Ranging in multi-band communication systems
System and methods include transmitting the same signal in all sub-bands in different time intervals and processing the corresponding received signals to achieve a time resolution proportional to the inverse of the whole bandwidth as opposed to that of a single sub-band. The systems and methods refine the coarse resolution that is achieved by conventional approaches, such as the correlation method, in a single sub-band by aligning the outputs of the matched filters to the received signals from all sub-bands and applying a fast Fourier Transform (FFT) in each time bin along the sub-band index.
1. A method for communications, the method comprising:
receiving a plurality of sub-band signals of a multi-band signal, wherein each of the plurality of sub-band signals has a corresponding base-band, each of the corresponding base-bands comprising a same base-band signal, and each of the same base-band signals are received at different tie intervals in each sub-band;
passing the plurality of sub-band signals through a plurality of matched filters to produce a plurality of filter outputs;
sampling the outputs of the plurality of matched filters to generate a plurality of sampled filter outputs;
aligning the plurality of sampled filter outputs into a matrix Y wherein matrix Y is aligned such that Y(m,n)=y m (n/w s ) where y m comprises a sub-band signal output of index m of a matched filter, n is a time index, and w s comprises a sampling rate;
applying an inverse FFT along sub-band indexes of matrix Y to produce a matrix Z; and
estimating a signal delay by determining a maximum of the plurality of sampled filter outputs in matrix Z after application of the inverse FFT.
2. The method of claim 1 , further comprising:
receiving an estimate of phase mismatch; and
compensating for the phase mismatch using the estimate after aligning the plurality of sampled filter outputs and before applying the inverse FFT.
3. The method of claim 1 , wherein estimating the signal delay includes determining time index n and index m where the matrix Z has a maximum.
4. The method of claim 1 , wherein the signal delay is determined according to index m and time index n where matrix Z has a maximum, the signal delay determined according to the formula
signal delay=( m+Nn )/( Nw s )
where N comprises the number of sub-band signals.
5. A system for providing high time resolution signal multiband communication, the system comprising:
one or more processors;
a memory including instructions, which when executed by the one or more processors, cause the one or more processors to:
receive a plurality of sub-band signals of a multi-band signal, wherein each of the plurality of sub-band signals has a corresponding base-band, each of the corresponding base-bands comprising a same base-band signal, and each of the same base-band signals are received at different tie intervals in each sub-band;
pass the plurality of sub-band signals through a plurality of matched filters to produce a plurality of filter outputs;
sample the plurality of filter outputs to generate a plurality of sampled filter outputs;
align the plurality of sampled filter outputs into a matrix Y wherein matrix Y is aligned such that Y(m,n)=y m (n/w s ) where y m comprises a sub-band signal output of index m of a matched filter, n is a time index, and w s comprises a sampling rate;
apply an inverse FFT along sub-band indexes of matrix Y to produce a matrix Z; and
estimate a signal delay based on matrix Z.
6. The system of claim 5 , comprising the memory including instructions, which when executed by the one or more processors, cause the one or more processors to:
receive an estimate of phase mismatch; and
compensate for the phase mismatch in matrix Y.