Up-sampling and cross-correlation for time of arrival determinations in passive entry/passive start systems

1. A portable access device for an access system of a vehicle, the portable access device comprising:

a receiver configured to receive a signal transmitted from an access module of the vehicle to the portable access device; and

a control module configured to

generate a differentiated signal based on the received signal,

up-sample the differentiated signal to generate a first up-sampled signal,

obtain or generate an expected signal,

up-sample the expected signal to generate a second up-sampled signal,

cross-correlate the first up-sampled signal and the second up-sampled signal to generate a cross-correlation signal,

based on the cross-correlation signal, determine a phase difference between the first up-sampled signal and the second up-sampled signal,

determine a round trip time of the signal received by the receiver, and

either

transmit the round trip time to the vehicle to gain access to the vehicle based on the round trip time, or

determine at least one of a location or a distance between the portable access device and the vehicle and transmit at least one of the location or the distance to the vehicle to gain access to the vehicle.

2. The portable access device of claim 1 , wherein the control module is configured to:

downconvert the signal to generate a downconverted signal;

sample the downconverted signal to generate a sampled signal;

perform an arctangent of the sampled signal to generate an arctangent signal; and

differentiate the arctangent signal to generate the differentiated signal.

3. The portable access device of claim 1 , wherein the control module is configured to:

determine at least one of a location or a distance of the portable access device relative to the vehicle based on the round trip time; and

transmit the at least one of the location or the distance to the vehicle to gain access to the vehicle based on the at least one of the location or the distance.

4. The portable access device of claim 1 , wherein the control module comprises:

a first up-sampler is configured to up-sample the differentiated signal to generate the first up-sampled signal; and

a second up-sampler is configured to up-sample the expected signal to generate the second up-sampled signal,

wherein an up-sample rate of the first up-sampler is a same sample rate as the second up-sampler.

5. The portable access device of claim 1 , wherein the control module comprises:

a sign module configured to determine a sign of the differentiated signal; and

a bit pattern module configured to generate the expected signal based on the sign of the differentiated signal.

6. The portable access device of claim 1 , wherein:

the control module is configured to obtain the expected signal; and

the expected signal is a predetermined signal obtained by the control module prior to receiving the received signal.

7. The portable access device of claim 1 , wherein:

the control module is configured to perform an iterative process comprising

multiply bits of the first up-sampled signal and the second up-sampled signal to generate resultant products,

sum the resultant products to generate a product-sum value, and

shift the second up-sampled signal relative to the first up-sampled signal;

the iterative process provides a plurality of product-sum values; and

the control module is configured to determine the phase difference based on the plurality of product-sum values.

8. The portable access device of claim 7 , wherein the control module is configured to reconstruct the signal transmitted from the access module of the vehicle to the portable access device based on zero-crossings of a portion of the cross-correlation signal associated with a maximum of the plurality of product-sum values.

9. The portable access device of claim 1 , wherein the control module comprises:

an up-sampler configured to up-sample the differentiated signal to generate the first up-sampled signal;

a sign module configured to determine a sign of the first up-sampled signal; and

a bit pattern module configured to generate the expected signal based on the sign of the first up-sampled signal.