Why to do single-tone desense test ? What is cross modulation ? what's the difference between cross modulation and intermodulation ? what is triple beat ?

1. DC Offset
In Frequency-Division Duplexing(FDD) communication system, Tx power can
leak to the LNA despite the duplexer isolation between the Rx and Tx band[5].
The typical duplexer isolation is 55dB in the CDMA Cellular band. Take
ACMD-7614 of AVAGO for example, as shown below[6] :
1

2. And the maximum Tx power can be as high as +27dBm at PA output, resulting in
-28dBm of Tx power at the Rx input port. We call the phenomenon that Tx power
leaks to the Rx port Tx leakage, which may saturate LNA and cause gain
reduction if the linearity of LNA is not high enough[5].
According to the cascade noise figure formula[5,11] :
less the LNA gain, higher the cascade noise figure and worse sensitivity.
2

3. Zero-IF RF front-end, i.e. direct-conversion receivers(DCR) are attractive for
cellular systems due to lower cost and Bill-of-Material (BOM)[2].
As shown in the figure below, DCR, as its name implies, RF signal downconverts
to baseband near 0 Hz directly.
3

4. As illustrated below, DC Offset is one of nonlinear effects as well.
Consequently, if Tx leakage saturates LNA, there will be DC offset, which will be
directed to the baseband signal processing IC, and may result in measurement
error and aggravate sensitivity[2,5].
4

5. Besides, because mixer input is LNA output, it means that mixer should have
higher linearity than LNA. Otherwise, due to nonlinearity of mixer, there is still
DC offset, even if LNA is linear.
5

6. IIP2
Intermodulation(IMD) is one of nonlinear effects as well. If there are two tones,
f1 and f2, with nearly identical frequency, f1 ≈ f2. If the LNA is nonlinear, there
will be 2 order IMD (IMD2).
IMD2 : f1-f2 ≈ 0 => DC Offset
That is to say, if the situation occurs, IMD2 is like DC offset and aggravates
sensitivity.
Similarly, even if LNA is linear, as long as mixer is nonlinear, there will be IMD2 as
well.
6

7. The IMD2 formula is as shown below:
= − +
C is correction constant. As shown above, we know that higher the input power,
higher the IMD2. Because FDD communication system, e.g., CDMA, has Tx leakage.
That is to say, Tx power at Rx port dominates IMD2.
The CDMA handset receiver needs to handle typically -110 dBm signals when
farthest from the base station[13]. In other words, if the equipment is at the
cellular boundary, which receives extremely weak signal. Besides, due to the
power control, the mobile's transmitter power is kept close to it's maximum level
i.e. 23 dBm, to maintain communication quality[14,28].
7

8. If the situation occurs, the receiver will activate high gain mode to reduce
cascade noise figure. As shown below :
But, higher the gain, worse the linearity[5]. In this case, in terms of IMD2 formula,
input power is maximum, but IIP2 is minimum. Thus, the IMD2 aggravates
sensitivity seriously.
8

9. Because DC Offset and IMD2 are the inherent obstacles of DCR, and difficult to
reject without attenuating baseband signal. Thus, some DCRs integrate DC
correction and IIP2 calibration circuit.
After calibration, the IIP2 improves indeed.
9

10. And the IMD2 reduces indeed.
Besides, by means of DC correction, the IIP2 improves as well.
10

11. As shown below, more the IIP2, better the sensitivity[1].
Because in FDD communication system adopting DCR, the sensitivity is highly
dependent on the IIP2 performance[1], that’s the reason why we have to care
IMD2 so much. Generally speaking, the CDMA receiver should have 55 dBm IIP2
with high gain mode. For example, the WTR3925 of Qualcomm has exactly 54
dBm IIP2 with high gain mode, and test conditions for the IIP2 measurements:
one signal tone and two equal-level CW jammers having levels as stated in the
table below[12] :
11

12. Adjacent Channel Selectivity
In the test specification of the 3GPP standard, the adjacent channel selectivity
(ACS) is a measure of the receiver’s ability to receive a wanted signal at its
assigned channel frequency in the presence of an strong adjacent channel signal
at a given frequency offset from the center frequency of the assigned (wanted)
channel, and with acceptable frame error rate(FER) [23].
As mentioned above, Intermodulation(IMD) is one of nonlinear effects as well. If
there are two tones near wanted signal, f1 and f2, with nearly identical frequency,
f1 ≈ f2. If the LNA is nonlinear, there will be 3 order IMD (IMD3).
IMD3 : 2f1-f2 or 2f2-f1 ≈ wanted signal.
As illustrated below :
12

