multiband transceivers - [chapter 4] design parameters of wireless radios

Multiband RF Transceiver System Chapter 4 Design Parameters of

Wireless Radios李健榮助理教授

Department of Electronic EngineeringNational Taipei University of Technology

Outline

• Sensitivity, Bit Error Rate (BER) and MinimumDetectable Signal (MDS)

• Inter-Symbol Interference (ISI) and Nyquist Signaling

• Nonlinearity and Distortion

• Selectivity

• Blocking, Desensitization, and Cross-Modulation

• Dynamic Range: SFDRand BDR

• Signal to Noise and Distortion Ratio (SNDR)

• Image Rejection Ratio (IRR)

2/47 Department of Electronic Engineering, NTUT

Design Parameters for Radio Receivers

• Typically, the specifications of different communicationssystems give fixed tests to characterize the functionality of thereceiver at different conditions. The basic parameters of thereceiver can be calculated or simulated straightforwardlygiving the block specifications for the circuit designer.

• Dynamic range (DR), Noise, Sensitivity, Inter-symbolInterference (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 atthe radio path, the power of the desired channel varies at theinput of the receiver.

The ratio between the highest and the smallest possible input power can be in theorder of 100 dB.

• The total dynamic range is typically optimized with anadjustable gain in the receiver.

inst

anta

neou

sdy

nam

ic r

ange

inst

anta

neou

sdy

nam

ic r

ange

tota

l dyn

amic

ran

ge

(a) (b)


Sensitivity

• Sensitivity:Define the minimum detectable signal (MDS) level, when there arenot anyinterferers present and the performance is limited by the noise (The total noisepower is a combination of the thermal noise within the channel bandwidth and theinternal noise of the receiver).

• The noise factor of the receiver defines the ratio of the internalnoise to the thermal noise at the input.

Here,SNRin andSNRout are the SNRs at the receiver input and output, respectively.G is the total gain of the receiver andNint is the receiver internal noise referred toinput. The noise factor in decibels is called the noise figure (NF).

( )1

in

in in out in int int

outout in in in

out

SSNR N N N N G N

FSSNR N G N G N

N

+ ⋅= = = = = +⋅ ⋅


Input-referred Noise Floor

• The thermal noise at the input:

whereBn is the noise bandwidth of the channel selection filter.

• At roomtemperature of 290 K, the thermal noise in dB is

• The input referred noise floor can be given in dBmas

in TH nN N kTB= =

174 (dBm Hz) 10logTH nN B= − +

INPUT THN N NF= +


Minimum Detectable Signal (MDS)

• MDS:

The sensitivity of the receiver is the smallest possible signal can be detected, whichhas a certain BER in the presence of noise. For example in QPSK, the typical BERspecification of 10−3 is achieved with Eb/N0 of 6.7 dB.

• Eb/N0 can be approximated equal toSNR, which is often calledthe carrier-to-noise ratio (C/N, or CNR).

Hence, the minimum SNR(SNRmin) depends on the required BER and the usedmodulation. The MDS can be given in decibels as

GDSP describes theimprovement due to the digital signal processing likeconvolutional coding or interleaving. The processing gain in CDMA systems isincluded in the GDSP.

minINPUT DSPMDS N SNR G= + −


Improvement from DSP Functions (I)

• The improvement of the DSP can be given as

where Gcode presents all digital functions except of despreading, andM1 is therequired implementationmargin 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= + −

ADC out

DespreadingGp

DecodingGCODE

Demod.310eP −=

Eb/N0

6.7 dBfor QPSK

( )c t

SNRout


Improvement from DSP Functions (II)

• The effect of the convolutionalcoding can be a couple ofdecibels.

• In CDMA systems, theprocessing gain can be in theorder of tens of decibels, and aweak desired signal is buriedtotally belowthe noise.

With other multiple access methods theprocessing gain is always unity.

Sin

NTH

GC/N

GSin

GNTH Sin

NTH

Sin

NTH

C/N

GP

C/N

C/N

NTH

Despreading

Input Output Referred to input

( )intTHG N N+

TH intN N+

PG G+

TH intN N+


Frii’s Formula

• The noise contribution ofdifferent blocks to the total noisefactor of the receiver is given in the Friis’ formula:

whereF1…Fn are the noise factors of the successive blocks from the front-endof the receiver, andG1…Gn are their power gains.

