System and method for sub-coherent integration for geo-location using weak or intermittent signals
View Patent ↗A signal is received from a mobile device as multiple data samples. The received signal includes a first component corresponding to a known reference signal and a second component corresponding to an unknown channel impairment or an unknown noise. A sequence of blocks is formed based on the received samples. The first component of the received signal corresponding to the reference signal is known to within a constant phase shift over each block. A plurality of function values are generated as a function of time, frequency, and phase, based on the received signal, corresponding to a plurality of times, a plurality of frequencies, and a plurality of phase sequences. A time, a frequency, and a phase sequence corresponding to an optimal value the function values are determined. The determined time is outputted as a time of arrival of the received signal.
1. A method for determining a time of arrival of a signal transmitted by a mobile device, the method comprising:
receiving a signal from a mobile device as a plurality of data samples, the received signal including a first component corresponding to a known reference signal and a second component corresponding to at least one of an unknown channel impairment and an unknown noise; forming a sequence of blocks based on the received samples, wherein the first component of the received signal corresponding to the reference signal is known to within a constant phase shift over each block; generating a first plurality of function values as a function of time, frequency, and phase, based on the received signal, wherein the function values of the first plurality correspond to a plurality of times, a plurality of frequencies, and a plurality of phase sequences, and the function values of the first plurality are calculated to compensate for frequency and phase discontinuities and drift; determining a time, a frequency, and a phase sequence corresponding to an optimal value of the first plurality of function values; and outputting the determined time as the time of arrival of the received signal.
2. The method of claim 1 , wherein the optimal value is a function value having a maximal magnitude.
3. The method of claim 1 , wherein the blocks in the sequence of blocks include a common number of samples.
4. The method of claim 1 , wherein generating the first plurality of function values includes computing:
f
(
ω
,
τ
,
Φ
)
=
exp
(
jϕ
1
)
∑
n
=
1
m
s
1
(
n
+
τ
)
*
r
1
(
n
)
exp
(
-
j
n
ω
)
+
…
+
exp
(
jϕ
K
)
∑
n
=
M
-
m
+
1
M
s
k
(
n
+
τ
)
*
r
k
(
n
)
exp
(
-
j
n
ω
)
,
wherein * denotes complex conjugation, ω represents frequency, τ represents time, Φ represents the sequence of phase values φ 1 , . . . , φ K , s represents the received signal, r represents the reference signal, subscripts to s and r represent portions of those signals corresponding to respective blocks, m represents a number of samples in each block, M represents a total number of received samples, and K represents a number of blocks in the sequence of blocks.
5. The method of claim 1 , wherein each phase sequence in the plurality of phase sequences is a sequence of phase values associated with respective blocks, and the phase values of each phase sequence in the first plurality are separated from one another by multiples of a phase spacing.
6. The method of claim 1 , wherein forming the sequence of blocks based on the received samples includes forming a reference block and a non-reference block, wherein a phase value associated with the reference block in the determined phase sequence is known to be zero.
7. The method of claim 1 , wherein each phase sequence in the plurality of phase sequences is a sequence of phase values associated with respective blocks, the method further including searching for a refined set of inputs that optimizes the function of time, frequency, and phase by searching a neighborhood around each phase value in the determined phase sequence.
8. The method of claim 1 , wherein generating the first plurality of function values includes:
generating, for each block, a second plurality of function values as a function of time and frequency, based on the received signal, wherein the function values of the second plurality correspond to the plurality of times and to the plurality of frequencies; and
for each time in the plurality of times, each frequency in the plurality of frequencies, and each phase sequence in the first plurality of phase sequences:
for each block, shifting the function value in the second plurality corresponding to said time, said frequency, and said block by a phase value of said phase sequence associated with said block, to generate a shifted value for said block; and
adding the shifted values for the respective blocks, to generate the function value in the first plurality corresponding to said time, frequency, and phase sequence.