13. Because the IMD3 is near wanted signal, which is not able to be filtered. It will
interfere the wanted signal.
Similarly, even if LNA is linear, as long as mixer is nonlinear, there will be IMD3 as
well.
13

14. In terms of linearity, more the IIP3, better the ACS. The WTR3925 of Qualcomm
has about -10 dBm IIP3(ACS) with high gain mode, and test conditions for this
IIP3 measurement: one signal tone and two equal-level CW jammers having
levels as stated in the table below[12] :
14

15. Cross Modulation
As mentioned above, as long as two tones pass through a nonlinear device
simultaneously, there will be IMD. Besides, if one of the two tones is nonconstant
envelope modulated signal, there will be cross modulation(XMD) as well. In other
words, with nonconstant envelope modulated signal, the nonlinearity results in
not only IMD, but also XMD. Conversely, no nonconstant envelope modulated
signal, no XMD[19].
15

16. In real environment, there are three tones at the CDMA Rx port : Tx signal, Rx
signal, and blocker(a.k.a. jammer)[5]
In terms of mathematics[18], assuming the LNA input signal x(t), with blocker
and TX leakage signal then we get:
The former is CW jammer, the latter is Tx signal. And the output signal can be
expressed as third order nonlinearity:
Substituting x(t) in y(t) and we get :
16

17. As shown above, the term shows the blocker signal being modulated by the
square of the amplitude of the TX leakage. Thus, the TX signal leakage signal is
cross-modulated with a strong blocker by the third-order non-linearities in the
LNA[13,18]. If the CW jammer is near Rx band, the cross modulated signal, i.e.
XMD, falling into the receive channel[24].
And the simulated spectrum at the output of the LNA is shown in the figure
below[14] :
17

18. And the measured spectrum at the output of the LNA is shown in the figure
below[13] :
The green trace shows the wanted signal without the presence of jammer or the
Tx signal, and the blue trace shows the noise-rise when the jammer and CDMA Tx
signal are turned on.
18

19. Consequently, with Tx leakage and jammer, the LNA nonlinearity can cause IMD3
and XMD simultaneously[26].
As mentioned above, the Tx leakage signal may saturate LNA. Nevertheless,
let’s take SKY74092-11 of SKYWORKS for example[17]. It is a LNA for CDMA, and
its P1dB is -7 dBm in high gain mode. As mentioned above, more the LNA gain,
worse the linearity. That is to say, its worst P1dB is -7 dBm. And as mentioned
above, the maximum Tx power can result in -28dBm of Tx power at the Rx input
port. In other words, it must have enough linearity to avoid being saturated by Tx
leakage signal. TX leakage produces very little desensitization of wanted RX
signal[14]. But the time varying envelope of the transmitter leakage signal can
cause excessive cross modulation of the strong single tone jammer largely due to
the third order nonlinearity of the LNA[14]. The formula is illustrated
below[18] :
19

20. C is correction constant. As mentioned above, both IMD3 and XMD are produced
due to nonlinearity simultaneously. And as seen from the formula, XMD is larger
than IMD3, and as shown below[5] :
As mentioned above, the increased transmitter leakage into the receiver is not
generally a problem on its own. Only the combination of TX leakage and Jammer
produces XMD that can’t be filtered away, and imposes requirement for high LNA
IIP3 and duplexer isolation[14]. After all, we note that XMD increases by 2dB as
the Tx leakage power increases by 1dB(i.e. duplexer isolation decreases by 1dB),
and as the IIP3 decreases by 1dB[7]. Generally speaking, the required LNA IIP3 is
approximately 8 dBm with duplexer isolation of 50dB[1, 7]. Take ACMD-7614 of
AVAGO and SKY74092-11 of SKYWORKS for example, their isolation and IIP3 are
55 dB and 9 dBm(high gain mode) respectively[17].
20

21. Therefore, the XMD consideration is shown in the figure below[14] :
With constant Tx power, more the isolation, less the XMD[14] :
In terms of spectrum, without Tx leakage, the noise floor is obviously lower[7] :
21

22. Besides, higher the IIP3, less the XMD[7] :
In terms of spectrum, higher the IIP3, lower the noise floor[7] :
22

23. Thus, it forces the use of highly linear LNAs which require very
high IP3 at the expense of large current[14, 15].
Or by means of linearization to reduce XMD[14] :
23

24. Single-tone desensitization
In designing CDMA receiver, one of the stringent requirements is the single
tone desensitization(STD) test[7].
Single-tone desensitization(STD) performance is a measure of a cell phone
receiver’s ability to receive a CDMA signal at its assigned channel frequency in
the presence of a nearby narrow-band jammer spaced at a given frequency offset
from the center frequency of the assigned channel, and in the presence of Tx
leakage signal. The receiver desensitization performance is measured by the FER
(≤ 0.5%)[13]. The figure is illustrated as below[14] :
24