• The NF requirements are relaxed in the backend of the chain.

• The Friis’ formula is defined for theavailable signal andnoise powers.

321 1

1 1 2

1

1 11... n

n

ii

F FFF F

G G GG

−

=

− −−= + + + +∏


Inter-Symbol Interference (ISI)

• Nyquist bandwidth constraint:

whereW0 is the bandwidth of the single sideband signal at baseband, andTs andRs

are the symbol period and rate of the transmitted information, respectively.

• Below that limit, the energy of the preceding and followingpulses or bits inevitably distort the detection of the bit. Thiscrosstalk between the successive bits is calledinter-symbolinterference (ISI) and can degrade the sensitivity.

0

1

2 2s

s

RW

T= =


Ideal Moment of Detection

• The maximal bandwidth efficiency requires a rectangularshape fromthe brick-wall baseband filter. Such a filter has asinc-type impulse response:

( ) 2

2

sin( )1

s

s

R j t ssR

s

R th t e df R

R tω π

π+

−= ⋅ =∫

1.2

1.0

0.8

0.6

0.4

0.2

0.0

−0.2

−0.4−4 −3 −2 −1 0 1 2 3 4

Symbol Period

No

rmal

ized

Am

plit

ud

e

The impulse response describes theenergyspread as a function of time. The maximum isreached when t=0 and at the multiples of thesymbol rate the function crosses the x-axis.

Hence, theideal moment for detection is at themaximum point, and if the data stream issampled exactly at the symbol rate, the energyof the other pulses is zero and no crosstalkoccurs


Nyquist Signaling

• Ideal brick-wall filter for Nyquist signaling is not realizable.

The other problem is the slow damping of the impulse response. A relative steepslope when crossing the x-axis makes the detection sensitive to timing errors.

• A special class of Nyquist filters can solve the problemwith acost of extra bandwidth.

( )

( )

( )( ) ( )

( )

2

11 ,

2

11 12cos ,

4 2 22

10 ,

2

s

s

s s

s

s

Rf

Rf R R

H f fR

Rf

α

αα απ

α

α

−<

−

− − += ≤ ≤

+ >

　　　　　　　　　　　

　　　　

　　　　　　　　　　

The impulse response iszero at each multiple of the symbol period, which is anecessary and sufficient condition for transmissionwithout ISI. A raised cosinefilter meets this criterion, and it is used in many communications systems.


Raised-Cosine Filter

• α is the roll-off factor, and it defines the required excess bandwidthfor the transmission. The minimumchannel spacing between twoadjacent channels is then

Practically, the spacing is slightly larger to allow feasible requirements for limitingthe transmitted power spectrum and for filtering the stronger adjacent channels inthe receiver.

( ),min 1ch sf R α= +

( )

( )

( )( ) ( )

( )

2

11 ,

2

11 12cos ,

4 2 22

10 ,

2

s

s

s s

s

s

Rf

Rf R R

H f fR

Rf

α

αα απ

α

α

−<

−

− − += ≤ ≤

+ >

　　　　　　　　　　　

　　　　

　　　　　　　　　　

00.20.51.0

α

( )H f

( )1 / 2sRα−/ 2sR( )1 / 2sRα+

f


Impulse Response of the Rasied-Cosine Filter

• The impulse response of the raised cosine filter is defined in

( ) ( ) ( )2 2 2

sin cos

1 4s s

ss s

tR tRh t R

tR t R

π παπ α

=−

1.2

1.0

0.8

0.6

0.4

0.2

0.0

−0.2

−0.4−4 −3 −2 −1 0 1 2 3 4

Symbol Period

No

rmal

ized

Am

plit

ud

e

00.20.51.0

αThe fastest damping is achieved withthe widest bandwidth. Often, the raisedcosine filter is distributed between thetransmitter and the receiver. Each unitcontains a root raised cosine filter,which transfer function is a square rootof the raised cosine response.


