks. Assuming that H(z) and F(z) are the known rational transfer matrices, the unknown rational transfer matrix, G^{T}(z), is determined by the following equation:

G ^{T}(z)=[F(z)U ^{T}(z ^{−1})]+H _{0} ^{−1}(z)

[52]
52. where

[53]
53. H(z)=H_{0}(z) U(z); [H_{0}(z) is the minimum phase equivalent of H(z)]

[54]
54. U(z)U^{T}(z^{−1})=I; Paraunitary

[55]
55. [F(z)U^{T}(z^{−1})]_{x}: Causal part of F(z)U^{T}(z^{−1})

[56]
56. As will be appreciated if G^{T}(z) were known and H(z) were unkown, then the equation would be solved for H(z) rather than G^{T}(z), and G^{T}(z) would be decomposed into the following:

G ^{T}(z)=G _{o} ^{T}(z)U(z)

[57]
57. where G_{o} ^{T}(z) is the minimum phase equivalent of G^{T}(z).

[58]
58. In a preferred embodiment, the rational transfer matrices of the analysis and/or synthesis filters are mathematically expressed in a polyphase filter representation. Exemplary equations defining the decomposition of the signal
40 by the analysis filters
44 an include the following:
$H\ue89e\left(z\right)=\sum _{l=0}^{M1}\ue89e{z}^{1}\ue89e{E}_{1}\ue89e\left({z}^{M}\right)$

[59]
59. where

[60]
60. M is the number of subbands (which is the same as the number of analysis filters in the analysis filter bank; l is the subband designation);
${E}_{1}\ue89e\left({z}^{M}\right)=\sum _{n=\infty}^{\infty}\ue89e{e}_{1}\ue89e\left(n\right)\ue89e{z}^{n}$

e _{l}(n)=h(Mn+l), 0≦l≦M−1

[61]
61. (known as a Type 1 polyphase filter representation) and
$H\ue89e\left(z\right)=\sum _{l=0}^{M1}\ue89e{z}^{\left(M1l\right)}\ue89e{R}_{1}\ue89e\left({z}^{u}\right)$

[62]
62. where

R _{1}(z ^{M})=E _{M−1−l}(z)

[63]
63. (known as Type 2 polyphase filter representation). As will be appreciated, other techniques exist for expressing a rational transfer matrix defining a filter system including impluse response and filter description.

[64]
64. Noble identities can be used to losslessly move the decimators to the left of the analysis filters and the Lfold upsampler and/or expander to the right of the synthesis filters. In this manner, the analysis and synthesis filters operate on lower rate data, thereby realizing significant computational savings. The noble identities include:

[65]
65. Identity I: Decimation by M followed by filtering defined by the mathematical function H(z) is equivalent to filtering by H(z^{M}) followed by decimation by M (FIG. 5A).

[66]
66. Identity II: Filtering by G(z) followed by an upsampling by L is equivalent to upsampling by L followed by filtering by G(z^{L}) (FIG. 5B).

[67]
67. By way of example, assume H(z) defines an order N finite impulse response (FIR) digital analysis filter with impulse response h(n), M=2, u(n) is the source signal and X(n) is the subband signal. Using the type 1 polyphase representation above, H(z) is decomposed to yield the following:

H(z)=H _{o}(z ^{2})+H _{1}(z ^{2})

[68]
68. Based on the foregoing, FIG. 6 is a polyphase representation based implementation of H(z) without noble identities and FIG. 7 is a polyphase representationbased implementation of the analysis filters H(z) using noble identities to move the decimators ahead of the analysis filters. In this configuration, H_{o}(z^{2}) and H_{1}(z^{2}) are FIR filters of order n_{o}+1 and n_{1}+1, where N=n_{o}+n_{1}+1. H_{o}(z^{2}) and H_{1}(z^{2}) operate at half the rate as compared to H(z) and therefore have two units of time in which to perform all the necessary computations, and the components are continually active (i.e., there are no resting times). Accordingly, there is an Mfold reduction in the number of multiplications and additions per unit of time when using both polyphase representation and the noble identities to implement an Mfold decimation filter.