25. When testing a CDMA front-end IC (or a zero-IF receiver) for single-tone
desensitization performance, it is important to note the interference components
created by the single-tone jammer and recreate the effects in the test setup.
There are two main contributors to single-tone desensitization performance:
XMD and reciprocal mixing. XMD is as mentioned above, so we discuss reciprocal
mixing next[13].
In STD test, the strong CW Jammer is near Rx signal. Reciprocal mixing occurs
when the single-tone jammer mixes with the receiver’s local oscillator (Rx LO).
Rx LO has finite phase noise that mixes with single-tone jammer, and creates an
interference component at the baseband, as illustrated in the figure above[13].
It can be seen that the receiver single-tone desensitization specification is a
key performance parameter that sets the LO phase noise requirement. Thus,
without Tx leakage, the reciprocal mixing product can aggravate sensitivity as
well.
25

26. In addition, it is important to note that the single-tone jammer’s own sidelobe
also contributes to the overall interference level. That is to say, without Tx
leakage and LO phase noise, single-tone jammer’s own sidelobe can aggravate
sensitivity as well, as illustrated below[13] :
Consequently, for accurate single-tone desensitization measurement, it is
necessary to choose a low sidelobe RF signal source so that the main
contributor to single-tone desensitization comes from the receiver LO’s phase
noise and not the RF signal generator’s sidelobe. The detailed STD test setup is as
illustrated below [13]:
26

27. As analyzed above, we know that STD test becomes the key determiner of the
linearity and phase noise requirements of the CDMA receiver[1].
27

28. Triple Beat
Triple beat(TB) test is employed to mimic the XMD distortion scenario and
validate the performance in CDMA receiver[4]. Consider three tones at LNA
input : f1, f2 and f3.
f1 and f2 are at Tx frequency, and f3 is at Rx frequency. There will be TB
components :
± ( − )
If f1 and f2 are very close, then the TB components shown above falls in Rx band.
The following figure shows the TB component produced due to f1 and f2 along
with f3, falling in the vicinity of f3[4].
As illustrated above, we define the amplitude between TB components and f3 as
triple beat ratio(TBR).
28

29. In terms of mathematics, consider a nonlinear LNA whose input-output
characteristic is represented by a 3rd order polynomial given by[4] :
where, Vo(t)is the output voltage of the LNA, and Vi(t)is the input voltage applied
to the LNA. Let’s assume Vi(t) has three tones, as shown in the formula below :
where
Substituting Vi(t) in Vo(t) and grouping the same order terms we get :
29

30. Still according to mathematical analysis[4], we conclude that the highest power
TB component is 6dB higher than IMD3 component produced by two tone test.
Thus, TB test is also the key determiner of the IIP3. Higher the IIP3, higher the
TBR. The WTR3925 of Qualcomm has about -4 dBm IIP3(TB) with high gain
mode, and test conditions for this IIP3 measurement: one signal tone, one CW
jammer, and two equal-level CW jammers (Tx signals) having levels as stated
below[12] :
30

31. Besides, some engineers are evaluating switches and duplexers to be used in
their CDMA transceiver designs, and for suppliers who are verifying the linearity
performance of their switches and duplexers. Qualcomm has published two
documents[20,21], which describe the TB test procedure.
31

32. Linearity
As mentioned above, we know that poor linearity leads to poor sensitivity.
The receiver cascade IIP3 formula is as below[5] :
As seen from the formula, linearity of latter stages becomes increasingly critical.
Besides, as mentioned above, mixer input is LNA output, it means that mixer has
higher input power than LNA. Thus, mixer has more stringent linearity
requirement than LNA. The nonlinearity of the mixer plays a role after the Tx
signal is down-converted[1]. An effective solution for improving linearity is using
an external SAW filter between LNA and mixer to make the mixer linearity
requirement relaxed by attenuating the out of bands blockers[1,5,25, 27].
32

33. As mentioned above, CDMA has Tx leakage, but Tx rejection by an external SAW
filter reduces the mixer linearity(e.g. IIP2 and IIP3) requirement. The SAW filter
has about 30 dB Tx rejection, and therefore the mixer is sufficiently protected
from XMD. With an external SAW filter , the IIP3 requirement for this mixer is
largly determined by the receive band 2-tone interference[14]. Besides, the
external SAW filter can be regarded as DC block to reject DC offset or IMD2 due to
LNA nonlinearity[22].
So, even though the receiver linearity is dominated by the mixer’s linearity, most
of the nonlinear distortion occurs in the LNA, as mentioned above.
As shown above, that’s the reason why XMD generated by mixer is 30-40dB
lower than that of LNA[7].
33