Gaussian Filtering

• Instead of Nyquist filters, some systems like GSMuseGaussian filtering. Both frequency and impulse responsesfollow the Gaussian bell-shaped curve, and hence there is noovershoot in the time domain. However, theGaussianfiltering is spectrally less efficient than the raised cosineapproach.


Nonlinearity and Distortion

• Before all other signals than the desired traffic channel areattenuated to a sufficiently lowlevel, the linearity of the signalpath is critical for the systemperformance.

• The characterization of the distortion can be typically limitedto 2nd- and 3rd-order products in weakly nonlinear receivers.

However, the transmitted power levels are typically so high with simultaneousrequirements of power efficiency that a much larger number of harmonics must bemodeled and controlled properly.


Nonlinear Effects and IMD

• The nonlinear characteristics of a memoryless systemcan begiven in power series as

where vin(t) is the excitation for the outputvout(t), and α0~αn describe thecoefficients of the different orders of nonlinearity.

( ) ( ) ( ) ( )2 30 1 2 3 ...out in in inv t v t v t v tα α α α= + + + +

The 3rd-order IMPs can fall in thepassband at any stage, and totaldistorting power must be below thesignal at least by SNRmin.

The 2nd-order IMPs can be filtered outbefore overlapping with the desiredchannel. Therefore, the 2nd-orderdistortion should be taken into accountonly with certain radio architectures.

LO1LO2LO3

ω2−ω1 2ω2−ω12ω1−ω2

ω2ω1

2ω1, 2ω2ω1+ω2

3ω1, 3ω22ω1+ω22ω2+ω1


Intercept Points

• The linearity performance in radio receivers is typicallyspecified 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 3,

3 1 3 13

2 2 2 2out 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= − − = − = + ∆

OIP2

OIP3

OP1dB

IP1dB IIP3 IIP2

PIN (dB)

POUT (dB)

3, 3

2 2in IMD in

in in

P P PP P

− ∆= + = +

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Pin

19/47

Cascaded Stages (I)

• The input intercept point of the cascaded stages can becalculated with

where IIP3n and gn are the input intercept point and power gain of thenth

cascaded stage as absolute values.

• As the first stages dominate noise behavior, IIP3 becomesmore critical when the gain in the chain increases.

1

11 1 2

1 2 3

1 1...

3 3 3 3 3

n

ii

n

gg g g

IIP IIP IIP IIP IIP

−

== + + + +∏


Cascaded Stages (II)

• Linearity is typically inversely proportional to the powerconsumption. Therefore trading the linearity with the supplycurrent along the cascaded stages as a function of the reduceddynamic 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 actualsignal path. In differential circuits the prediction of the 2nd-order nonlinearity isdifficult, because theoretically the components cancel each other and theperformance depends on the symmetry.


IP1dB and IIP3

• The gain of the systembegin to vary at a certain signal levelwhen nonlinear components at the fundamental frequencyhave risen to the same order with the output amplitudeα1A.

• The 1-dB compression is defined at the point when the gain isdropped by 1-dB fromthe 1st-order behavior.

• The well-known approximation is thatIP1dB is 9.6 dB belowtheIIP3.

In practice, several different components and their nonlinearities dominate thebehavior. Therefore the given value is only a rule of thumb, and the typical ratio incommunication circuits is 5~15 dB.

11dB

3

0.145Aαα

≈


Selectivity

• While sensitivity describes the performance in the noisyenvironment and ISI crosstalk between consecutive symbols,the selectivity defines the tolerance against other radiotransmissions.

� Adjacent Channel Interference:

The unwanted power at the nearby channels can not be filtered out because it islocated too close to the desired channel.

� Linearity:

The power can alias to the desired channel due to nonlinearities or sometimesdue to the fundamental nature of the particular radio architecture.

� Saturation:

The large interferer can saturate the gain of the receiver, which prevents thedetection of a weak signal.


Adjacent Channel Interference

• The adjacent channel power after the filtering:

whereH(f) is the channel selection filter,S(f) is modulated channel PSD andfch isthe spacing between adjacent channels. The transmitter filtering is included in S(f).

( ) ( )adj chP H f S f f df∞

−∞= ⋅ −∫

INPUT OUTPUT

Stop-band

Pass-band

Transition band

min 3 dBSNR +

OUTOF

BAND

OUTOF

BAND

SYSTEM BAND• The filtering requirement istypically defined with a mask.


