VIEWS: 4 PAGES: 56 POSTED ON: 2/17/2014
Simplified System Diagrams for Typical RF Tx & Rx Prof. C. Patrick Yue, ECE, UCSB Frequency Terminology RF – Radio Frequency Modulated by baseband (BB) signal BB data are digital LO – Local Oscillator Produced by a PLL IF – Intermediate Frequency Not used in Direct Conversion transceivers Channel selection i performed at IF Ch l l ti is f d t Often times, the analog-to digital conversion is done at IF Prof. C. Patrick Yue, ECE, UCSB Modulation Prof. C. Patrick Yue, ECE, UCSB Time and Frequency Domain of Analog Modulation Prof. C. Patrick Yue, ECE, UCSB Time and Frequency Domain Plot of Digital Modulation Prof. C. Patrick Yue, ECE, UCSB Constellation of BPSK and QPSK Prof. C. Patrick Yue, ECE, UCSB Transition between Symbols Different variations of QPSK is employed to minimized the transitions Reduces the channel capacity, e.g. for p/4-QPSK, it achieves ~1.62 bit/Hz < the limit of 2 R d th h l it f /4 QPSK hi 1 62 bit/H th li it f bit/Hz A major objective in digital modulation is to ensure that the RF trajectory from one phase state to another does not go through the origin. The transition is slow so that if the trajectory goes through the origin, the amplitude of the carrier will be below the noise floor for a considerable time and it will not be possible to recover its frequency (increases BER). Prof. C. Patrick Yue, ECE, UCSB Channel Capacity of Different Modulation Scheme Bandwidth, Capacity and Eb/No requirements for symbol error rate of 10^-5 (what is the equivalent BER?) S htt // d i / ti l / i t bl A ti l jht l? ti l ID 208802825 Source: http://www.commsdesign.com/article/printableArticle.jhtml?articleID=208802825 Prof. C. Patrick Yue, ECE, UCSB Modulation Scheme and BER Prof. C. Patrick Yue, ECE, UCSB Trade-Offs in Modulation Scheme vs. Bandwidth (Throughput) vs Power Consumption Constant amplitude, aka constant envelop, modulation is more power efficient but less throughput U d in systems where power is scared Used i t h i d Cellular Space communication information, Modulation with amplitude information like quadrature amplitude modulation (QAM) less power efficient, but provides more throughput Used in systems where spectrum is at a premiere DSL giga bit Wireline examples: DSL, giga-bit Ethernet Wireless examples: WLAN (IEEE 802.11) Prof. C. Patrick Yue, ECE, UCSB Amplitude Modulation (Transmitter) Transmitter Output 0 x(t) y(t) 2cos(2πfot) Vary the amplitude of a sine wave at carrier frequency fo according to a baseband modulation signal DC component of baseband modulation signal influences transmit signal and receiver possibilities - DC value greater than signal amplitude shown above Allows simple envelope detector for receiver Creates spurious tone at carrier frequency (wasted power) M.H. Perrott MIT OCW Frequency Domain View of AM Transmitter X(f) avg(x(t)) Transmitter Output f Y(f) 0 x(t) y(t) f -fo 0 fo 2cos(2πfot) 1 1 f -fo 0 fo Baseband signal is assumed to have a nonzero DC component in above diagram - Causes impulse to appear at DC in baseband signal - Transmitter output has an impulse at the carrier frequency For coherent detection, does not provide key information about information in baseband signal, and therefore is a waste of power M.H. Perrott MIT OCW Impact of Having Zero DC Value for Baseband Signal X(f) avg(x(t)) =0 Transmitter Output f Y(f) 0 x(t) y(t) f -fo 0 fo 2cos(2πfot) 1 1 f -fo 0 fo Impulse in DC portion of baseband signal is now gone - Transmitter output now is now free from having an impulse at the carrier frequency (for ideal implementation) M.H. Perrott MIT OCW Frequency Domain View of AM Receiver (Coherent) X(f) Transmitter Output f Y(f) 0 x(t) y(t) f -fo 0 fo 2cos(2πfot) Z(f) 1 1 Lowpass Receiver Output f -fo 0 fo f -2fo -fo 0 fo 2fo Lowpass y(t) z(t) r(t) 2cos(2πfot) 1 1 f -fo 0 fo M.H. Perrott MIT OCW Impact of 90 Degree Phase Misalignment X(f) Transmitter Output f Y(f) 0 x(t) y(t) f -fo 0 fo 2cos(2πfot) Z(f) 1 1 Lowpass Receiver Output f =0 -fo 0 fo 2fo f -2fo -fo 0 fo Lowpass y(t) z(t) r(t) 2sin(2πfot) j fo f -fo 0 -j M.H. Perrott MIT OCW Quadrature Modulation 1 1 Transmitter Output f It(f) -fo 0 fo Yi(f) 1 1 1 it(t) f f -fo 0 fo 0 2cos(2πfot) y(t) Qt(f) 2sin(2πfot) 1 j Yq(f) qt(t) fo f f 0 j -fo 0 fo -j f -fo 0 -j Takes advantage of coherent receiver’s sensitivity to phase alignment with transmitter local oscillator - We essentially have two orthogonal transmission channels (I and Q) available to us - Transmit two independent baseband signals (I and Q) onto two sine waves in quadrature at transmitter M.H. Perrott MIT OCW Accompanying Receiver 1 1 1 1 Transmitter Output Receiver Output f f It(f) -fo 0 fo Yi(f) -fo 0 fo Ir(f) 1 1 1 Lowpass 2 it(t) ir(t) f f f -fo 0 fo 0 2cos(2πfot) y(t) y(t) 2cos(2πfot) 0 Qt(f) Qr(f) 2sin(2πfot) 2sin(2πfot) Lowpass 1 j Yq(f) 2 qt(t) qr(t) fo f f f 0 j -fo 0 j 0 fo -j fo f f -fo 0 -fo 0 -j -j Demodulate using two sine waves in quadrature at receiver - Must align receiver LO signals in frequency and phase to transmitter LO signals Proper alignment allows I and Q signals to be recovered as shown M.H. Perrott MIT OCW Impact of 90 Degree Phase Misalignment 1 1 j Transmitter Output f1 Receiver Output f f It(f) -fo 0 fo Yi(f) -f1 0 Ir(f) 1 1 1 -j 2 it(t) ir(t) f f f -fo 0 fo 0 2cos(2πfot) y(t) y(t) 2sin(2πfot) 0 Qt(f) Qr(f) 2sin(2πfot) 2cos(2πfot) 1 j Yq(f) 2 qt(t) qr(t) fo f f f 0 j -fo 0 1 1 0 fo -j f f -fo 0 -fo 0 fo -j I and Q channels are swapped at receiver if its LO signal is 90 degrees out of phase with transmitter - However, no information is lost! - Can use baseband signal processing to extract I/Q signals despite phase offset between transmitter and receiver M.H. Perrott MIT OCW Simplified View Baseband Input Receiver Output It(f) Ir(f) 1 Lowpass 2 it(t) ir(t) f f 0 2cos(2πfot) 0 2cos(2πfot) Qt(f) 2sin(2πfot) 2sin(2πfot) Qr(f) 1 Lowpass 2 qt(t) qr(t) f f 0 0 For discussion to follow, assume that - Transmitter and receiver phases are aligned - Lowpass filters in receiver are ideal - Transmit and receive I/Q signals are the same except for scale factor add AWGN Channel and Rayleigh Fading Channel in Simulink In reality - RF channel adds distortion, causes fading - Signal processing in baseband DSP used to correct problems M.H. Perrott MIT OCW Analog Modulation Baseband Input Receiver Output Lowpass it(t) ir(t) t t 2cos(2πf1t) 2cos(2πf1t) 2sin(2πf1t) 2sin(2πf1t) Lowpass qt(t) qr(t) t t I/Q signals take on a continuous range of values (as viewed in the time domain) Used for AM/FM radios, television (non-HDTV), and the first cell phones Newer systems typically employ digital modulation instead M.H. Perrott MIT OCW Digital Modulation Baseband Input Receiver Output Lowpass it(t) ir(t) t t 2cos(2πf1t) 2cos(2πf1t) 2sin(2πf1t) 2sin(2πf1t) Lowpass qt(t) qr(t) t t Decision Boundaries Sample Times I/Q signals take on discrete values at discrete time instants corresponding to digital data - Receiver samples I/Q channels Uses decision boundaries to evaluate value of data at each time instant I/Q signals may be binary or multi-bit - Multi-bit shown above M.H. Perrott MIT OCW Advantages of Digital Modulation Allows information to be “packetized” - Can compress information in time and efficiently send as packets through network - In contrast, analog modulation requires “circuit- switched” connections that are continuously available Inefficient use of radio channel if there is “dead time” in information flow Allows error correction to be achieved - Less sensitivity to radio channel imperfections Enables compression of information - More efficient use of channel Supports a wide variety of information content - Voice, text and email messages, video can all be represented as digital bit streams M.H. Perrott MIT OCW Add summary of modulation schemes Constant Envelope Modulation The Issue of Power Efficiency Baseband Power Amp Input Transmitter Baseband to RF Modulation Output Variable-Envelope Modulation Constant-Envelope Modulation Power amp dominates power consumption for many