[69]
69. Subband signal processing can take a variety of forms. In one embodiment shown in FIG. 8 which depicts a receiver and antenna architecture, the source signal 40 and subband signals 48 an are in analog form and a plurality of quantizers or analogtodigital converters are used to convert the subband signals 48 an to digital form before further processing 82 (e.g., correlation for encoded subband signals, subband signal digital beamforming in multiple antenna systems, etc.) and/or synthesis of the digital subband signals 78 an is performed. As noted above, the subband signals 48 an are preferably sampled by each of the decimators or downsamplers 64 an at a rate of at least about twice the bandwidth of the corresponding subband signal 48 an to maintain fidelity. As shown in FIG. 9, each quantizer, or analogtodigital converter, 74 an determines the digital word or representation 90 an that corresponds to the bin 86 an having boundaries capturing the amplitude of the analog subband signal at that time and outputs the digital word or representation that represents the selected quantization level assigned to the respective bin. The digital subband signals 78 an are converted 94 an from radio frequency (RF) to base band frequency and optionally subjected to further signal processing 60. The processed subband signals 98 are formed into a digital composite signal 102 by the synthesis filter bank 60.

[70]
70. To provide increased accuracy, noise rejecting quantizers can be utilized as the quantizers
74 an. As will be appreciated, a noise rejecting quantizer assigns more bits to the portions of the subband signal having less noise (and therefore more signal) and fewer bits to the noisy portion. This selective assignment is accomplished by adaptively moving the bin boundaries so as to narrow the bin width (thereby increasing quantization fidelity. An example of a design equation for a LloydMax noise rejecting quantizer is as follows:
${t}_{k}=\frac{{x}_{k1}+{x}_{k}}{2}+\frac{{\delta}^{2}\ue89e\left({x}_{k}\right){\delta}^{2}\ue89e\left({x}_{k1}\right)}{2\ue89e\left({x}_{k}{x}_{k1}\right)};\text{\hspace{1em}}\ue89e{x}_{k}={e}_{k}\frac{1}{2}\ue89e\frac{\uf74c{\delta}^{2}\ue89e\left({x}_{k}\right)}{\uf74c{x}_{k}}$

[71]
71. where:

[72]
72. x is the signal to be quantized;

[73]
73. N is the number of quantization levels;

[74]
74. k is signal identifier;

[75]
75. σ is the noise covariance.

[76]
76. The mean squared quantization error (MSE) ξ
^{2 }is as follows:
${\xi}^{2}={\left(E\ue89e\left(x\hat{x}\right)\right)}^{2}={E}_{x}^{2}+\sum _{k=0}^{N1}\ue89e\left[{\sigma}^{2}\ue89e\left({x}_{k}\right)+{x}_{k}^{2}2\ue89e{x}_{k}\ue89e{e}_{k}\right]\ue89e{P}_{k}$

[77]
77. where:

[78]
78. {x_{k}}_{o} ^{N−1 }are the representation points;

[79]
79. {c_{k}}_{o} ^{N−1 }are the quantization bins;

[80]
80. {t_{k}}_{o} ^{N−1 }are the bin thresholds;

[81]
81. f_{y}(y) is the probability density function of y;

[82]
82. y=x+n, where x is the signal component and n the noise component;
$\begin{array}{c}{e}_{k}=\mathrm{Ex}y\ue89e\text{\hspace{1em}}\ue89e\epsilon \ue89e\text{\hspace{1em}}\ue89e{C}_{k}]=1/{P}_{k}\ue89e{\int}_{{t}_{k}}^{{t}_{k+1}}\ue89eE\ue8a0\left[xy=\alpha \right]\ue89e\mathrm{fy}\ue8a0\left(\alpha \right)\ue89e\text{\hspace{1em}}\ue89e\uf74c\alpha ;\text{\hspace{1em}}\ue89e\mathrm{and}\\ {P}_{k}=P\ue8a0\left[y\ue89e\text{\hspace{1em}}\ue89e\epsilon \ue89e\text{\hspace{1em}}\ue89e{C}_{k}\right]={\int}_{{t}_{k}}^{{t}_{k+1}}\ue89e\mathrm{fy}\ue8a0\left(\alpha \right)\ue89e\uf74c\alpha \end{array}$

[83]
83. The LM equations require that the bin thresholds be equidistant from the representation points and that each representation point be the conditional mean of x in the corresponding quantization bin. As will be appreciated, a LloydMax (LM) quantizer substantially minimizes the mean squared error between the discrete approximation of the signal and its continuous representation.

