Trade-off between Sensitivity and Dynamic Range in
Designing Digital Radar Receivers
1,2
1
2
2
3
1
Zhijian Li , L.P. Ligthart , Peikang Huang , Weining Lu , W.F. van der Zwan
2
Nanjing Electronic Equipment Institute, 35 Hou Biao Ying St., 210007 Nanjing, China
IRCTR, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands
3
The Second Academy of China Aerospace, 52 Yong Ding Rd., 100854 Beijing, China
Abstract - For optimizing a radar system and the digital radar
receiver in particular, the designer is always confronted with
trade-offs between sensitivity and dynamic range. In the paper
the impact of effective noise figure of the Analog to Digital
Converter (ADC) on receiver performance is discussed. Next
different definitions of dynamic range are presented. An S-band
IF sampling digital receiver for different scenarios is analyzed
and compared theoretically. A scenario for studying the
compromise between sensitivity and dynamic range is proposed
and simulated using Agilent Advanced Design System (ADS)
simulation software. Finally, simulation results are presented to
demonstrate the validity of the theoretical analysis.
I.
INTRODUCTION
Digital receiver concepts are widely used in radar and
communication systems. Fig. 1 shows a most basic block
diagram of the digital receiver. Due to the limited availability
of ADCs with a high sampling frequency and a high number
of bits, the ADC is a crucial component to be selected when
designing a digital receiver [1]. The RF front-end is then
designed to match with the selected ADC. The RF front-end
characteristics, such as the noise figure (NF), gain, 1-dB
compression point (P1dB) and third-order intercept point (IP3),
are chosen to optimize the receiver performance.
For a given bandwidth, the cascade NF defines the
sensitivity of the receiver and determines the lowest input RF
power that can be detected by the receiver. The dynamic range
(DR) of a receiver is the measure of the receiver’s ability to
handle a range of signal strengths, from the weakest to the
strongest.
The highest sensitivity can be realized by using a low noise
amplifier (LNA) with the lowest NF and highest available
gain in order to minimize the impact of a high NF of the
succeeding stage in the receiver chain. The largest DR can be
realized by using a LNA with the largest third-order intercept
point at the input (IIP3). This maximum IIP3 can be obtained
by using a LNA with the highest third-order intercept point at
the output (OIP3) and a moderate gain. However, it is not
realistic to get a LNA with the lowest NF and the largest IIP3.
Figure 1 Basic block diagram of a digital receiver
978-1-4244-1880-0/08/$25.00 ©2008 IEEE.
In this paper an IF sampling digital receiver used for an Sband radar application is presented. The receiver design for
optimizing sensitivity and DR is analyzed using various
scenarios. After comparison between the scenarios, a
compromise scenario is proposed and simulated using ADS.
The simulation results for this compromise scenario are given
to demonstrate the validity of our approach based on the herepresented theoretical analysis.
The rest of the paper is organized as follows. Section II
describes the general design consideration of the receiver.
Some definitions of DR are given in Section III. Section IV
presents in detail the theoretical analysis of sensitivity and DR
for different scenarios. Section V gives the simulation results
of an S-band digital radar receiver for the compromise
scenario. Some final conclusions are described in Section VI.
II. GENERAL DESIGN CONSIDERATION OF RECEIVER
For most modern receiver chains starting with the LNA and
ending with an ADC, it is important to understand not only the
limitations of the input power and noise at the receiver input,
but also to consider the requirements and limitations of the
ADC.
While using a high performance ADC in a digital receiver,
the NF of ADC (NFADC) should be taken into account, in order
to determine the cascade NF of the complete receiver. The
NFADC is normally much higher than the NF of the RF frontend (NFRF). From sensitivity point of view, the overall gain of
the receiver should therefore be high enough in order to
decrease the NF degradation (ΔNF) caused by the ADC.
However, from DR point of view the overall gain of the
receiver should not be too high. Otherwise the maximum input
signal level of the receiver will be relatively low due to the
limitation of the full-scale input level (PFS) of the ADC.
