Multiband Transceivers - [Chapter 4] Design Parameters of Wireless Radios
Multiband RF Transceiver System
Chapter 4 Design Parameters of
Department of Electronic Engineering
National Taipei University of Technology
• Sensitivity, Bit Error Rate (BER) and Minimum
Detectable Signal (MDS)
• Inter-Symbol Interference (ISI) and Nyquist Signaling
• Nonlinearity and Distortion
• Blocking, Desensitization, and Cross-Modulation
• Dynamic Range: SFDR and BDR
• Signal to Noise and Distortion Ratio (SNDR)
• Image Rejection Ratio (IRR)
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Design Parameters for Radio Receivers
• Typically, the specifications of different communications
systems give fixed tests to characterize the functionality of the
receiver at different conditions. The basic parameters of the
receiver can be calculated or simulated straightforwardly
giving the block specifications for the circuit designer.
• Dynamic range (DR), Noise, Sensitivity, Inter-symbol
Interference (ISI), Selectivity, Linearity and Distortion,
Spurious Free Dynamic Range (SFDR).
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Instantaneous Dynamic Range (DR)
• Depending on the distance to the transmitter and conditions at
the radio path, the power of the desired channel varies at the
input of the receiver.
The ratio between the highest and the smallest possible input power can be in the
order of 100 dB.
• The total dynamic range is typically optimized with an
adjustable gain in the receiver.
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Define the minimum detectable signal (MDS) level, when there are not any
interferers present and the performance is limited by the noise (The total noise
power is a combination of the thermal noise within the channel bandwidth and the
internal noise of the receiver).
• The noise factor of the receiver defines the ratio of the internal
noise to the thermal noise at the input.
Here, SNRin and SNRout are the SNRs at the receiver input and output, respectively.
G is the total gain of the receiver and Nint is the receiver internal noise referred to
input. The noise factor in decibels is called the noise figure (NF).
in in out in int int
outout in in in
SNR N N N N G N
SSNR N G N G N
= = = = = +
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Input-referred Noise Floor
• The thermal noise at the input:
where Bn is the noise bandwidth of the channel selection filter.
• At room temperature of 290 K, the thermal noise in dB is
• The input referred noise floor can be given in dBm as
in TH nN N kTB= =
174 (dBm Hz) 10logTH nN B= − +
INPUT THN N NF= +
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Minimum Detectable Signal (MDS)
The sensitivity of the receiver is the smallest possible signal can be detected, which
has a certain BER in the presence of noise. For example in QPSK, the typical BER
specification of 10−3 is achieved with Eb/N0 of 6.7 dB.
• Eb/N0 can be approximated equal to SNR, which is often called
the carrier-to-noise ratio (C/N, or CNR).
Hence, the minimum SNR (SNRmin) depends on the required BER and the used
modulation. The MDS can be given in decibels as
GDSP describes the improvement due to the digital signal processing like
convolutional coding or interleaving. The processing gain in CDMA systems is
included in the GDSP .
minINPUT DSPMDS N SNR G= + −
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Improvement from DSP Functions (I)
• The improvement of the DSP can be given as
where Gcode presents all digital functions except of despreading, and M1 is the
required implementation margin for digital algorithms.
• The sensitivity of the receiver can thus be given as
( ) ( ) minTH p code IMDS NF N G G M SNR= + − + − +
1DSP P codeG G G M= + −
( )c t
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Improvement from DSP Functions (II)
• The effect of the convolutional
coding can be a couple of
• In CDMA systems, the
processing gain can be in the
order of tens of decibels, and a
weak desired signal is buried
totally below the noise.
With other multiple access methods the
processing gain is always unity.
Input Output Referred
( )intTHG N N+
TH intN N+
TH intN N+
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• The noise contribution of different blocks to the total noise
factor of the receiver is given in the Friis’ formula:
where F1…Fn are the noise factors of the successive blocks from the front-end
of the receiver, and G1…Gn are their power gains.
• The NF requirements are relaxed in the backend of the chain.
• The Friis’ formula is defined for the available signal and
1 1 2
G G G
= + + + +
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Inter-Symbol Interference (ISI)
• Nyquist bandwidth constraint:
where W0 is the bandwidth of the single sideband signal at baseband, and Ts and Rs
are the symbol period and rate of the transmitted information, respectively.
