Acquisition of Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 231

If 1 ms of data is processed coherently, the equivalent bandwidth is 1 kHz
(1/10 − 3 sec). Because the cw signal is narrow band, the amplitude of the signal
is not affected by narrowing the bandwidth. However, the noise is limited by the
bandwidth, and the equivalent noise power is at 144 dBm at 1 kHz bandwidth.

Thus 1 ms coherent integration can produce a S / N of 14 dB (

−

− 130 + 144) for

an input of 130 dBm. From past acquisition experience this approach gen-

erates satisfactory results. Therefore it further confirms that S / N

−

= 14 dB is a

reasonable value to use for signal acquisition.
If 2 ms of data are processed coherently, the corresponding bandwidth is
500 Hz, and the noise floor is at − 147 dBm. This method produces an S / N of
17 dB ( − 130 + 147). In general, the additional coherent integration gain G c of
n ms over 1 ms is

G c = 10 log (n)

( 10 . 6 )

3 and 10 dB, respectively.
The length of coherent integration is limited by the navigation data, and the
navigation data occur every 20 ms. One common maximum length used for weak
signal acquisition is 10 ms because, in two consecutive 10 ms of input data, at
least one set of data is without a navigation data phase transition. The coherent
gain of 10 ms is 10 dB. Additional gain must be obtained from noncoherent
integration. The following discussion is based on this assumption.
Sometimes the acquisition can use longer than 10 ms of data for coherent
integration. For example, one can use 16 ms for coherent integration and ignore
the navigation phase transition. The output will be degraded if navigation data
transition is included in the data set. Other methods can be used to accommodate
the phase transition. For example, performing 20 ms coherent integration can
generate 1 set of correlation outputs. This acquisition can be performed 20 times
by sliding the input data 1 ms each time to generate 20 sets of outputs. If there
is no data transition in the input data, then all the 20 sets of outputs should have
similar amplitude. If there is a data transition, then the highest output in the 20
sets should represent the 20 ms of input data without data transition. However,
when the signal is weak, the highest output cannot be easily identified.

If n = 2 and 10 ms, the additional gains are G c =

10.6 NONCOHERENT INTEGRATION

Noncoherent integration uses the outputs generated from coherent integrations
to achieve additional S / N gain. Typically a set of long input data is divided
into many blocks and coherent integration is performed on all the blocks. After
the coherent integration every frequency output is complex and can be put into
amplitude form. The amplitudes from the all coherent integration of the same
frequency are summed. As a result, the otherwise weak signal will be enhanced,
leading to a higher S / N .
For example, from 1 ms coherent acquisition, 2500 amplitudes in time domain
will be generated. If 20 frequency bins each separated by 1 kHz are covered,