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Design Parameters of Wireless Radios

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- 1. Multiband RF Transceiver System Chapter 4 Design Parameters of Wireless Radios 李健榮 助理教授 Department of Electronic Engineering National Taipei University of Technology
- 2. Outline • Sensitivity, Bit Error Rate (BER) and Minimum Detectable Signal (MDS) • Inter-Symbol Interference (ISI) and Nyquist Signaling • Nonlinearity and Distortion • Selectivity • Blocking, Desensitization, and Cross-Modulation • Dynamic Range: SFDR and BDR • Signal to Noise and Distortion Ratio (SNDR) • Image Rejection Ratio (IRR) 2/47 Department of Electronic Engineering, NTUT
- 3. 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). Department of Electronic Engineering, NTUT3/47
- 4. 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. instantaneous dynamicrange instantaneous dynamicrange totaldynamicrange (a) (b) Department of Electronic Engineering, NTUT4/47
- 5. Sensitivity • Sensitivity: 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). ( ) 1 in in in out in int int outout in in in out S SNR N N N N G N F SSNR N G N G N N + ⋅ = = = = = + ⋅ ⋅ Department of Electronic Engineering, NTUT5/47
- 6. 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= + Department of Electronic Engineering, NTUT6/47
- 7. Minimum Detectable Signal (MDS) • 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= + − Department of Electronic Engineering, NTUT7/47
- 8. 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= + − ADC out Despreading Gp Decoding GCODE Demod. 3 10eP − = Eb/N0 6.7 dB for QPSK ( )c t SNRout Department of Electronic Engineering, NTUT8/47
- 9. Improvement from DSP Functions (II) • The effect of the convolutional coding can be a couple of decibels. • 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. Sin NTH G C/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+ Department of Electronic Engineering, NTUT9/47
- 10. Frii’s Formula • 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 noise powers. 32 1 1 1 1 2 1 1 11 ... n n i i F FF F F G G G G − = − −− = + + + + ∏ Department of Electronic Engineering, NTUT10/47
- 11. 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. 0 1 2 2 s s R W T = = Department of Electronic Engineering, NTUT11/47
- 12. 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: ( ) 2 2 sin( ) 1 s s R j t s sR s R t h t e df R R t ω 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 NormalizedAmplitude 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 occurs Department of Electronic Engineering, NTUT12/47
- 13. 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 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. ( ) ( ) ( ) ( ) ( ) ( ) 2 1 1 , 2 1 1 12cos , 4 2 2 2 1 0 , 2 s s s s s s R f R f R R H f f R R f α α α απ α α − < − − − + = ≤ ≤ + > 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. Department of Electronic Engineering, NTUT13/47
- 14. Raised-Cosine Filter • 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 the receiver. ( ),min 1ch sf R α= + ( ) ( ) ( ) ( ) ( ) ( ) 2 1 1 , 2 1 1 12cos , 4 2 2 2 1 0 , 2 s s s s s s R f R f R R H f f R R f α α α απ α α − < − − − + = ≤ ≤ + > 0 0.2 0.5 1.0 α ( )H f ( )1 / 2sRα− / 2sR ( )1 / 2sRα+ f Department of Electronic Engineering, NTUT14/47
- 15. Impulse Response of the Rasied-Cosine Filter • The impulse response of the raised cosine filter is defined in ( ) ( ) ( ) 2 2 2 sin cos 1 4 s s s s s tR tR h t R tR t R π πα π 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 NormalizedAmplitude 0 0.2 0.5 1.0 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. Department of Electronic Engineering, NTUT15/47
- 16. Gaussian Filtering • 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 approach. Department of Electronic Engineering, NTUT16/47
- 17. 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. Department of Electronic Engineering, NTUT17/47
- 18. 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. LO1LO2LO3 ω2−ω1 2ω2−ω12ω1−ω2 ω2ω1 2ω1, 2ω2 ω1+ω2 3ω1, 3ω2 2ω1+ω2 2ω2+ω1 Department of Electronic Engineering, NTUT18/47
- 19. Intercept Points • 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 3, 3 1 3 1 3 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= − − = − = + ∆ OIP2 OIP3 OP1dB IP1dB IIP3 IIP2 PIN (dB) POUT (dB) 3, 3 2 2 in IMD in in in P P P P P − ∆ = + = + Department of Electronic Engineering, NTUT Pin 19/47
- 20. Cascaded Stages (I) • The input intercept point of the cascaded stages can be calculated with 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. 1 11 1 2 1 2 3 1 1 ... 3 3 3 3 3 n i i n g g g g IIP IIP IIP IIP IIP − = = + + + + ∏ Department of Electronic Engineering, NTUT20/47
- 21. 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. Department of Electronic Engineering, NTUT21/47
- 22. 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 the IIP3. 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. 1 1dB 3 0.145A α α ≈ Department of Electronic Engineering, NTUT22/47
- 23. Selectivity • While sensitivity describes the performance in the noisy environment and ISI crosstalk between consecutive symbols, the selectivity defines the tolerance against other radio transmissions. 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. Linearity: The power can alias to the desired channel due to nonlinearities or sometimes due to the fundamental nature of the particular radio architecture. Saturation: The large interferer can saturate the gain of the receiver, which prevents the detection of a weak signal. Department of Electronic Engineering, NTUT23/47