• Below that limit, the energy of the preceding and following
pulses or bits inevitably distort the detection of the bit. This
crosstalk between the successive bits is called inter-symbol
interference (ISI) and can degrade the sensitivity.
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Ideal Moment of Detection
• The maximal bandwidth efficiency requires a rectangular
shape from the brick-wall baseband filter. Such a filter has a
sinc-type impulse response:
j t s
h t e df R
= ⋅ =∫
−4 −3 −2 −1 0 1 2 3 4
The impulse response describes the energy
spread as a function of time. The maximum is
reached when t=0 and at the multiples of the
symbol rate the function crosses the x-axis.
Hence, the ideal moment for detection is at the
maximum point, and if the data stream is
sampled exactly at the symbol rate, the energy
of the other pulses is zero and no crosstalk
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• Ideal brick-wall filter for Nyquist signaling is not realizable.
The other problem is the slow damping of the impulse response. A relative steep
slope when crossing the x-axis makes the detection sensitive to timing errors.
• A special class of Nyquist filters can solve the problem with a
cost of extra bandwidth.
( ) ( )
1 12cos ,
4 2 2
f R R
H f f
− − +
= ≤ ≤
The impulse response is zero at each multiple of the symbol period, which is a
necessary and sufficient condition for transmission without ISI. A raised cosine
filter meets this criterion, and it is used in many communications systems.
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• α is the roll-off factor, and it defines the required excess bandwidth
for the transmission. The minimum channel spacing between two
adjacent channels is then
Practically, the spacing is slightly larger to allow feasible requirements for limiting
the transmitted power spectrum and for filtering the stronger adjacent channels in
( ),min 1ch sf R α= +
( ) ( )
1 12cos ,
4 2 2
f R R
H f f
− − +
= ≤ ≤
( )H f
( )1 / 2sRα−
( )1 / 2sRα+
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Impulse Response of the Rasied-Cosine Filter
• The impulse response of the raised cosine filter is defined in
( ) ( )
2 2 2
h t R
tR t R
−4 −3 −2 −1 0 1 2 3 4
αThe fastest damping is achieved with
the widest bandwidth. Often, the raised
cosine filter is distributed between the
transmitter and the receiver. Each unit
contains a root raised cosine filter,
which transfer function is a square root
of the raised cosine response.
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• Instead of Nyquist filters, some systems like GSM use
Gaussian filtering. Both frequency and impulse responses
follow the Gaussian bell-shaped curve, and hence there is no
overshoot in the time domain. However, the Gaussian
filtering is spectrally less efficient than the raised cosine
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Nonlinearity and Distortion
• Before all other signals than the desired traffic channel are
attenuated to a sufficiently low level, the linearity of the signal
path is critical for the system performance.
• The characterization of the distortion can be typically limited
to 2nd- and 3rd-order products in weakly nonlinear receivers.
However, the transmitted power levels are typically so high with simultaneous
requirements of power efficiency that a much larger number of harmonics must be
modeled and controlled properly.
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Nonlinear Effects and IMD
• The nonlinear characteristics of a memoryless system can be
given in power series as
where vin(t) is the excitation for the output vout(t), and α0~αn describe the
coefficients of the different orders of nonlinearity.
( ) ( ) ( ) ( )2 3
0 1 2 3 ...out in in inv t v t v t v tα α α α= + + + +
The 3rd-order IMPs can fall in the
passband at any stage, and total
distorting power must be below the
signal at least by SNRmin.
The 2nd-order IMPs can be filtered out
before overlapping with the desired
channel. Therefore, the 2nd-order
distortion should be taken into account
only with certain radio architectures.
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• The linearity performance in radio receivers is typically
specified with the input referred intercept points.
The 3rd- and 2nd-order input intercept points (IIP3 and IIP2) are defined in the two-
tone test when operating at the weakly nonlinear region.
3 1 3 1
2 2 2 2
out IMD in IMD inIIP P P G P P= − − = −
2 2, 22 2 2out IMD in IMD in inIIP P P G P P P P= − − = − = + ∆
IP1dB IIP3 IIP2
in IMD in
P P P
= + = +
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Cascaded Stages (I)
• The input intercept point of the cascaded stages can be
where IIP3n and gn are the input intercept point and power gain of the nth
cascaded stage as absolute values.