Blocking Test

• The main concern should be paid to detection of weak signalsin the presence of strong channels (Blocker). The behavior canbe observed with a blocking test, in which the desired weakchannel should be detected when a strong signal lies at someoffset fromthe weak channel.

• In cellular systems, the test is typically defined at severaldifferent offsets. The unwanted strong signalcan be asinusoid or a modulated channel. Two different mechanismsfor signal corruption can be found:desensitization andcross-modulation.


Blocking: Strong Signal Compresses the Gain

• The gain of the signal atω1 in the presence of a high blocker,i.e.A1<<A2 , can be given as

• Hence, the performance is violated due to 3rd-ordernonlinearity alsowhen a strong signal at any possiblefrequency compresses the gain.

231 1 2

1

31

2A

αα αα

′ = +

BLOCKER

SNRmin+3dB


Desensitization

• Desensitization:

When the low-frequency components are upconverted in RF amplifiers around ahigh frequency blocking signal due to the 2nd-order nonlinearity.

• Although the out-of-band signals are filtered before the gainblock, the upconversion of the internal low-frequency noiseincluding the flicker noise of an RF amplifier might rise thenoise to an unacceptable level.

BLOCKER BLOCKER

SNRmin+3dB SNRmin


Cross-Modulation (I)

• Cross-modulation:

If another of the two interfering signals in the two-tone testcarries amodulation, a part of it can be transferred to the other carrier.

• The modulated channel can be formulated by

The fundamental frequency termω1 can be rewritten as

The last term indicates that the cross-modulation due to the 3rd-order nonlinearitymay double the occupied bandwidth of the modulated channel, and therefore it cancause similar effects as spectral regrowth in power amplifiers.

( ) ( ) ( ) ( )1

2 23 2

, 1 1 1 3 1 3 1 2

3 3cos 1 2 cos cos 2

4 2 2 2out m m

m mv t t A A A A m t tω ω α α α ω ω

= ⋅ + + + + +

( )2 21 cos cosmA m t tω ω+


Cross-Modulation (II)

• If there is a strong out-of-band tone, like power leakage of thePA in simultaneous reception with the transmission, it maycross-modulate with an in-band blocker.

Although in most cases the cross-modulation does not dominate the 3rd-ordernonlinearity in the receivers, the unexpected behavior might be possible torecognize by studying the interaction of different modulated traffic channels.

ω1 ω2 −ωmωm−2ωm 2ωm

−ωm ωm

PA leakageBlocker

PA leakageBlocker


Dynamic Range: SFDR and BDR (I)

• It is not possible to give a single unique parameter, whichdefines the dynamic range of the receiver as seen fromanumber of differentnon-idealities.

• Maybe the most objective measure is the instantaneousdynamic range close to the sensitivity level of the receiver.This can be given as aspurious-free dynamic range (SFDR)or as ablocking dynamic range (BDR) at the input of thereceiver.

The former, which is based on the 3rd-order intermodulation and noise figure, is themost widely used. The definition omits the role of the gain control as a function ofthe incoming signal level. Therefore the total dynamic range of the receiver canbemuch larger.


Dynamic Range: SFDR and BDR (II)

• SFDR:

It is defined at the point where the 3rd-order intermodulation products are equalwith the noise power.

NOUT

SFDR

POUT (dB)

SFDR

BDRIIP3

NINPUT IP1dB

PIN (dB)

( ) ( )THINPUT NNFIIPNIIPSFDR −−=−= 33

23

3

2

1dB 1dBINPUT THBDR IP N IP NF N= − = − −

When the linearity of the receiver is improved,SFDR rises slower than BDR. Therefore theSFDR becomes more critical compared to theblocking test when a large dynamic range isrequired.


SFDR v.s. NF and System Bandwidth (I)

• The concept of the dynamic range in the radio receivers hassignificance only after the bandwidth, modulation, multipleaccess and a certain reference level (sensitivity), are known.

