Patent Application
20230359693
The present invention relates to correlation computation, and more particularly, to a correlation computation method for sharing common data and computation for different code sequences to be correlated with a data sequence and an associated apparatus.
The global navigation satellite system (GNSS) is often described as an “invisible utility”, and is so effective at delivering two essential services—time and position—accurately, reliably and cheaply that many aspects of the modern world have become dependent upon them. Each satellite of the GNSS is equipped with a highly precise atomic clock. When four or more satellites are in view, a GNSS receiver can measure the distance to each satellite by estimating the signal transmission time delay from the satellite to the receiver. From these measurements, a GNSS-embedded device can derive its own position and synchronize to the accurate GNSS system time.
A GNSS satellite signal is modulated by pseudo random noise (PRN) code. The PRN code is a code sequence with randomly distributed 0's and 1's. Each satellite transmits a unique PRN code. Hence, the GNSS receiver identifies any of the satellites by its unique PRN code. The unique PRN code is continuously repeated. The GNSS receiver uses a local replica version of the satellite signal to correlate the received satellite signal. The purpose of the correlation process is to synchronize the timing between the local replica and the received satellite signal. Because the timing is unknown and dynamic, the received satellite PRN code sequence must be correlated with a plurality of its time-shifted versions. If the satellite PRN code sequence is unknown, the receiver must try all the possible sequences. Lots of computations, including multiplication operations and summation operations, are required if the code sequence is long and/or there are many satellite code sequences to correlate. Thus, there is a need for an innovative correlation computation design with reduced computation complexity.
One of the objectives of the claimed invention is to provide a correlation computation method for sharing common data and computation for different code sequences to be correlated with a data sequence and an associated apparatus.
According to a first aspect of the present invention, an exemplary correlation computation method is disclosed. The exemplary correlation computation method includes: obtaining a first sum of all data samples included in a data sequence; obtaining a second sum of selected data samples that are selected from the data sequence according to code bits included in a first code sequence; and deriving, by a processing circuit, a first correlation value between the data sequence and the first code sequence from the first sum and the second sum.
According to a second aspect of the present invention, an exemplary correlation computation apparatus is disclosed. The exemplary correlation computation apparatus includes an accumulation-based circuit and a processing circuit. The accumulation-based circuit is arranged to obtain a first sum of all data samples included in a data sequence, and obtain a second sum of selected data samples that are selected from the data sequence according to code bits included in a first code sequence. The processing circuit is arranged to derive a first correlation value between the data sequence and the first code sequence from the first sum and the second sum.
These and other objectives of the present invention will no doubt become obvious to those of ordinary skill in the art after reading the following detailed description of the preferred embodiment that is illustrated in the various figures and drawings.
Certain terms are used throughout the following description and claims, which refer to particular components. As one skilled in the art will appreciate, electronic equipment manufacturers may refer to a component by different names. This document does not intend to distinguish between components that differ in name but not in function. In the following description and in the claims, the terms “include” and “comprise” are used in an open-ended fashion, and thus should be interpreted to mean “include, but not limited to . . . ”. Also, the term “couple” is intended to mean either an indirect or direct electrical connection. Accordingly, if one device is coupled to another device, that connection may be through a direct electrical connection, or through an indirect electrical connection via other devices and connections.
The accumulation-based circuit 102 is arranged to obtain a sum S of all data samples included in a data sequence rn. For example, the data sequence rn is a data block of N (N>1) received data samples {rn, n=0, . . . , N−1} output from an analog-to-digital converter (ADC). Hence, the sum S can be expressed by the following formula.
S=Σ
n=0
N-1
r
n (1)
The ADC can capture one sample of the received signal per PRN code bit. Or several samples per PRN code bit are captured by the ADC and are processed further to get a data sample per PRN code bit. On the other hand, the samples per PRN code bit can be used to correlate with the corresponding samples of a local PRN code bit. Other signal processing might be applied before correlation, such as carrier frequency or Doppler frequency removal. In order to describe our invention more clearly, the following embodiments use one sample per PRN code bit and without other signal processing.
In this embodiment, the correlation computation apparatus 100 is used to correlate the same data sequence rn with M (M>1) code sequences (i.e., PRN codes) Cm,n {Cm,n, m=0, . . . , M−1, n=0, . . . , N−1} for generating M correlation values S0-SM-1, respectively. In other words, each of the code sequences C0,n-CM-1,n has N code bits (also called chips due to bearing no useful data information). With regard to computation of a correlation value Si (i={0, . . . , M−1}) between the data sequence rn and a code sequence Ci,n, the accumulation-based circuit 102 is arranged to obtain a partial sum Pi of selected data samples that are selected from the data sequence rn according to code bits included in the code sequence Ci,n; and the processing circuit 104 is arranged to derive the correlation value Si between the data sequence rn and the code sequence Ci,n from the sum S and the partial sum Pi.