• As the first stages dominate noise behavior, IIP3 becomes
more critical when the gain in the chain increases.
11 1 2
1 2 3
3 3 3 3 3
g g g
IIP IIP IIP IIP IIP
= + + + +
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Cascaded Stages (II)
• Linearity is typically inversely proportional to the power
consumption. Therefore trading the linearity with the supply
current along the cascaded stages as a function of the reduced
dynamic range is a possible optimization approach.
• The IIP2 products do not fall directly at the signal band.
Instead, they convert down to the baseband.
Therefore the cascaded gain of an IIP2 product is different compared to the actual
signal path. In differential circuits the prediction of the 2nd-order nonlinearity is
difficult, because theoretically the components cancel each other and the
performance depends on the symmetry.
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IP1dB and IIP3
• The gain of the system begin to vary at a certain signal level
when nonlinear components at the fundamental frequency
have risen to the same order with the output amplitude α1A.
• The 1-dB compression is defined at the point when the gain is
dropped by 1-dB from the 1st-order behavior.
• The well-known approximation is that IP1dB is 9.6 dB below
In practice, several different components and their nonlinearities dominate the
behavior. Therefore the given value is only a rule of thumb, and the typical ratio in
communication circuits is 5~15 dB.
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• While sensitivity describes the performance in the noisy
environment and ISI crosstalk between consecutive symbols,
the selectivity defines the tolerance against other radio
Adjacent Channel Interference:
The unwanted power at the nearby channels can not be filtered out because it is
located too close to the desired channel.
The power can alias to the desired channel due to nonlinearities or sometimes
due to the fundamental nature of the particular radio architecture.
The large interferer can saturate the gain of the receiver, which prevents the
detection of a weak signal.
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Adjacent Channel Interference
• The adjacent channel power after the filtering:
where H(f) is the channel selection filter, S(f) is modulated channel PSD and fch is
the spacing between adjacent channels. The transmitter filtering is included in S(f).
( ) ( )adj chP H f S f f df
= ⋅ −∫
min 3 dBSNR +
• The filtering requirement is
typically defined with a mask.
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• The main concern should be paid to detection of weak signals
in the presence of strong channels (Blocker). The behavior can
be observed with a blocking test, in which the desired weak
channel should be detected when a strong signal lies at some
offset from the weak channel.
• In cellular systems, the test is typically defined at several
different offsets. The unwanted strong signal can be a
sinusoid or a modulated channel. Two different mechanisms
for signal corruption can be found: desensitization and cross-
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Blocking: Strong Signal Compresses the Gain
• The gain of the signal at ω1 in the presence of a high blocker,
i.e. A1<<A2 , can be given as
• Hence, the performance is violated due to 3rd-order
nonlinearity also when a strong signal at any possible
frequency compresses the gain.
1 1 2
′ = +
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When the low-frequency components are upconverted in RF amplifiers around a
high frequency blocking signal due to the 2nd-order nonlinearity.
• Although the out-of-band signals are filtered before the gain
block, the upconversion of the internal low-frequency noise
including the flicker noise of an RF amplifier might rise the
noise to an unacceptable level.
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If another of the two interfering signals in the two-tone test carries a
modulation, a part of it can be transferred to the other carrier.
• The modulated channel can be formulated by
The fundamental frequency term ω1 can be rewritten as
The last term indicates that the cross-modulation due to the 3rd-order nonlinearity
may double the occupied bandwidth of the modulated channel, and therefore it can
cause similar effects as spectral regrowth in power amplifiers.
( ) ( ) ( ) ( )1
, 1 1 1 3 1 3 1 2
cos 1 2 cos cos 2
4 2 2 2
out m m
v t t A A A A m t tω ω α α α ω ω
= ⋅ + + + + +
( )2 21 cos cosmA m t tω ω+
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• If there is a strong out-of-band tone, like power leakage of the
PA in simultaneous reception with the transmission, it may
cross-modulate with an in-band blocker.
Although in most cases the cross-modulation does not dominate the 3rd-order
nonlinearity in the receivers, the unexpected behavior might be possible to
recognize by studying the interaction of different modulated traffic channels.
ω1 ω2 −ωm ωm
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Dynamic Range: SFDR and BDR (I)
• It is not possible to give a single unique parameter, which
defines the dynamic range of the receiver as seen from a
number of different non-idealities.