Different noise figures Effect of the system bandwidth

30

20

10

0

−10

−20

−30

−40

−5050 60 70 80 90 100

SFDR (dB) Bn(Hz)

0

−10

−20

−30

−40

−5010k 100k 1M 10M

IIP

3 (

dB

m)

IIP

3 (

dB

m)

NF=5 dB, Bn=200 kHzNF=10 dB, Bn=200 kHzNF=5 dB, Bn=4000 kHz

NF=5 dBNF=10 dB

wide-bands y s t e m srequire ahigher IIP3


SFDR v.s. NF and System Bandwidth (II)

• For the reasons given above, SFDR is not a very usefulparameter to compare different receivers operating in differentsystems.

The SFDR should be normalized to a fixed bandwidth for the fair comparisonbecause the inclusion of the bandwidth in the definition of SFDR misinterprets theratio of the circuit oriented parameters NF and IIP3.

• If we assume thatNF is in the limits of 5~10 dB andIIP3between –20 and –10 dBm(typical numbers for current ICs), theSFDR is according to 61~71 dB for 200 kHz and 52~62 for 4MHz bandwidths, respectively.

• The realistic dynamic range is about 60~70 dB, however, therequired total dynamic range is typically larger than that. Thiscan be achieved with a proper gain control.


Signal-to-Noise+DistortionRatio (SNDR)

• The definition of the SFDR is not valid anymore because theSNR is larger than the minimumrequired value for themodulation. If it is assumed that the IMP has approximatelythe same properties as noise in the detector, the signal-to-noise+distortion ratio (SNDR) can be used to estimate therequiredIIP3 for a certain dynamic range.

The assumption is simplifying, because the modulated channel including digitalinformation has not similar statistical properties as white noise. However, the first-order estimate gives quickly an initial value for more accurate system simulations.


IIP3 Requirement (I)

• The problemat 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 athigh signal levels,IIP3 must be increased as well. This can beformulated by keeping the minimumrequired SNR constant whenthe power level is increased as given in a linear scale as

wherePMDS is the power of the minimum detectable signal and the relative input powercompared to MDS. The factor two is added because by the definition of the SFDR, thereference signal is 3 dB above the sensitivity level because the third-order product isequal with the noise power.

min3,

2MDS MDS

INPUT IMD in INPUT

P P DRSNR

N P N

⋅ ⋅= =+

( )3, 2 1IMD in INPUTP N P⇒ = ∆ −


IIP3 Requirement (II)

• IIP3 can be given in decibels as

whereIIP3Hi means the requiredIIP3 at high signal levels.IIP3Hi as a function of∆P is given in the figure.

( )

( )

( )

3,

3

3 13 3 dB

2 23 1

3 dB2 2

3 1 10log 2 1

2 2

1 3 10log

2 2 1

Hi MDS IMD in

MDS INPUT

IIP P SFDR P P

P SFDR N

P P

PIIP

P

= + + + ∆ −

= + + −

+ ∆ − ⋅ ∆ −

∆= + ⋅ ∆ −

　　　

　　　

　　　

33 3,

3 1 3 13

2 2 2 2 2out IMD in IMD in in

PIIP P P G P P P

∆= − − = − = +

IIP

3 Hi(d

Bm

)

30

20

10

0

-10

-200 10 20 30 40

∆P (dB)


IIP3 Requirement (III)

• There is only slight bending due to noise when operating closeto the sensitivity level. It is evident thatthe dynamic range isdominated purely by the nonlinearities at high signal levels.

• The linearity requirements become rapidly unreasonable whenthe power level is increased.

• In the front-end of a receiver a large gain step is oftenavailable to achieve a better linearity. Then the noise figureshould be estimated again, because the noise figure is hardlyconstant after the gain control close to the input of the receiver.

• If it is acceptable to reduce the instantaneous dynamic range athigh signal levels, the SFDR termcan be reduced. The relaxeddynamic range is multiplied with factor 1.5 when specifyingIIP3.


Image Rejection Ratio (I)

• An image rejection mechanismis needed in the most radiosystems.

• The different receiver architectures are actually defined basedon the different ways to cancel the image.

• The image rejection ratio (IRR) is simply the difference of thepassband and stopband amplifications in decibels.