wireless systems - Linear power amps more power consuming than nonlinear ones Constant-envelope modulation allows nonlinear power amp - Lower power consumption possible M.H. Perrott MIT OCW Simplified Implementation for Constant-Envelope Baseband to RF Modulation Power Amp Baseband Input Transmit Transmitter Filter Output Constant-Envelope Modulation Constant-envelope modulation limited to phase and frequency modulation methods Can achieve both phase and frequency modulation with ideal VCO - Use as model for analysis purposes - Note: phase modulation nearly impossible with practical VCO M.H. Perrott MIT OCW Example Constellation Diagram for Phase Modulation Q 000 100 001 Decision 101 011 Boundaries I 111 010 110 Decision Boundaries I/Q signals must always combine such that amplitude remains constant - Limits constellation points to a circle in I/Q plane - Draw decision boundaries about different phase regions M.H. Perrott MIT OCW Transitioning Between Constellation Points Q 000 100 001 Decision 101 011 Boundaries I 111 010 110 Decision Boundaries Constant-envelope requirement forces transitions to allows occur along circle that constellation points sit on - I/Q filtering cannot be done independently! - Significantly impacts output spectrum M.H. Perrott MIT OCW Constellation Diagram Q 00 01 11 10 00 Decision 01 Boundaries I 11 10 Decision Boundaries We can view I/Q values at sample instants on a two- dimensional coordinate system Decision boundaries mark up regions corresponding to different data values Gray coding used to minimize number of bit errors that occur if wrong decision is made due to noise M.H. Perrott MIT OCW Impact of Noise on Constellation Diagram Q 00 01 11 10 00 Decision 01 Boundaries I 11 10 Decision Boundaries Sampled data values no longer land in exact same location across all sample instants Decision boundaries remain fixed Significant noise causes bit errors to be made M.H. Perrott MIT OCW Transition Behavior Between Constellation Points Q 00 01 11 10 00 Decision 01 Boundaries I 11 10 Decision Boundaries Constellation diagrams provide us with a snapshot of I/Q signals at sample instants Transition behavior between sample points depends on modulation scheme and transmit filter M.H. Perrott MIT OCW Choosing an Appropriate Transmit Filter data(t) p(t) x(t) Td t * Td t t Sdata(f) |P(f)|2 Sx(f) f 0 1/Td f 0 1/Td f 0 Transmit filter, p(t), convolved with data symbols that are viewed as impulses - Example so far: p(t) is a square pulse Output spectrum of transmitter corresponds to square of transmit filter (assuming data has white spectrum) - Want good spectral efficiency (i.e. narrow spectrum) M.H. Perrott MIT OCW Highest Spectral Efficiency with Brick-wall Lowpass data(t) p(t) x(t) Td t * -Td 0 Td t t Sdata(f) |P(f)|2 Sx(f) f 0 1/(2Td) f 0 1/(2Td) f 0 Use a sinc function for transmit filter - Corresponds to ideal lowpass in frequency domain Issues - Nonrealizable in practice - Sampling offset causes significant intersymbol interference M.H. Perrott MIT OCW Requirement for Transmit Filter to Avoid ISI data(t) p(t) x(t) Td Td Td t * t t Time samples of transmit filter (spaced Td apart) must be nonzero at only one sample time instant - Sinc function satisfies this criterion if we have no offset in the sample times Intersymbol interference (ISI) occurs otherwise Example: look at result of convolving p(t) with 4 impulses - With zero sampling offset, x(kT ) correspond to d associated impulse areas M.H. Perrott MIT OCW Derive Nyquist Condition for Avoiding ISI (Step 1) data(t) p(t) x(t) Td Td Td t * t t impulse train p(t) p(kTd) Td Td Td t t t Consider multiplying p(t) by impulse train with period Td - Resulting signal must be a single impulse in order to avoid ISI (same argument as in previous slide) M.H. Perrott MIT OCW Derive Nyquist Condition for Avoiding ISI (Step 2) impulse train P(f) 1/Td F{p(kTd)} 1/Td 1/Td f * f f 0 impulse train p(t) p(kTd) Td Td Td t t t In frequency domain, the Fourier transform of sampled p(t) must be flat