[84]
84. The noise covariance, δ, can be estimated by linear mean squared error estimation techniques. Linear mean squared error estimates are characterized by the following equation:

{circumflex over (X)}=Ty=R
_{xy}
R
_{yy}
^{−1}
y

[85]
85. where T is the Wiener filter, R_{xy }is the cross covariance between x and y and R_{yy }is the covariance of y.

[86]
86. R_{xy }and R_{yy }are unknown and require estimation. A number of techniques can be used to estimate R_{xy }and R_{yy}, including an adaptive Wiener filter (e.g., using the linear mean squared algorithm), direct estimation, sample matrix inversion and a recursive, adaptive Wiener filter, with a recursive, adaptive Wiener filter being more preferred.

[87]
87. The recursive, adaptive Wiener filter is explained in Thomas, J. K., Canonical Correlations and Adaptive Subspace Filtering, Ph.D Dissertation, University of Colorado Boulder, Department of Electrical and Compute Engineering, pp.1110, June 1996. which is incorporated herein by reference in its entirety. In a recursive, adaptive Wiener filter assume {acute over (T)}_{M }denotes the filter when M measurements of X and Y are used. Then {acute over (T)}_{M }is the adaptive Wiener filter

{acute over (T)} _{M} =X _{M} Y _{M}*(Y _{M} Y _{M}*)^{−1} =Ŕ _{xy} Ŕ _{yy} ^{−1},

X _{M} =[x _{1} x _{2 } . . . x _{M} ]; X _{M+1} =[x _{M} x]

Y _{M} =[y _{1} y _{2 } . . . y _{M} ]; Y _{M+1} =[y _{M} y]

[88]
88. If another measurement of x and y is taken, and one more column is added to X_{M }and Y_{M }to build {acute over (T)}_{M+1}:

{acute over (T)}
_{M+1}
=X
_{M}
Y
_{M}
*Ŕ
_{M+1}
^{−1}
+xy*Ŕ
_{M+1}
^{−1 }

[89]
89. The estimate of _{M+1 }is {acute over (X)}_{M+1 }

{acute over (X)}
_{M+1}
={acute over (T)}
_{M+1}
Y
_{M+1 }

[90]
90. Using the estimate of X
_{M+1}, one can read off {acute over (X)}
_{M+1}, which is the estimate of x:
${\hat{x}}_{M+1}=\frac{1}{1+{r}^{2}}\ue89e{\stackrel{~}{x}}_{M}+\frac{{r}^{2}}{1+{r}^{2}}$

[91]
91. where r^{2}=y*Ŕ_{M} ^{−1}y and {tilde over (x)}_{M+1}={acute over (T)}_{M}y.

[92]
92. Based on the above, when one observes y, the best estimate of the unknown x is {tilde over (x)}, with corresponding estimation error {tilde over (E)}
_{M+1 }and covariance {tilde over (Q)}
_{M+1}. If the unknown x becomes available after a delay, then {tilde over (X)}
_{M+1 }can be updated to {acute over (x)}
_{M+1 }with error covariance É
_{M+1 }and covariance {tilde over (Q)}
_{M+1}. The two covariances are related by the following formula:
${\stackrel{~}{Q}}_{M+1}={\hat{Q}}_{M+1}+\frac{{r}^{2}}{1+{r}^{2}}\ue89e\mathrm{xx}*$

[93]
93. By way of example and as illustrated in FIG. 19, consider a digital communication application in which the modulation scheme involves transmitting x_{0 }and x_{1 }when bits 0 and 1 are to be sent. During the setup of the communication link, the transmitter sends a known bit sequence across the unknown channel. Let X_{M }be the matrix of signals that correspond to the known bit sequence. The receiver observes Y_{M}, which is the channel filtered and noise corrupted version of X_{M}. Since the receiver knows the bit pattern, and therefore X_{M}, it is able to build {acute over (T)}_{M}. Therefore we refer to X_{M }and Y_{M }as the training set.