9. The method of claim 1 , wherein each phase sequence in the plurality of phase sequences is a sequence of phase values associated with respective blocks, and wherein generating the first plurality of function values includes:
generating, for each block, a second plurality of function values as a function of time and frequency, based on the received signal, wherein the function values of the second plurality correspond to the plurality of times and to the plurality of frequencies;
sorting the phase sequences in the plurality of phase sequences into a sequence of phase sequences according to an order, wherein each pair of adjacent phase sequences in the sequence of phase sequences differ at exactly one phase value and are equal to one another at the other phase values; and
for each time and frequency:
evaluating the function of time, frequency, and phase at said time, said frequency, and an initial phase sequence in the sequence of phase sequences, and
evaluating the function of time, frequency, and phase at said time, said frequency, and each phase sequence other than said initial phase sequence sequentially according to the order, by adjusting a function value of said function of time, frequency, and phase at said time, said frequency, and a predecessor phase sequence with a term dependent on the function value in the second plurality corresponding to said time, said frequency, and the block associated with the phase values that differ between said phase sequence and said predecessor phase sequence.
10. The method of claim 9 , wherein the phase values of each phase sequence are each expressible as 2*π*k/L, wherein L is an integer, and k is an integer greater than or equal to 0 and less than or equal to L−1.
11. The method of claim 1 , wherein each phase sequence in the plurality of phase sequences is a sequence of phase values associated with respective blocks, and the sequence of blocks includes K blocks, and the phase values of each phase sequence are each expressible as 2*π*k/L, wherein L is an integer, and k is an integer greater than or equal to 0 and less than or equal to L−1, the method further comprising:
determining a plurality of codes, each code having K symbols, one symbol corresponding to each block, each symbol being mappable to a value between 0 and L−1, wherein the plurality of codes are a closed group under an algebraic operation;
determining a representative set of codes in the plurality of codes, wherein the representative set is a subgroup of the closed group;
for each code in the representative set, providing a phase sequence in said plurality of phase sequences based on said code, wherein each phase value of said phase sequence is assigned as 2*π*p/L, wherein p is a symbol of said code corresponding to the block associated with said phase value, to provide the plurality of phase sequences.
12. The method of claim 1 , wherein each received sample is in one of the blocks.
13. The method of claim 1 , wherein forming the sequence of blocks based on the received samples includes:
dividing the received samples into a plurality of blocks;
sorting the plurality of blocks according to a predetermined metric; and
determining a subset of the sorted plurality of blocks that satisfy a predetermined condition; and
providing the determined subset as the sequence of blocks.
14. A non-transitory computer readable storage medium having instructions stored tangibly thereon, the instructions when executed by a processor causing the processor to perform the operations of:
receiving a signal from a mobile device as a plurality of data samples, the received signal including a first component corresponding to a known reference signal and a second component corresponding to at least one of an unknown channel impairment and an unknown noise; forming a sequence of blocks based on the received samples, wherein the first component of the received signal corresponding to the reference signal is known to within a constant phase shift over each block; generating a first plurality of function values as a function of time, frequency, and phase, based on the received signal, wherein the function values of the first plurality correspond to a plurality of times, a plurality of frequencies, and a plurality of phase sequences, and the function values of the first plurality are calculated to compensate for frequency and phase discontinuities and drift; determining a time, a frequency, and a phase sequence corresponding to an optimal value of the first plurality of function values; and outputting the determined time as the time of arrival of the received signal.
15. The computer readable storage medium of claim 14 , wherein each phase sequence in the plurality of phase sequences is a sequence of phase values associated with respective blocks, and wherein causing the processor to perform the generation of the first plurality of function values includes causing the processor to perform the operations of:
generating, for each block, a second plurality of function values as a function of time and frequency, based on the received signal, wherein the function values of the second plurality correspond to the plurality of times and to the plurality of frequencies;
sorting the phase sequences in the plurality of phase sequences into a sequence of phase sequences according to an order, wherein each pair of adjacent phase sequences in the sequence of phase sequences differ at exactly one phase value and are equal to one another at the other phase values; and
for each time and frequency:
evaluating the function of time, frequency, and phase at said time, said frequency, and an initial phase sequence in the sequence of phase sequences, and
evaluating the function of time, frequency, and phase at said time, said frequency, and each phase sequence other than said initial phase sequence sequentially according to the order, by adjusting a function value of said function of time, frequency, and phase at said time, said frequency, and a predecessor phase sequence with a term dependent on the function value in the second plurality corresponding to said time, said frequency, and the block associated with the phase values that differ between said phase sequence and said predecessor phase sequence.