34. Some LNAs adopt differential architecture to reject even order nonlinearity
distortion[1].
Because Tx leakage signal at mixer input is very small due to the external SAW
filter between the LNA and the mixer[13]. Thus, the external SAW filter after the
LNA stage has been an essential component in FDD communication system(e.g.
CDMA) adopting DCR architecture [1].
Nevertheless, such external SAW filters are expensive and bulky, a SAW–less
receiver system is desirable since it eliminates the SAW filter as well as the
external matching components[1].
But, on the other hand, a SAW-less receiver places an additional linearity burden
on the mixer and the following stages. That is to say, in a SAW-less receiver, the
mixer becomes the most critical component in terms of the linearity performance
of the receiver[1].
In order to get low conversion loss from a passive mixer, typically a high LO
power is needed, which may result in significant LO leakage due to the finite
mixer port to port isolation[2]. LO leakage causes self-mixing, thereby generating
a static DC level aggravating sensitivity. As shown below :
34

35. Although passive mixers have LO leakage issue[2,5]. Nevertheless, compared to
active mixers, passive mixers give better linearity performance. The flicker noise
(1/f) of the mixer can corrupt the integrated noise, but the passive mixer will not
introduce significant flicker noise, since there is no dc current[1]. Consequently, a
passive mixer is an essential component in a SAW-less receiver.
There have been several efforts to implement a SAW-less CDMA receiver. An
embedded filtering passive receiver mixer is used to overcome transmitter
power leakage without the use of an external SAW filter, and it has 37dB Tx
rejection[1].
35

36. In addition, it also has better low frequency noise(e.g. IMD2) rejection than
conventional architecture.
The additional rejection provided by embedded filtering passive mixer
dramatically improves system linearity performance. It has +65.3dB TBR, which
is better than conventional architecture by about 20 dB[1]. And it has
better IIP2@45MHz than conventional architecture by about 10 dB.
Consequently, as shown above, the proposed embedded filtering passive mixer
has better IMD2 rejection than conventional architecture[1].
36

37. Reference
[1] A Highly Linear SAW-less CMOS Receiver Using a Mixer with Embedded Tx
Filtering for CDMA
[2] Introduction to IQ signal, Slideshare
[3] Cancellation Techniques for LO Leakage and DC Offset in Direct Conversion
Systems
[4] Carrier Triple Beat Test
[5] Sensitivity or selectivity -- How does eLNA impact the receriver
performance, Slideshare
[6] ACMD-7614 UMTS Band 1 Duplexer, AVAGO
[7] A NIGHTMARE FOR CDMA RF RECEIVER: THE CROSS MODULATION, IEEE
[8] Characterization of Cross Modulation in Multichannel Amplifiers Using a
Statistically Based Behavioral Modeling Technique, IEEE
[9] Presentation on Cross Modulation in a Full Duplex Transceiver, Agilent
[10] Cross-modulation in a CDMA Mobile Phone Receiver
[11] System(board level) noise figure analysis and optimization, Slideshare
[12] WTR39xx Wafer-level RF Transceiver Device Specification, Qualcomm
[13] Measuring single-tone desensitization for CDMA receivers
[14] Presentation on Cross Modulation in CDMA Mobile Phone Transceivers,
KEYSIGHT
[15] LNA design for CDMA front end, NXP
37

38. [16] RF System Design of Transceivers for Wireless Communications
[17] Dual-Band LNA for CDMA, Femtocell, and PCS Mobile Handset Applications,
SKYWORKS
[18] IP2 and IP3 Nonlinearity Specifications for 3G/WCDMA Receivers
[19] RF Microelectronics 2nd edition, Razavi
[20] Duplexer Linearity Test Procedure, Qualcomm
[21] RF Switch Linearity Test Procedure, Qualcomm
[22] BGA824N6, Silicon Germanium Low Noise Amplifier for Global Navigation
Satellite Systems (GNSS), Infineon
[23] Ultra Low Noise Amplifiers Improve Cell Coverage and Reduce Costs
[24] Presentation on Cross Modulation in a Full Duplex Transceiver, KEYSIGHT
[25] A CDMA2000 Zero-IF Receiver With Low-Leakage Integrated Front-End
[26] A Single–Chip 10-Band WCDMA/HSDPA 4-Band GSM/EDGE SAW-less CMOS
Receiver With DigRF 3G Interface and 90 dBm IIP2
[26] DC Offsets in Direct-Conversion Receivers: Characterization and
Implications
[27] Circuits and Systems for Future Generations of Wireless Communications
[28] Interference Mitigation Techniques for SAW-less CDMA Receivers
38