[94]
94. Once the communication link is established, the transmitter sends a signal x, which corresponds to a data bit. The receiver observes the corresponding y and uses it to estimate x using {acute over (T)}_{M}:

{tilde over (x)}={acute over (T)}
_{M}
y

[95]
95. The receiver determines r^{2}, cos^{2}θ and sin^{2}θ.

[96]
96. When cos^{2}θ is approximately equal to 1, {tilde over (x)} is deemed to be a good estimate of x and is used to decide if a 1 or 0 was sent. If, however, cos^{2}θ<<1, then the estimate {tilde over (x)} is scaled by cos^{2}θ, as required by equation 14, before it is used to decide if a 1 or 0 was sent. Once the decision of 1 or 0 is made, the true x is known and can be used to build {acute over (x)} as required by equation 14 above and as illustrated in FIG. 19. The x and y are also added to the training set to update {acute over (T)}_{M}.

[97]
97. In another embodiment, the source signal 40 is digital and the analysis filters are therefore digital, signal processing is performed by a digitaltoanalog converter, and the synthesis filters are analog. FIG. 10 depicts a subband digital transmitter according to this embodiment. The signal 100 is in digital format and is transmitted to a bank of analysis filters 104 an to form a plurality of digital subband signals 108 an; the digital subband signals 108 an are processed by digitaltoanalog converters 112 an to form analog subband signals 116 an; the analog subband signals 116 an are amplified by amplifiers 120 an to form amplified subband signals 124 an; and the amplified subband signals 124 an transmitted via antennas 128 an.

[98]
98. In another embodiment shown in FIG. 11, a subband analog transmitter is depicted where the signal 140 is analog and not digital. The signal 140 is decomposed into a plurality of analog subband signals 144 an by analog analysis filters 148 an and the analog subband signals 144 an amplified by amplifiers 152 an, and the amplified subband signals transmitted by antennas 156 an.

[99]
99. In yet another embodiment shown in FIG. 12, a subband receiver is depicted that is compatible with the subband analog transmitter of FIG. 11. Referring to FIG. 12, a plurality of subband signals 160 an are received by a plurality of antennas 164 an, the received subband signals 168 an down converted from radio frequency to baseband frequency by down converters 172 an; the down converted subband signals 176 an which are in analog form are converted by quantizers 180 an from analog to digital format; and the digital subband signals 184 an combined by synthesis filters 188 an to form the digital composite signal 192.

[100]
100. In any of the abovedescribed transmitter or receiver embodiments, when the subband signals are encoded waveforms such as Code Division Multiple Access (CDMA) or precision P(Y) GPS code signals, the subband signals can be encoded or decoded to realize computational savings. In a receiver, for example, the subband signals are correlated with a replica of the transmitted signal prior to detection. The correlation process can be performed before or after synthesis filtering or before conversion to digital (and therefore in analog) or after conversion to digital (and therefore in digital). The approach is particularly useful for the rapid, direct acquisition of wideband pseudorandom noise encoded waveforms, like CDMA type signals and the P(Y) GPS code, in a manner that is robust with respect to multipath effects and wideband noise. Because the Msubband signals have narrow bandwidths and therefore can be searched at slower rates, correlation of the subband signals rather than the signal or the composite signal can be performed with over an Mfold reduction in computation and therefore reduce the individual component cost.

[101]
101. To provide further reductions in computational requirements, the number of subbands requiring correlation at any trial time and Doppler frequency can be reduced. The pseudorandom nature of the coded signals implies that a coded signal will only lie in certain known subbands at any given time. According to the rankreduction principle and as illustrated by FIG. 13, subbands 200 aj outside of the subbands 204 aj containing the coded signal can be eliminated to reduce the effects of wideband noise in the acquisition and/or tracking of pseudorandom signals. This is accomplished by eliminating any subband in which the noise component exceeds the signal component (i.e., the SNR is less than 1). Such an elimination increases the bias squared, which is the power of the signal components that are eliminated, while drastically decreasing the variance, which is the power of the noise that was eliminated. In this manner, the mean squared error between the computed correlation function and the noisefree version of the correlation function is significantly reduced.