• Maybe the most objective measure is the instantaneous
dynamic range close to the sensitivity level of the receiver.
This can be given as a spurious-free dynamic range (SFDR)
or as a blocking dynamic range (BDR) at the input of the
The former, which is based on the 3rd-order intermodulation and noise figure, is the
most widely used. The definition omits the role of the gain control as a function of
the incoming signal level. Therefore the total dynamic range of the receiver can be
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Dynamic Range: SFDR and BDR (II)
It is defined at the point where the 3rd-order intermodulation products are equal
with the noise power.
( ) ( )THINPUT NNFIIPNIIPSFDR −−=−= 3
1dB 1dBINPUT THBDR IP N IP NF N= − = − −
When the linearity of the receiver is improved,
SFDR rises slower than BDR. Therefore the
SFDR becomes more critical compared to the
blocking test when a large dynamic range is
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SFDR v.s. NF and System Bandwidth (I)
• The concept of the dynamic range in the radio receivers has
significance only after the bandwidth, modulation, multiple
access and a certain reference level (sensitivity), are known.
Different noise figures Effect of the system bandwidth
50 60 70 80 90 100
SFDR (dB) Bn(Hz)
10k 100k 1M 10M
NF=5 dB, Bn=200 kHz
NF=10 dB, Bn=200 kHz
NF=5 dB, Bn=4000 kHz
s y s t e m s
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SFDR v.s. NF and System Bandwidth (II)
• For the reasons given above, SFDR is not a very useful
parameter to compare different receivers operating in different
The SFDR should be normalized to a fixed bandwidth for the fair comparison
because the inclusion of the bandwidth in the definition of SFDR misinterprets the
ratio of the circuit oriented parameters NF and IIP3.
• If we assume that NF is in the limits of 5~10 dB and IIP3
between –20 and –10 dBm (typical numbers for current ICs), the
SFDR is according to 61~71 dB for 200 kHz and 52~62 for 4
MHz bandwidths, respectively.
• The realistic dynamic range is about 60~70 dB, however, the
required total dynamic range is typically larger than that. This
can be achieved with a proper gain control.
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Signal-to-Noise+Distortion Ratio (SNDR)
• The definition of the SFDR is not valid anymore because the
SNR is larger than the minimum required value for the
modulation. If it is assumed that the IMP has approximately
the same properties as noise in the detector, the signal-to-
noise+distortion ratio (SNDR) can be used to estimate the
required IIP3 for a certain dynamic range.
The assumption is simplifying, because the modulated channel including digital
information has not similar statistical properties as white noise. However, the first-
order estimate gives quickly an initial value for more accurate system simulations.
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IIP3 Requirement (I)
• The problem at high signal levels is the cubic ratio between the 3rd-
order IMP and the interfering tone when the power level is increased.
Therefore if the same instantaneous dynamic range is required at
high signal levels, IIP3 must be increased as well. This can be
formulated by keeping the minimum required SNR constant when
the power level is increased as given in a linear scale as
where PMDS is the power of the minimum detectable signal and the relative input power
compared to MDS. The factor two is added because by the definition of the SFDR, the
reference signal is 3 dB above the sensitivity level because the third-order product is
equal with the noise power.
INPUT IMD in INPUT
P P DR
N P N
( )3, 2 1IMD in INPUTP N P⇒ = ∆ −
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IIP3 Requirement (II)
• IIP3 can be given in decibels as
where IIP3Hi means the required IIP3 at high signal levels. IIP3Hi as a function of
∆P is given in the figure.
3 3 dB
10log 2 1
2 2 1
Hi MDS IMD in
IIP P SFDR P P
P SFDR N
= + + + ∆ −
= + + −
+ ∆ − ⋅ ∆ −
= + ⋅ ∆ −
3 1 3 1
2 2 2 2 2
out IMD in IMD in in
IIP P P G P P P
= − − = − = +
0 10 20 30 40
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IIP3 Requirement (III)
• There is only slight bending due to noise when operating close
to the sensitivity level. It is evident that the dynamic range is
dominated purely by the nonlinearities at high signal levels.
• The linearity requirements become rapidly unreasonable when
the power level is increased.
• In the front-end of a receiver a large gain step is often
available to achieve a better linearity. Then the noise figure
should be estimated again, because the noise figure is hardly
constant after the gain control close to the input of the receiver.