- 24. 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 ∞ −∞ = ⋅ −∫ INPUT OUTPUT Stop- band Pass- band Transition band min 3 dBSNR + OUT OF BAND OUT OF BAND SYSTEM BAND • The filtering requirement is typically defined with a mask. Department of Electronic Engineering, NTUT24/47
- 25. Blocking Test • 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- modulation. Department of Electronic Engineering, NTUT25/47
- 26. 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. 23 1 1 2 1 3 1 2 A α α α α ′ = + BLOCKER SNRmin+3dB Department of Electronic Engineering, NTUT26/47
- 27. Desensitization • Desensitization: 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. BLOCKER BLOCKER SNRmin+3dB SNRmin Department of Electronic Engineering, NTUT27/47
- 28. Cross-Modulation (I) • Cross-modulation: 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 2 2 3 2 , 1 1 1 3 1 3 1 2 3 3 cos 1 2 cos cos 2 4 2 2 2 out m m 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+ Department of Electronic Engineering, NTUT28/47
- 29. Cross-Modulation (II) • 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 −2ωm 2ωm −ωm ωm PA leakage Blocker PA leakage Blocker Department of Electronic Engineering, NTUT29/47
- 30. 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 receiver. 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 much larger. Department of Electronic Engineering, NTUT30/47
- 31. Dynamic Range: SFDR and BDR (II) • SFDR: It is defined at the point where the 3rd-order intermodulation products are equal with the noise power. NOUT SFDR POUT (dB) SFDR BDR IIP3 NINPUT IP1dB PIN (dB) ( ) ( )THINPUT NNFIIPNIIPSFDR −−=−= 3 3 2 3 3 2 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 required. Department of Electronic Engineering, NTUT31/47
- 32. 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 30 20 10 0 −10 −20 −30 −40 −50 50 60 70 80 90 100 SFDR (dB) Bn(Hz) 0 −10 −20 −30 −40 −50 10k 100k 1M 10M IIP3(dBm) IIP3(dBm) NF=5 dB, Bn=200 kHz NF=10 dB, Bn=200 kHz NF=5 dB, Bn=4000 kHz NF=5 dB NF=10 dB wide-band s y s t e m s require a higher IIP3 Department of Electronic Engineering, NTUT32/47
- 33. 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 systems. 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. Department of Electronic Engineering, NTUT33/47
- 34. 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. Department of Electronic Engineering, NTUT34/47
- 35. 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. min 3, 2MDS MDS INPUT IMD in INPUT P P DR SNR N P N ⋅ ⋅ = = + ( )3, 2 1IMD in INPUTP N P⇒ = ∆ − Department of Electronic Engineering, NTUT35/47
- 36. 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 3 1 3 3 dB 2 2 3 1 3 dB 2 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 P IIP P = + + + ∆ − = + + − + ∆ − ⋅ ∆ − ∆ = + ⋅ ∆ − 3 3 3, 3 1 3 1 3 2 2 2 2 2 out IMD in IMD in in P IIP P P G P P P ∆ = − − = − = + IIP3Hi(dBm) 30 20 10 0 -10 -20 0 10 20 30 40 ∆P (dB) Department of Electronic Engineering, NTUT36/47
- 37. 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 IIP3. Department of Electronic Engineering, NTUT37/47
- 38. Image Rejection Ratio (I) • An image rejection mechanism is needed in the most radio systems. • 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 IN OUT Image Image Department of Electronic Engineering, NTUT38/47
- 39. 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 90 ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 cos 1 2 cos 2 cos 1 2 cos image wanted P A B AB A A IRR 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 Department of Electronic Engineering, NTUT39/47
- 40. 0 IRR(dB) -10 -20 -30 -40 -50 -60 -70 0 IRR(dB) -10 -20 -30 -40 -50 -60 -70 0.1 1 100.1 1 10 θ (deg) θ (deg) 1.0 dB 0.5 dB 0.3 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 in the range of 30~40 dB if special techniques have not been adopted. Both an excellent gain and phase balance are required to achieve good image rejection. Noted that the effect will be cancelled out if amplitude errors dominate. Department of Electronic Engineering, NTUT40/47
- 41. Required IRR • 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= ∆ + + Department of Electronic Engineering, NTUT41/47
- 42. 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. Pre-selection filter ωLO ωLO ωLO Inside the system band Inside the system band Outside the system band Department of Electronic Engineering, NTUT42/47
- 43. Quadrature Demodulation • In the direct conversion architecture, the amplitude and phase accuracy is critical, and more difficult to implement than at low-frequency demodulators. RF IN ( )cos LOtω ( )sin LOtω 90 ( )I t ( )Q t carrier recovery symbol timing recovery parallel to serial DATA out Department of Electronic Engineering, NTUT43/47
- 44. 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. error vector Q I Department of Electronic Engineering, NTUT44/47
- 45. 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. Q I Q I Department of Electronic Engineering, NTUT45/47
- 46. 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. 0.01 1E-3 1E-4 1E-5 6 7 8 9 10 SNR (dB) BER ideal 1 deg 3 deg 5 deg 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. Department of Electronic Engineering, NTUT46/47
- 47. Summary • 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 Department of Electronic Engineering, NTUT minINPUTMDS N SNR= + INPUTMDS N= min 1INPUTMDS N SNR M= + + min 1INPUT p codeMDS N SNR M G G= + + − − 47/47

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