[102]
102. As shown in FIG. 14 to perform the correlation in the subband signals in GPS, CDMA, and other pseudorandom or random waveform applications, the replicated code
208 from the code generator
212 must be passed through an analysis filter bank
216 that is identical to the analysis filter bank
220 used to decompose the signal
224. Because the correlation must be performed for different segments of the replicated code
208, each indexed by some start time, this decomposition is necessary for all trial segments of the replicated code
208. A plurality of subband correlators
228 an receive both the subband signals
232 an and the replicated subband signals
236 an and generate a plurality of subband correlation signals
240 an. The subband correlation signals
240 an are provided by the following equation:
${q}_{m,n}^{\left(i\right)}\ue89e\left(j\right)=\sum _{k=1}^{N}\ue89e{x}_{m}\ue89e\left(k+j\right)\ue89e{p}_{n}^{\left(i\right)}\ue89e\left(k\right)$

[103]
103. where:

[104]
104. q(k) is the subband correlation signal;

[105]
105. p_{n} ^{(i)}(k) is the component of the i^{th }trial segment of the P(Y) code in the n^{th }subb^{and; }

[106]
106. x_{m}(k) is the component of the measurement that lies in the m^{th }subband;

[107]
107. N is the number of samples over which the correlation is performed.

[108]
108. The subband correlation signals 240 an are upsampled and interpolated by the synthesis filters 244 an and then squared and combined. The resulting composite signal 248 is the correlation function that can be further processed and detected.

[109]
109. After the subband correlation signals 240 an are generated, the signals, for example, can be processed by a RAKE processor, which is commonly a maximal SNR combiner, to align in both time and phase multipath signals before detection and thereby provide improved signaltonoise ratios and detection performance. As will be appreciated, a signal can be fragmented and arrive at a receiver via multiple paths (i.e., multipath signals) due to reflections from other objects, particularly in urban areas. The formation of a number of multipath signals from a source signal can degrade the correlation peaks, which contributes to the degradation of the detections. The RAKE processor determines the time and phase delays of these multipath signals by searching for correlation peaks in the correlation function and identifying the time and phase delays for each of the peaks. The RAKE processor then uses the time and phase delay estimates to realign the multipath signals so that they can add constructively and enhance the correlation peaks. The peak enhancement improves detection because of the increase in signaltonoise ratio.

[110]
110.FIG. 15 depicts an embodiment of a signal processing architecture incorporating these features. Referring to FIG. 11, the signals
300 are received by one or more antennas
304, down converted by a down converter
308 to intermediate frequency, filtered by one or more filters
312, and passed through an analogtodigital converter
316 to form a digital signal
320. The digital signal
320 is passed through an analysis filter bank
324 to generate a plurality of subband signals
328 an, and the subband signals
328 an to a plurality of subband correlators
332 an as noted above to form a plurality of subband correlation signals
336 an. The subband correlation signals
336 an are passed to a synthesis filter bank
340 to form a correlation function
344 corresponding to the signal
300. The correlation function
344 is passed to a predetector
348 to determine an estimated transmit time and frequency and an amplitude and delay for each of the correlation peaks. The estimated transmit time and frequency
352 are provided to a code generator
356 and the amplitude and time delay
360 associated with each correlation peak are provided to the RAKE processor
364. The code generator
356 determines a replicated code
368 corresponding to the signal
300 based on the estimated trial time and frequency. Using the correlation peak amplitudes and time and/or phase delays, the RAKE processor
364, as shown in FIG. 16, shifts the input sequence y(k) by the amounts of the multipath time and/or phase delays and then weights each shifted version by the amplitude of the peak of the correlation function corresponding to that peak to form a RAKED signal
372 (denoted by y
_{R}(k)). The RAKED sequence is commonly defined by the following mathematical equation:
${y}_{R}\ue89e\left(k\right)=\frac{1}{\sum _{i=1}^{p}\ue89e{A}_{i}}\ue89e\sum _{i=1}^{p}\ue89e{A}_{i}\ue89e{\uf74d}^{j\ue89e\text{\hspace{1em}}\ue89e\phi \ue89e\text{\hspace{1em}}\ue89e\uf74e}\ue89ey\ue89e\left(k+{t}_{i}\right)$