16. The computer readable storage medium of claim 14 , wherein each phase sequence in the plurality of phase sequences is a sequence of phase values associated with respective blocks, and the sequence of blocks includes K blocks, and the phase values of each phase sequence are each expressible as 2*π*k/L, wherein L is an integer, and k is an integer greater than or equal to 0 and less than or equal to L−1, wherein the instructions when executed by the processor further cause the processor to perform the operations of:
determining a plurality of codes, each code having K symbols, one symbol corresponding to each block, each symbol being mappable to a value between 0 and L−1, wherein the plurality of codes are a closed group under an algebraic operation;
determining a representative set of codes in the plurality of codes, wherein the representative set is a subgroup of the closed group;
for each code in the representative set, providing a phase sequence in said plurality of phase sequences based on said code, wherein each phase value of said phase sequence is assigned as 2*π*p/L, wherein p is a symbol of said code corresponding to the block associated with said phase value, to provide the plurality of phase sequences.
17. A method for determining a time of arrival of a signal transmitted by a mobile device, the method comprising:
receiving a signal from a mobile device as a plurality of data samples, the received signal including a first component corresponding to a known reference signal and a second component corresponding to at least one of an unknown channel impairment and an unknown noise; forming a sequence of blocks based on the received samples; dividing the sequence of blocks into plural sets of blocks, wherein for each set, the first component of the received signal corresponding to the reference signal is known to within a constant phase shift over each block in said set; for each set: generating a plurality of function values as a function of time, frequency, and phase, based on the received signal, wherein the function values of the plurality correspond to a plurality of times, a plurality of frequencies, and a first plurality of phase sequences, and the function values are calculated to compensate for frequency and phase discontinuities and drift, and determining a time, a frequency, and a phase sequence associated with said set corresponding to an optimal value of the first plurality of function values; and determining the time of arrival based on the determined times associated with respective sets.
18. The method of claim 17 , wherein determining the time of arrival includes selecting an earliest time among the determined times associated with respective sets.
19. The method of claim 17 , wherein determining the time of arrival includes selecting a median time among the determined times associated with respective sets.
20. A method for determining a time of arrival of a signal transmitted by a mobile device, the method comprising:
receiving a signal from a mobile device as a plurality of data samples, the received signal including a first component corresponding to a known reference signal and a second component corresponding to at least one of an unknown channel impairment and an unknown noise;
forming a sequence of blocks based on the received samples, wherein the first component of the received signal corresponding to the reference signal is known to within a constant phase shift over each block;
generating, for each block, a first plurality of function values as a function of time and frequency, based on the received signal, wherein the function values of the first plurality correspond to a plurality of times and to a plurality of frequencies;
sorting the sequence of blocks according to a predetermined metric;
dividing the sorted sequence of blocks into plural sets of blocks, wherein the sets are ranked according to an order;
at an initial processing stage Z 0 , determining at least one candidate phase sequence based on a function of time, frequency, and phase and based on an initial set S 0 among the sets of blocks;
at each stage Z i of one or more subsequent processing stages corresponding to respective distinct sets other than said initial set S 0 , determining at least one candidate phase sequence based on the function of time, frequency, and phase, further based on a set S j corresponding to said processing stage, and further based on the sets preceding set S j , wherein an initial subsequence of each candidate phase sequence determined at stage Z i includes one of the candidate phase sequences determined at a stage Z i-1 preceding stage Z i ;
determining a time, a frequency, and a phase sequence that optimize the function of time, frequency, and phase based on the at least one candidate phase sequence determined at a last processing stage among the subsequent processing stages; and
outputting the determined time as the time of arrival of the received signal.