As one of the examples, the transmitted data of a satellite is modulated by bitwise XOR with a code sequence (i.e., a PRN code) according to code-division multiple access (CDMA) spectrum sharing scheme. The resulting spread-spectrum sequence is modulated by binary phase shift keying (BPSK) for transmission, where a logic value 0 of the spread-spectrum sequence is mapped to +1 for BPSK modulation, and a logic value 1 of the spread-spectrum sequence is mapped to −1 for BPSK modulation. At the receiver side, the correlation value Si between the data sequence rn {rn, n=0, . . . , N−1} and the code sequence Ci,n {Ci,n, n=0, . . . , N−1} may be computed using the following formula.
The above formula (2) can be reformulated as below.
S
i=Σn=0N-1Di,n·rn=Σn=0N-1(1−2·Ci,n)·rn=Σn=0N-1rn−2·Σn=0N-1Ci,n·rn=S−2·Pi (3)
In the above formula (3), the partial sum Pi can be expressed by the following formula.
Based on above formulas (1), (3) and (4), the correlation computation apparatus 100 shown in
Since data samples in the data sequence rn that are paired with the corresponding zero code bits Ci,n=0 have no contribution to the partial sum Pi, the accumulation-based circuit 102 is allowed to obtain the partial sum Pi by accumulating data samples paired with the corresponding non-zero code bits Ci,n=1 only. Since the number of selected data samples selected from the data sequence rn (which is a data block of N data samples) for computation of the partial sum Pi is smaller than the number of all data samples included in the data sequence rn (which is a data block of N data samples), the computation of the partial sum Pi has reduced complexity. In a typical PRN code, one half of the code bits are 1's, and the other half of the code bits are 0's. That is, the number of zero code bits 0 in the code sequence Ci,n is equal to the number of non-zero code bits 1 in the same code sequence Ci,n, and half of computation can be reduced therefore. It should be noted that only addition operations are required by computation of the partial sum Pi.
In accordance with the above formula (3), the processing circuit 104 obtains a multiplication result (i.e., 2·Pi) from multiplying the partial sum Pi by a predetermined factor (i.e., 2), and then generates the correlation value Si between the data sequence rn and the code sequence Ci,n by subtracting the multiplication result (i.e., 2·Pi) from the sum S of all data samples (i.e., S=Σn=0N-1rn). The same sum S can be shared among computation of correlation values S0-SM-1 for code sequences C0,n-CM-1,n, and thus the computation complexity of the correlation values S0-SM-1 can be reduced greatly.
As shown in
Based on above formulas (1), (4) and (5), the correlation computation apparatus 100 shown in
Regarding the exemplary designs shown in
In some embodiments of the present invention, the accumulation-based circuit 102 is arranged to categorize all data samples included in the data sequence rn into J (J>1) data words, each having D (D>1) consecutive data samples, where N=J·D; and is further arranged to categorize all code bits included in each code sequence Ci,n into J (J>1) code words Ei,j (j={0, . . . , J−1}), each having D (D>1) consecutive code bits. Note that we can also choose D and J so that N=J·D−k. That is, we can add k dummy bits to the data samples. For example, k one's are added to the tail of the received and local code sequence, respectively. With regard to computation of the correlation value Si for the code sequence Ci,n, the accumulation-based circuit 102 is arranged to accumulate J selected combinational sums one by one to generate the partial sum Pi. For a specific data word (which consists of D consecutive data samples) being one of the data words in the data sequence rn, the accumulation-based circuit 102 generates (2D−1) combinational sums Wj,e that are pre-computed sums obtained according to D data samples included in the specific data word, where e={1, . . . , 2D−1}. After the (2D−1) combinational sums Wj,e are available, the accumulation-based circuit 102 refers to a specific code word Ei,j (which is one of the code words in the code sequence Ci,n and paired with the specific data word) to select one of the (2D−1) combinational sums Wj,e as one of the J selected combinational sums that are involved in computation of the partial sum Pi for the code sequence Ci,n.