to avoid ISI - We see this in two ways for above example Fourier transform of an impulse is flat Convolution of P(f) with impulse train in frequency is flat M.H. Perrott MIT OCW A More Practical Transmit Filter Raised-cosine filter is quite popular in many applications p(t) P(f) 1-α 1+α 2Td 2Td t f -1/Td 0 1/Td -Td 0 Td Transition band in frequency set by “rolloff” factor, α Rolloff factor = 0: P(f) becomes a brick-wall filter Rolloff factor = 1: P(f) looks nearly like a triangle Rolloff factor = 0.5: shown above M.H. Perrott MIT OCW Raised-Cosine Filter Satisfies Nyquist Condition Nyquist Condition Nyquist Condition Observed in Time Observed in Frequency p(t) P(f) t f -1/Td 0 1/Td -Td 0 Td In time - p(kT ) = 0 for all k not equal to 0 d In frequency - Fourier transform of p(kT ) is flat - Alternatively: Addition of shifted P(f) centered about k/T d d leads to flat Fourier transform (as shown above) M.H. Perrott MIT OCW Spectral Efficiency With Raised-Cosine Filter data(t) p(t) x(t) Td t t * -Td 0 Td t Sdata(f) |P(f)|2 Sx(f) f 0 1/(2Td) f 0 1/(2Td) f 0 More efficient than when p(t) is a square pulse Less efficient than brick-wall lowpass - But implementation is much more practical Note: Raised-cosine P(f) often “split” between transmitter and receiver M.H. Perrott MIT OCW Receiver Filter: ISI Versus Noise Performance Raised-Cosine Filter Lowpass It(t) it(t) ir(t) Ir(t) f Baseband 2cos(2πf1t) 2cos(2πf1t) Receiver Input 2sin(2πf1t) 2sin(2πf1t) Output Lowpass Qt(t) qt(t) qr(t) Qr(t) f Conflicting requirements for receiver lowpass - Low bandwidth desirable to remove receiver noise and to reject high frequency components of mixer output - High bandwidth desirable to minimize ISI at receiver output M.H. Perrott MIT OCW Split Raised-Cosine Filter Between Transmitter/Receiver Additional Raised-Cosine Raised-Cosine Lowpass Filter Filter Filtering It(t) it(t) ir(t) Ir(t) f f f Baseband 2cos(2πf1t) 2cos(2πf1t) Receiver Input 2sin(2πf1t) 2sin(2πf1t) Output Qt(t) qt(t) qr(t) Qr(t) f f f We know that passing data through raised-cosine filter does not cause additional ISI to be produced - Implement P(f) as cascade of two filters corresponding to square root of P(f) Place one in transmitter, the other in receiver Use additional lowpass filtering in receiver to further reduce high frequency noise and mixer products M.H. Perrott MIT OCW Modeling The Impact of VCO Phase Modulation Recall unmodulated VCO model Phase Sout(f) Noise Phase/Frequency Spurious modulation Signal Overall phase noise Noise SΦmod(f) Φtn(t) f fo Φmod(t) Φout out(t) f 2cos(2πfot+Φout(t)) 0 Relationship between sine wave output and instantaneous phase Impact of modulation - Same as examined with VCO/PLL modeling, but now we consider Φout(t) as sum of modulation and noise components M.H. Perrott MIT OCW Relationship Between Sine Wave Output and its Phase Key relationship (note we have dropped the factor of 2) Using a familiar trigonometric identity Approximation given |Φtn(t)| << 1 M.H. Perrott MIT OCW Relationship Between Output and Phase Spectra Approximation from previous slide Autocorrelation (assume modulation signal independent of noise) Output spectral density (Fourier transform of autocorrelation) - Where * represents convolution and M.H. Perrott MIT OCW Impact of Phase Modulation on the Output Spectrum Phase Sout(f) Noise Phase/Frequency Spurious modulation Signal Overall phase noise Noise SΦmod(f) Φtn(t) f fo Φmod(t) Φout out(t) f 2cos(2πfot+Φout(t)) 0 Sout(f) Phase/Frequency modulation Signal Overall phase noise SΦmod(f) Φtn(t) f fo Φmod(t) Φout out(t) f 2cos(2πfot+Φout(t)) 0 Spectrum of output is distorted compared to SΦmod(f) Spurs converted to phase noise M.H. Perrott MIT OCW I/Q Model for Phase Modulation Applying trigonometric identity Can view as I/Q modulation - I/Q components are coupled and related nonlinearly to Φmod(t) Sa(f) it(t) SΦmod(f) cos(Φmod(t)) f Sy(f) 0 Φmod(t) cos(2πf2t) y(t) Sb(f) sin(2πf2t) f f 0 qt(t) -fo 0 fo sin(Φmod(t)) f 0 M.H. Perrott MIT OCW Multiple