The parameters of our selected ADC correspond to the 12bit AD12401 from Analog Devices [2]. For this ADC PFS is
14.08dBm, the SNR (SNRADC) is 63dBFS for a -1dBFS input
signal and the sampling frequency (fs) equals 400MHz. The
effective NFADC can be described as follows [3]:
⎛
⎛ f ⎞⎞
NFADC = ( PFS − 1 − SNRADC ) − ⎜ KT + 10 lg ⎜ s ⎟ ⎟
⎝ 2 ⎠⎠
⎝
⎛
⎛ 400 ×106 ⎞ ⎞
= (14.08 − 1 − 63) − ⎜⎜ −174 + 10 lg ⎜
⎟ ⎟⎟
2
⎝
⎠⎠
⎝
= 41.07 dB
where
(1)
KT is -174dBm/Hz
ICMMT2008 Proceedings
58
B. CDR
CDR is the difference in dB between the receiver noise
floor and the input 1-dB compression point (P1dB_input). CDR
can be expressed as follows:
X: 0.1
Y: 57.4
56
54
X: 0.4
Y: 51.23
G + NFRF (dB)
52
CDR = P1dB _ input − PRx _ noise _ floor
(8)
For some radar applications with high linear DR, the
linearity margin should be considered in the receiver design.
In such applications, CDR does not make sense.
50
48
46
44
X: 3
Y: 41.09
42
40
0
0.5
1
1.5
ΔNF (dB)
2
2.5
3
Figure 2 Relation between G+NFRF and ΔNF
Fig. 2 gives the relation between the summation of the gain
and NFRF i.e. (G+NFRF in dB) and ΔNF. The figure learns that
the higher G+NFRF, the lower is ΔNF. The equations for
deriving this relationship are
F −1
(2)
F = F + ADC
(4)
ILDR will be used in our analysis to optimize the receiver
performance. Therefore, in the following sections DR refers to
ILDR. In Section V, a realistic P1dB and IP3 for every
component are selected to meet the requirements for CDR and
SFDR of the receiver.
(5)
IV. THEORETICAL ANALYSIS FOR DIFFERENT SCENARIOS
(6)
The scenario leading to the optimum sensitivity and DR will
be analyzed in detail in this section.
The equations, given below, are related to our theoretical
analysis of the receiver. They describe the noise floor, the
maximum input level (considering 1 dB linearity margin of
the ADC), the sensitivity and DR, respectively. The chosen
receiver bandwidth (B) is 50MHz. The SNR, which will be
used to estimate the sensitivity, is supposed to be 10dB.
(10)
PRx _ noise _ floor = KTB + NFRF + ΔNF
RF
g
FADC − 1
F
ΔF =
= 1+
FRF
g × FRF
NF = NFRF + ΔNF
F −1
g × FRF = ADC
ΔF − 1
where
⎛ 100.1× NFADC − 1 ⎞
G + NFRF = 10 lg ⎜ 0.1×ΔNF
⎟
−1 ⎠
⎝ 10
(3)
F is the overall noise factor of receiver,
NF is the overall noise figure of the receiver in dB,
FRF is the noise factor of the RF front-end,
NFRF is the noise figure of the RF front-end in dB,
FADC is the noise factor of the ADC,
NFADC is the effective noise figure of the ADC in dB,
ΔF is the noise factor degradation due to FADC,
ΔNF is the NF degradation due to NFADC in dB,
g is the gain of the RF front-end,
G is the gain of the RF front-end in dB.
III. DEFINITIONS OF DYNAMIC RANGE
There are various definitions for dynamic range, such as
desensitization dynamic range (DDR), spur-free dynamic
range (SFDR), 1-dB compression dynamic range (CDR) [4],
and ideal linear dynamic range (ILDR). The definitions of
SFDR, CDR and ILDR will be presented next.
A. SFDR
SFDR is the difference in dB between the receiver noise
floor (PRx_noise_floor) and the level of each of two (with equal
amplitude) out-of-band interfering tones that produce an inband spurious product equal in power to the noise floor.
Generally, the IIP3 is used to predict the spurious product.