[111]
111. where:

[112]
112. p is the number of multipath signals (and therefore number of peaks);

[113]
113. A_{i }is the amplitude of the i^{th }peak;

[114]
114. t_{i }is the time delay of the i^{th }peak;

[115]
115. φ is the phase delay of the i^{th }peak;

[116]
116. y(k) is the input sequence into the code correlator. The RAKED signal 372 and the replicated code 368 are correlated in a correlator 376 to provide the actual transmit time and frequency 380 which are then used by detector 384 to detect the signal.

[117]
117. There are a number of variations of the abovedescribed system. The variations are useful in specific application such as GPS, CDMA, and radar.

[118]
118. In one variation of the system of FIG. 15 that is depicted in FIGS. 1718, multiplexed radar transmitted receiver architectures are depicted. The radar signals 400 an are a number of coded waveforms that operate in separate, contiguous subbands (referred to as “radar subband signals”). As shown in FIG. 17, the radar signals 40 are simultaneously transmitted by a plurality of transmitters 404 an that each include a plurality of analysis filters (not shown) to form the various radar subband signals 400 an. Referring to FIG. 18, the various radar subband signals 400 an are received by a signal receptor 410 and passed through a plurality of bandpass filters 414 an. A bandpass filter 414 an having unique bandpass characteristics corresponds to each of the radar subband signals. The various filtered subband signals 416 an are sampled by a plurality of decimators 422 an and quantized by a plurality of quantizers 426 an to form digital subband signals 430 an. The digital subband signals 430 an are analyzed by a plurality of detectors 434 an to form a corresponding plurality of detected signals 438 an. The detectors 434 an use a differently coded waveform for each of the transmitted radar subband signals 400 an so that the subband radar signals can be individually separated upon reception. As noted above in FIGS. 1415, the coded radar waveform is decomposed by a plurality of analysis filters (not shown) that are identical to the analysis filters in the receiver to provide replicated subband signals to the detectors 434 an. Each detector 434 an correlates a radar subband signal 430 an with its corresponding replicated subband signal to form a plurality of corresponding detected signals 438 an. The detected signals 438 an are analyzed by a synthesis filter bank 412 an to form a composite radar signal 446.

[119]
119. In a variation of the system of FIG. 15, a bank of analysis filters and synthesis filters can be implemented both directly before and after the correlation step (not shown) to provide the abovenoted reductions in computational requirements.

[120]
120. In another variation of the system of FIG. 15, the analysis filters can be relocated before the analogtodigital converter 316 to form the subband signals before as opposed to after conversion.

[121]
121. In another variation shown of the system of FIG. 15 that is depicted in FIG. 20, the RAKE processor 364 can account for the relative delays in antenna outputs of the signal 300 (which is a function of the arrangement of the antennas as well as the angular location of the signal source) by summing the antenna outputs without compensating for the relative output delays. The correlation process may result in N×p peaks, where N is the number of antenna outputs and p is the number of multipath induced peaks. The Np peaks are then used to realign and scale the input data before summation. The RAKE 364 in effect has performed the phasedelay compensation usually done in beamsteering. The advantages of this approach compared to conventional beam steering techniques include that it is independent of antenna array geometries and steering vectors, it does not require iterative searches for directions as in LMS and its variants, and it is computationally very efficient. This approach is discussed in detail in copending application having Ser. No. 08/916,884, and filed on Aug. 21, 1997.

[122]
122. While various embodiments of the present invention have been described in detail, it is apparent that modifications and adaptations of those embodiments will occur to those skilled in the art. However, it is to be expressly understood that such modifications and adaptations are within the scope of the present invention, as set forth in the following claims.