Access Techniques The Issue of Multiple Access Want to allow communication between many different users Freespace spectrum is a shared resource - Must be partitioned between users Can partition in either time, frequency, or through “orthogonal coding” (or nearly orthogonal coding) of data signals M.H. Perrott MIT OCW Frequency-Division Multiple Access (FDMA) Channel Channel Channel 1 2 N f Place users into different frequency channels Two different methods of dealing with transmit/receive of a given user - Frequency-division duplexing - Time-division duplexing M.H. Perrott MIT OCW Frequency-Division Duplexing Duplexer Antenna Transmitter TX RX TX f RX Transmit Receive Receiver Band Band Separate frequency channels into transmit and receive bands Allows simultaneous transmission and reception - Isolation of receiver from transmitter achieved with duplexer - Cannot communicate directly between users, only between handsets and base station Advantage: isolates users Disadvantage: deplexer has high insertion loss (i.e. attenuates signals passing through it) M.H. Perrott MIT OCW Time-Division Duplexing Switch Antenna Transmitter TX Receiver RX switch control Use any desired frequency channel for transmitter and receiver Send transmit and receive signals at different times Allows communication directly between users (not necessarily desirable) Advantage: switch has low insertion loss relative to duplexer Disadvantage: receiver more sensitive to transmitted signals from other users M.H. Perrott MIT OCW Time-Division Multiple Access (TDMA) Time Slot Time Slot Time Slot Time Slot Time Slot N 1 2 N 1 t Time Frame Place users into different time slots - A given time slot repeats according to time frame period Often combined with FDMA - Allows many users to occupy the same frequency channel M.H. Perrott MIT OCW Channel Partitioning Using (Nearly) “Orthogonal Coding” Uncorrelated Signals Correlated Signals 1 x(t) y(t) 1 x(t) y(t) A B -1 -1 1 c(t) 1 c(t) B B -1 -1 1 1 -1 -1 1 x(t) y(t) 1 x(t) y(t) -A -B -1 -1 1 c(t) 1 c(t) B B -1 -1 1 1 -1 -1 Consider two correlation cases - Two independent random Bernoulli sequences Result is a random Bernoulli sequence - Same Bernoulli sequence Result is 1 or -1, depending on relative polarity M.H. Perrott MIT OCW Code-Division Multiple Access (CDMA) Separate Transmit Signals Td Transmitters Combine x1(t) y1(t) in Freespace PN1(t) y(t) x2(t) y2(t) PN2(t) Tc Assign a unique code sequence to each transmitter Data values are encoded in transmitter output stream by varying the polarity of the transmitter code sequence - Each pulse in data sequence has period T d Individual pulses represent binary data values - Each pulse in code sequence has period T c Individual pulses are called “chips” M.H. Perrott MIT OCW Receiver Selects Desired Transmitter Through Its Code Separate Transmit Signals Transmitters Combine x1(t) y1(t) in Freespace PN1(t) x2(t) y2(t) PN2(t) PN1(t) Lowpass r(t) x(t) y(t) Receiver (Desired Channel = 1) Receiver correlates its input with desired transmitter code - Data from desired transmitter restored - Data from other transmitter(s) remains randomized M.H. Perrott MIT OCW Frequency Domain View of Chip Vs Data Sequences Tc data(t) p(t) x(t) 1 1 1 -1 t * Tc t -1 t data(t) p(t) x(t) 1 1 1 Td -1 t * Td t -1 t Sdata(f) |P(f)|2 Sx(f) Td Td Tc Tc f f f 0 0 1/Td 1/Tc 0 1/Td 1/Tc Data and chip sequences operate on different time scales - Associated spectra have different width and height M.H. Perrott MIT OCW Frequency Domain View of CDMA Sx1(f) Sy1(f) Td Transmitter 1 x1(t) y1(t) Tc f f Sx(f) 0 1/Td PN1(t) 0 1/Tc PN1(t) Td Sx1(f) Sx2(f) Sy2(f) Td Lowpass y(t) Transmitter 2 r(t) x2(t) y2(t) Tc Tc f 0 1/Td 1/Tc f f 0 1/Td PN2(t) 0 1/Tc CDMA transmitters broaden data spectra by encoding it onto chip sequences CDMA receiver correlates with desired transmitter code - Spectra of desired channel reverts to its original width - Spectra of undesired channel remains broad Can be “mostly” filtered out by lowpass M.H. Perrott MIT OCW