SFDR can be expressed as follows:
SFDR = 2 3 ( IIP3 − PRx _ noise _ floor )
C. ILDR
ILDR can be used to describe the receiver DR, when the
P1dB and IP3 for all the components in the receiver are ideal
(e.g. 100dBm).
ILDR is the difference in dB between the receiver noise
floor and the maximum input level (PRx_input_max), which drives
the ADC input signal to the full-scale level. ILDR can be
expressed as follows:
(9)
ILDR = PRx _ input _ max − PRx _ noise _ floor
(7)
PRx _ input _ max = PFS − 1 − G
(11)
Sensitivity = PRx _ noise _ floor + SNR
(12)
DR = PRx _ input _ max − PRx _ noise _ floor
(13)
The sensitivity and DR of the receiver are limited by either
the RF front-end or the ADC. Fig. 3 gives the relation between
receiver sensitivity and overall gain and fig. 4 gives the
relation between receiver DR and overall gain. Fig. 3 and fig.
4 learn that there exists some cut-off gain Gc [5]. If the
receiver overall gain is lower than Gc, the sensitivity and the
DR are limited by the ADC. If the receiver overall gain is
higher than Gc, the sensitivity and the DR are limited by the
RF front-end.
From NF point of view, the precise definition of Gc can be
expressed as follows: when the overall gain equals Gc, the
NFRF equals ΔNF. It means that the overall NF equals two
times NFRF. When the overall gain is higher or lower than Gc,
the overall NF is determined mainly by NFRF or NFADC.
Equation (6) can be expressed as
⎛ 100.1× NFADC − 1 ⎞
Gc = 10 lg ⎜ 0.1× NFRF
⎟ − NFRF
−1 ⎠
⎝ 10
(14)
-45
A. The Highest Sensitivity Scenario
In the highest sensitivity scenario, the gain of the RF frontend should be as high as possible and the NF of the LNA as
low as possible. The overall gain can be set at some value,
which enables ΔNF to be equal to 0.1dB. Fig. 2 shows that
G+NFRF equals 57.4dB. Model 1 of the LNA is proposed to be
used in this scenario. Considering an insertion loss of BPF1,
the cascade NFRF is supposed to be approximately 1.2dB.
Thus the overall gain of the RF front-end becomes 56.2dB.
The receiver performance can be calculated using (10) to
(13). We derive that the noise floor equals -95.71dBm, the
maximum input level -43.12dBm, the sensitivity -85.71dBm
and the DR 52.59dB.
-50
Sensitivity (dBm)
-55
-60
-65
-70
-75
limited by ADC
-80
-85
0
10
20
30
limited by RF front-end
Gc40
Gain (dB)
50
60
70
80
B. The Largest DR Scenario
In the largest DR scenario, the gain of the RF front-end
should not be too high while the P1dB_out of LNA should be as
high as possible. The overall gain can be set at Gc, which
enables ΔNF to be equal to 3dB. Fig. 2 shows that G+NFRF is
41.09dB. Model 2 of the LNA is proposed to be used in this
scenario. The cascade NFRF is supposed to be approximately
2.3dB. The overall gain of the RF front-end becomes 38.79dB.
The receiver performance can be calculated using (10) to
(13). The noise floor equals -91.71dBm, the maximum input
level -25.71dBm, the sensitivity -81.71dBm and the DR 66dB.
As can be seen from fig. 4, when the receiver overall gain is
low enough, the maximum DR approaches 69dB. But in
reality, the dynamic range of ADC (DRADC) is limited by its
quantization level. DRADC can also be expressed as [6]
Figure 3 Relation between receiver sensitivity and overall gain
70
65
limited by RF front-end
limited by ADC
60
DR (dB)
55
50
45
40
35
30
25
0
10
20
30
Gc40
Gain (dB)
50
60
70
80
(
DRADC = 10 lg 22 N −3 k 2
Figure 4 Relation between receiver DR and overall gain
There is another definition of Gc which is convenient for use
in a practical design. When the overall gain equals Gc, the FRF
equals (FADC-1)/g. Under this condition, ΔNF equals 3dB. It
means that the overall NF is 3 dB higher than NFRF. Because
FADC is much higher than 1, (6) can be expressed as
Gc = 10 lg ( FADC − 1) − NFRF
≈ NFADC − NFRF
(15)
Fig. 5 shows a typical block diagram of an S-band digital
radar receiver. The performance of the RF front-end (e.g., NF,
gain, P1dB and IP3) are determined by the cascade performance
of the components in the RF front-end. The overall NF is
mainly determined by the first stage amplifier (LNA) and the
preceding passive components (RF BPF1).
