volume55-number1 - Flipbook - Page 8
Figure 4 shows the blocks used in modern wideband digital conversion
(as relevant to this discussion). The flow consists of sampling, digital
downconverting, digital filtering, decimating, and fast Fourier transforming the
data stream.
First, the data sampled at fS is digital downconverted to baseband (complex I/Q)
using a fine-tuned NCO. The data stream is then filtered using a programmable
low-pass digital filter. This predecimation digital filtering sets the IF bandwidth
and is the first of two different operations to set the receiver noise floor PN. As
the IF bandwidth gets smaller, the integrated in-band noise power decreases as
the filtering attenuates the wideband noise.
IF (noise) channel bandwidth = fS /2M
(6)
Next, decimating by M reduces the effective sampling rate to fS/M, keeping every
Mth sample and throwing out the samples in between.
Thus, the downstream FFT processing gets a data stream with rate fS/M and
bandwidth fS/2M. Finally, the FFT length N sets the bin width and capture time,
which is the second step in setting the noise floor.
FFT bin = [IF channel BW] / [N/2] Hz = fS /[MN] Hz
Processing Bandwidth and System Performance
Trade-Offs
(7)
Decimation and FFT Impact to Wideband Digital
Receiver Noise Floor
Figure 5 relates the wideband digital receiver’s processing noise floor (K) to the
ADC’s noise spectral density (L), which is the widely available data sheet FOM for
ADC additive noise. Existing ADI literature does a nice job explaining processing
gain, NSD, SNR, and quantization noise.7
The most useful relation from Figure 5 is:
K=L+F
Or, in other words
Processing noise floor (dBFS) = NSD (dBFS/Hz) +
10Log10[fs/(MN)/Hz] (dB)
Even though increasing the decimation factor M has the same proportional
effect in reducing the noise floor (Figure 5, C) as increasing the FFT length N
(Figure 5, E), it is important to note the mechanisms are entirely different. The
decimation step involves band-limiting the channel using digital filtering. This
sets the effective noise bandwidth that determines the total integrated noise in
the channel (Figure 5, D). It also sets the maximum instantaneous spectral bandwidth of a detectable signal. Compare this to the FFT step, which does not filter
per se, but spreads the total integrated noise in the channel over N/2 bins and
defines the spectral line resolution. The higher N, the more bins, and the lower
the noise content per bin.8 Together, decimation gain M and FFT gain N define
the FFT bin width, and they are often lumped together in discussions of processing bandwidth (Figure 5, F), but their values must be balanced based upon their
respective nuanced impact to signal bandwidth, spectral resolution, sensitivity,
and latency requirements, as discussed in the next section.
(8)
The processing noise floor (Figure 5, K) is the same as PN and can be dropped
into Equation 1 and Equation 2. Note that the designer carefully selects M and N
based upon design trade-offs and constraints discussed in the next section.
Relating decimation M and FFT N back to high priority performance attributes:
Latency is the time to sense and process successive spectral captures, and it
requires as short a time as possible. Many systems require near real-time operation. This dictates M × N be as small as possible. As the FFT size increases, the
spectral resolution improves and noise floor decreases as the integrated noise is
spread over more bins. The trade-off is acquisition time, which is a big deal and
is simply:
The minimum detectable pulse width (PW) sets the minimum allowable IF
channel bandwidth as the spectral content of a shorter time pulse spreads
over a relatively wider frequency band. If the IF channel bandwidth is too
narrow, the signal spectral content truncates, and the short time pulse isn’t
detected properly. Minimum IF BW, which sets maximum allowable M, must meet
the criteria:
RF BW
fS/2
(10)
fs/[2M] > [1/PW] Hz
Rate = fS
Rate = fS/M
Digital
Downconverter
*!+ADC
(9)
Time = N × M × ts (seconds)
Digital
Filter
Decimate
M
BW = fS/2M
NSD FOM
Figure 4. Simple block diagram of ADC data decimation and FFT.
FFT
Length N
FFT Bin =
fS/M
N
G ADC Full Scale (dBFS)
A
ADC SNR dB
H ADC Thermal and Quantization Noise (dBFS)
B
ADC Nyquist BW
10Log (fS/2) dB
C
Filter and Decimate M
10Log (M) dB
D"
Filter and Decimate M
10Log (fS/2M) dB
J Channel Noise (dBFS)
FFT N
10Log (N/2) dB
Filter, Decimate, FFT
10Log (fS/[MN]) dB
FFT Bin Width Hz
E
K Processing
Noise Floor (dBFS)
F
L ADC NSD (dBFS/Hz)
Figure 5. Relationship of decimation and FFT gain operations to commonly referenced noise levels.
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Analog Dialogue Volume 55, Number 1