Suppose that 3 (D=3) data samples in the data sequence rn is grouped as one data word. For each data word, the accumulation-based circuit 102 computes 7 combinational sums Wj,e, each being a partial sum of the data word that is computed in a way similar to that specified in the formula (4), where e={1, 2, . . . , 7} and there are J data words per data sequence rn (which is a data block of N data samples). Suppose that 3 data samples grouped into the same data word are labeled by {Rn, Rn-1, Rn-2}. The combinational sum Wj,1 is obtained from data sample Rn-2 that is selected from the data samples {Rn, Rn-1, Rn-2} according to code bits included in a code word “001” which is labeled by a decimal value e=1. The combinational sum Wj,2 is obtained from a selected data sample Rn-1 that is selected from the data samples {Rn, Rn-1, Rn-2} according to code bits included in a code word “010” which is labeled by a decimal value e=2. The combinational sum Wj,3 is computed as Wj,3=Rn-1+Rn-2 where data samples Rn-1 and Rn-2 are selected from the data samples {Rn, Rn-1, Rn-2} according to code bits included in a code word “011” with a decimal value label e=3. The combinational sum Wj,4 (Wj,4=Rn) is obtained from one data sample Rn selected from the data samples {Rn, Rn-1, Rn-2} according to code bits included in a code word “100” with a decimal value label e=4. The combinational sum Wj,5 (Wj,5=Rn+Rn-2) is obtained from Rn and Rn-2 that are selected from the data samples {Rn, Rn-1, Rn-2} according to code bits included in a code word “101” with a decimal label value e=5. The combinational sum Wj,6 (Wj,6=Rn+Rn-1) is obtained from Rn and Rn-1 that are selected from the data samples {Rn, Rn-1, Rn-2} according to code bits included in a code word “110” with a decimal label value e=6. The combinational sum Wj,7 (Wj,7=Rn+Rn-1+Rn-2) is obtained from all data samples Rn, Rn-1, and Rn-2 that are selected from the data samples {Rn, Rn-1, Rn-2} according to code bits included in a code word “111” with a decimal label value e=7. It should be noted that, since partial sum accumulation is skipped for the code word “000”, no combinational sum is pre-computed for the code word “000”.
In one exemplary implementation, the sum S of all data samples included in the data sequence rn can be computed using the above formula (1). Alternatively, since the combinational sum Wj,7 (Wj,7=Rn+Rn-1+Rn-2) is pre-computed for each of the J data words, the sum S of all data samples included in the data sequence rn can be obtained from accumulating combinational sums Wj,7 pre-computed for J data words. Specifically, the above formula (1) may be reformulated as below.
S=Σ
n=0
N-1
r
n=Σj=0J-1Wj,7 (6)
Since there are J data words in the data sequence rn {rn, n=0, . . . , N−1} and one of the pre-computed combinational sums Wj,e (j={0, . . . , J−1}) is selected as a partial sum of each data word according to a corresponding code word Ei,j in a code sequence Ci,n, the partial sum Pi (i={0, . . . , M−1}) may be computed using the following formula (7).
In other words, the combinational sum Wj,1 pre-computed for the current data word is selected and output for accumulation if the code word Ei,j corresponding to the current data word is “001”. The combinational sum Wj,2 pre-computed for the current data word is selected and output for accumulation if the code word Ei,j corresponding to the current data word is “010”. The combinational sum Wj,3 pre-computed for the current data word is selected and output for accumulation if the code word Ei,j corresponding to the current data word is “011”. The combinational sum Wj,4 pre-computed for the current data word is selected and output for accumulation if the code word Ei,j corresponding to the current data word is “100”. The combinational sum Wj,5 pre-computed for the current data word is selected and output for accumulation if the code word Ei,j corresponding to the current data word is “101”. The combinational sum Wj,6 pre-computed for the current data word is selected and output for accumulation if the code word Ei,j corresponding to the current data word is “110”. The combinational sum Wj,7 pre-computed for the current data word is selected and output for accumulation if the code word Ei,j corresponding to the current data word is “111”.
After the partial sum Pi (i={0, . . . , M−1}) is available, the correlation value Si (i={0, . . . , M−1}) can be computed using the above formula (3) or (5). Based on the formulas (3), (6) and (7), the correlation computation apparatus 100 shown in
For each data block, computation of combinational sums and selection of one of the combinational sums in the circuit block 402 may be summarized by the following table.
One combinational sum is computed once and may be shared among the computation of multiple partial sums for different code sequences. For example, if the code word Ei,j in the code sequence Ci,n and the code word EM-1,j in the code sequence CM-1,n have the same code bits “110”, the pre-computed combinational sum Wj,6 is selected and involved in the computation of the partial sum P1, and is also selected and involved in the computation of the partial sum PM-1. In this way, the computation complexity of the partial sums P0-PM-1 can be further reduced by reusing the pre-computed combinational sums.
Those skilled in the art will readily observe that numerous modifications and alterations of the device and method may be made while retaining the teachings of the invention. Accordingly, the above disclosure should be construed as limited only by the metes and bounds of the appended claims.
This application claims the benefit of U.S. Provisional Application No. 63/338,913, filed on May 6, 2022. The content of the application is incorporated herein by reference.
| Number | Date | Country | |
|---|---|---|---|
| 63338913 | May 2022 | US |