When designing the RF front-end, the LNA is the prime
component to be selected to optimize the receiver performance.
The primary specifications of two S-band LNAs which can be
used in this design are given in table I. OIP3 is typically 10 to
15dB higher than output 1-dB compression point (P1dB_out). A
value of 13dB is selected in the following analysis.
TABLE I
PRIMARY SPECIFICATIONS OF TWO LNAS
Model
Gain
NF
P1dB_out
P1dB_in
OIP3
IIP3
(dB)
(dB)
(dBm)
(dBm)
(dBm)
(dBm)
Model 1
40
0.4
13
-26
26
-14
Model 2
35
1.5
25
-9
38
3
)
= 6.021N − 9.031 − 20 lg k
(16)
N is the number of bits in the ADC,
k is the ratio of the input rms noise level to the
quantization level of the ADC.
If the value of k is less than one, it means that the receiver
noise at the input of the ADC is less than the quantization
noise, which results in a loss of detectability. Generally, k is at
least equal to 1. The maximum DRADC can be expressed by
where
DRADC _ max = 6.021× 12 − 9.031 − 20 lg1
= 63.22dB
(17)
Therefore, the maximum dynamic range of the receiver is
limited to 63.22dB for 12-bit ADC.
C. The Compromise Scenario
In the compromise scenario, the overall gain can be set at
some value, which enables ΔNF to be equal to 0.4dB. Fig. 2
shows that in this case G+NFRF is 51.23dB. Model 2 of the
LNA is proposed to be used in this scenario in order to keep a
higher DR. The cascade NFRF is supposed to be approximately
2.3dB. The overall gain of the RF front-end then results into
48.93dB.
The receiver performance can be calculated using (10) to
(13). The noise floor equals -94.31dBm, the maximum input
level -35.85dBm, the sensitivity -84.31dBm and the DR
58.46dB.
Figure 5 Typical block diagram of an S-band digital radar receiver
Budget
Budget
NonlinearAnalysis=yes
NonlinearHarmonicOrder=3
CmpMaxPin=45 _dBm
NoiseFreqSpan=50 MHz
P_1Tone
PORT1
Num=1
Z=50 Ohm
P=dbmtow(-35.9)
Freq=RF_freq
VAR
VAR1
RF_freq=3315 MHz
Var
Eqn
BUDGET
VAR
VAR2
LO_freq=3440 MHz
Var
Eqn
Amplifier
LNA
S21=dbpolar(35,0)
NF=1.5 dB
TOI=38
GainCompPower=25
BPF_Butterworth
RFBPF1
Fcenter=RF_freq
BWpass=100 MHz
Apass=1 dB
IL=0.8 dB
Var
Eqn
VAR
VAR3
IF_freq=LO_freq - RF_freq
Amplifier
IFAMP1
S21=dbpolar(21.3,0)
NF=3.7 dB
TOI=46
GainCompPower=29
MixerWithLO
MIX1
DesiredIF=LO_freq - RF_freq
ConvGain=dbpolar(-7,0)
NF=7 dB
TOI=31
BPF_Butterworth
RFBPF2
Fcenter=RF_freq
BWpass=100 MHz
Apass=1 dB
IL=0.8 dB
LPF_Butterworth
LPF
Fpass=200 MHz
Apass=1 dB
IL=0.8 dB
Amplifier
IFAMP2
S21=dbpolar(10,0)
NF=8.7 dB
TOI=50
GainCompPower=21.5
Attenuator
ATTN
Loss=7 dB
VSWR=1.2
Amplifier
ADC
S21=dbpolar(0,0)
NF=41.07 dB
BPF_Butterworth
AAF
Fcenter=IF_freq
BWpass=70 MHz
Apass=1 dB
IL=0.8 dB
Term
Term2
Num=2
Z=50 Ohm
Figure 6 Block diagram used for budget analysis in an S-band digital radar receiver scheme
D. Comparison for Different Scenarios
The analysis results of different scenarios are shown in table
II. The sensitivity of the highest sensitivity scenario is 4 dB
better than that of the largest DR scenario. The DR of the
largest DR scenario is 10.63dB better than that of the highest
sensitivity scenario.