ωLO1 ωLO2 ωLO3

ωLO1 ωLO2 ωLO3

IN OUT

Image Image


Image Rejection Ratio (II)

• Two alternative methods, Hartley and Weaver receivers,widely called as image-reject receivers, to remove theunwanted image without filtering have been developed.

RF in IF out( )cos LOtω

( )sin LOtω

90°

( )( )

( )( )

2 2 2

2 2 2

2 cos 1 2 cos

2 cos 1 2 cosimage

wanted

P A B AB A AIRR

P A B AB A A

θ δ θ δθ δ θ δ

+ − ± + ∆ − ∆ ±= = =

+ + + ∆ + ∆∓ ∓

A, B: gains of two branchesθ: error from the 90° shift δ: phase error after the downconversion

Defining the gain error as ∆A=B/A


0

IRR

(dB

)

-10

-20

-30

-40

-50

-60

-70

0

IRR

(dB

)

-10

-20

-30

-40

-50

-60

-700.1 1 100.1 1 10

θ (deg) θ (deg)

1.0 dB0.5 dB0.3 dB

0.1 dB

2.0 dB

0 dB

PUP/PLOW

PLOW/PUP

δ=2

δ=1

δ=0

IRR at Different Gain and Phase Errors

• In analog structures, the achievable IRR has been typically inthe range of 30~40 dB if special techniques have not beenadopted.

Both an excellent gain andphase balance are requiredto achieve good imagerejection.

Noted that theeffect will becancelled outif amplitudeerrorsdominate.


Required IRR

• If we assume that the IRR specification can be calculated likethe other selectivity parameters, which means that the desiredchannel is typically 3 dB above the sensitivity level, the IRRcan be given in decibels as

where∆P is again the dynamic range i.e. the ratio of the unwanted image frequencyto the desired channel.

In the test, the noise level compared to the signal is 3 dB below the minimumrequired, and the image must be attenuated to the same level with the noise to meetthe BER requirement. Therefore the 3-dB term is needed.

min3 dBIRR P SNR= ∆ + +


Location of Image Channel

• The IRR requirement depends on the selected intermediatefrequency if the spectral mask of the unwanted channels is notflat. Three different cases are shown.

• For the image channel is located outside the systemband, theradio spectrumof the image must be carefully examined in thefrequency plan, because it may contain high power levels andthe attenuation of a preselection filter might be only in theorder of 25~30 dB.

Pre-selectionfilter

ωLO ωLO ωLO

Inside the system band Inside the system band Outside the system band


Quadrature Demodulation

• In the direct conversion architecture, the amplitude and phaseaccuracy is critical, and more difficult to implement than atlow-frequency demodulators.

RF IN

( )cos LOtω

( )sin LOtω

90°

( )I t

( )Q t

carrierrecovery

symboltiming

recovery

parallelto

serial

DATA out


Error Vector Magnitude (EVM)

• The phase and amplitude errors cause relative shifts ofsymbols in the constellation diagram.

• The variable errors caused by noise, nonlinearities and othertime-variant measures are often given with the concept of errorvector magnitude (EVM).

The EVM gives the rms variation of thesymbols from the ideal constellation points,typically in “%”. EVM is the summationvector of different nonidealities. It iscommonly used especially when estimatingthe performance of the transmitter.

errorvector

Q

I


Constant Error Vector (I/Q Mismatch)

• In the receivers, the fixed amplitude and phase errors betweenthe channels in the quadrature demodulation do not modify themagnitude of the error vector. Instead, the shape of theconstellation is changed.

Q

I

Q

I


BER Degradation from I/Q Mismatch

• The effect of fixed phase or amplitude errors in thedemodulator should be studied with BER simulations ratherthan with EVM.

0.01

1E-3

1E-4

1E-56 7 8 9 10

SNR (dB)

BE

Rideal

1 deg3 deg5 deg

Example of a WCDMA receiver A phase error of 1° causespractically negligible deteriorationon the performance and with 5°error the degradation is less than 1dB even at a low BER of 10−5.


Summary

• This chapter presented the dynamic range to define that hownoise and linearity impacts the receiver performance.

• The minimumdetectable 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= +INPUTMDS N=

min 1INPUTMDS N SNR M= + +

min 1INPUT p codeMDS N SNR M G G= + + − −

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