• If it is acceptable to reduce the instantaneous dynamic range at
high signal levels, the SFDR term can be reduced. The relaxed
dynamic range is multiplied with factor 1.5 when specifying
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Image Rejection Ratio (I)
• An image rejection mechanism is needed in the most radio
• The different receiver architectures are actually defined based
on the different ways to cancel the image.
• The image rejection ratio (IRR) is simply the difference of the
passband and stopband amplifications in decibels.
ωLO1 ωLO2 ωLO3
ωLO1 ωLO2 ωLO3
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Image Rejection Ratio (II)
• Two alternative methods, Hartley and Weaver receivers,
widely called as image-reject receivers, to remove the
unwanted image without filtering have been developed.
RF in IF out( )cos LOtω
( )sin LOtω
2 2 2
2 2 2
2 cos 1 2 cos
2 cos 1 2 cos
P A B AB A A
P A B AB A A
θ δ θ δ
θ δ θ δ
+ − ± + ∆ − ∆ ±
= = =
+ + + ∆ + ∆∓ ∓
A, B: gains of two branches
θ: error from the 90 shift
δ: phase error after the downconversion
Defining the gain error as ∆A=B/A
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0.1 1 100.1 1 10
θ (deg) θ (deg)
IRR at Different Gain and Phase Errors
• In analog structures, the achievable IRR has been typically in
the range of 30~40 dB if special techniques have not been
Both an excellent gain and
phase balance are required
to achieve good image
Noted that the
effect will be
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• If we assume that the IRR specification can be calculated like
the other selectivity parameters, which means that the desired
channel is typically 3 dB above the sensitivity level, the IRR
can be given in decibels as
where ∆P is again the dynamic range i.e. the ratio of the unwanted image frequency
to the desired channel.
In the test, the noise level compared to the signal is 3 dB below the minimum
required, and the image must be attenuated to the same level with the noise to meet
the BER requirement. Therefore the 3-dB term is needed.
min3 dBIRR P SNR= ∆ + +
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Location of Image Channel
• The IRR requirement depends on the selected intermediate
frequency if the spectral mask of the unwanted channels is not
flat. Three different cases are shown.
• For the image channel is located outside the system band, the
radio spectrum of the image must be carefully examined in the
frequency plan, because it may contain high power levels and
the attenuation of a preselection filter might be only in the
order of 25~30 dB.
ωLO ωLO ωLO
Inside the system band Inside the system band Outside the system band
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• In the direct conversion architecture, the amplitude and phase
accuracy is critical, and more difficult to implement than at
( )cos LOtω
( )sin LOtω
( )I t
( )Q t
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Error Vector Magnitude (EVM)
• The phase and amplitude errors cause relative shifts of
symbols in the constellation diagram.
• The variable errors caused by noise, nonlinearities and other
time-variant measures are often given with the concept of error
vector magnitude (EVM).
The EVM gives the rms variation of the
symbols from the ideal constellation points,
typically in “%”. EVM is the summation
vector of different nonidealities. It is
commonly used especially when estimating
the performance of the transmitter.
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Constant Error Vector (I/Q Mismatch)
• In the receivers, the fixed amplitude and phase errors between
the channels in the quadrature demodulation do not modify the
magnitude of the error vector. Instead, the shape of the
constellation is changed.
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BER Degradation from I/Q Mismatch
• The effect of fixed phase or amplitude errors in the
demodulator should be studied with BER simulations rather
than with EVM.
6 7 8 9 10
Example of a WCDMA receiver
A phase error of 1 causes
practically negligible deterioration
on the performance and with 5
error the degradation is less than 1
dB even at a low BER of 10−5.
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• This chapter presented the dynamic range to define that how
noise and linearity impacts the receiver performance.
• The minimum detectable signal (MDS):
(1) Only noise:
(2) Consider SNR: (BER requirement)
(3) Leave some margin: (ISI,.ect)
(4) Consider digital processing gain:
• Dynamic range (DR):
(1) Spurious comes from a number of different non-idealities that limit the
maximum acceptable power.
(2) SNDR => Linearity requirement (for specific SNRmin requirement)
• IRR issue
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minINPUTMDS N SNR= +
min 1INPUTMDS N SNR M= + +
min 1INPUT p codeMDS N SNR M G G= + + − −