The values of sensitivity and DR of the compromise
scenario are moderate. They are equal to -84.31dBm and
58.46dB, respectively. The ΔNF for the compromise scenario
is a reasonable value of 0.4dB. This value can be used as a
criterion in IF sampling digital receiver design.
TABLE II
COMPARISON BETWEEN DIFFERENT SCENARIOS
Scenario
ΔNF
NFRF
NF
Gain
Sensitivity
DR
(dB)
(dB)
(dB)
(dB)
(dBm)
(dB)
Highest Sensitivity
0.1
1.2
1.3
56.2
-85.71
52.59
Largest DR
3.0
2.3
5.3
38.79
-81.71
63.22
0.4
2.3
2.7
48.93
-84.31
58.46
Compromise
a
a
Fig. 6 shows the block diagram used for budget analysis in
an S-band digital radar receiver scheme. The primary
specifications of some key components are shown in table III.
The simulation results are shown in table IV.
TABLE III
PRIMARY SPECIFICATIONS OF SOME COMPONENTS
a
NF
Gain
Sensitivity
DR
SFDR
CDR
(dB)
(dB)
(dBm)
(dB)
(dB)
(dB)
2.71
48.96
-84.31
57.97
58.20
65.28
VI. CONCLUSIONS
While designing an IF sampling digital radar receiver, the
impact of NFADC on the receiver performance should be taken
into account. The highest sensitivity scenario and the largest
DR scenario are theoretically analyzed and compared. The
compromise scenario with moderate sensitivity and DR have
been proposed and simulated. The simulation results
demonstrate the validity of our theoretical analysis.
ACKNOWLEDGMENT
Funding for this research is provided by STW, The
Netherlands. The authors would like to thank the reviewers for
their helpful comments and their thorough review. The authors
also thank E.P. Lys, O.A. Krasnov, P. Hakkaart and J.H.
Zijderveld for their help in this work.
REFERENCES
[1]
a
NF
Gain
P1dB
(dB)
(dB)
(dBm)
(dBm)
LNA
1.5
35
25
38
Mixer
7
-7
17
31
IF Amp1
3.7
21.3
29
46
IF Amp2
8.7
10
21.5
50
a
TABLE IV
SIMULATION RESULTS FOR THE COMPROMISE SCENARIO
Limited by quantization noise of ADC.
V. SIMULATION FOR THE COMPROMISE SCENARIO
Component
Table IV shows that the sensitivity and DR are nearly the
same as our theoretical analysis results. A realistic P1dB and
IP3 for every component have been selected. Therefore, SFDR
approaches DR and CDR is 7.31dB higher than DR.
IP3
Refer to output for amplifier, refer to input for mixer.
[2]
[3]
[4]
[5]
[6]
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AD12401 12-Bit 400MSPS A/D Converter, Analog Device Inc., 2006.
“How Quantization and Thermal Noise Determine an ADC’s Effective
Noise Figure,” App. Note AN1197, MAXIM Integrated Products, 2002.
R.E. Watson, “Receiver Dynamic Range: Part 2,” WJ Tech-notes, vol.
14, no. 2 March/April 1987.
J. Halamek, I. Viscor and M. Kasal, “Dynamic range and acquisition
system,” Measurement Science Review, vol. 1, no. 1, pp. 71-74, 2001.
Merrill I. Skolnik, Introduction to Radar Systems. 3rd ed., New York:
McGraw-Hill, 2001, p.140.