Modulation and Multiplexing Joe Montana IT 488 - Fall 2003
Agenda • Modulation Concept • Analog Communication • Digital Communication • Digital Modulation Schemes • Error Detection and Correction
Why Modulate Signals? • If we transmit signal through electromagnetic waves, we need antennas to recover them at a remote point. • At low frequencies (baseband), the wavelengths are very large. • Ex. Voice, at approx. 4 kHz, has a wavelength of 75 Km!! • If we “move” those signals to higher frequencies, we can get more manageable antennas. • After receiving the signal, we need to “move” them back to the original frequency band (baseband) through demodulation. • Therefore, you can see the modulation task as “giving wings” to the information message.
Modulation – Basic Principles • Modulation is achieved by varying the amplitude, phase or frequency of a high frequency sinusoid. • The initial high frequency sinusoid that will have a parameter modified is called the “Carrier”. • The original message signal (baseband) is called the “Modulating” signal. • The resulting bandpass signal is the “Modulated” signal, which is a combination of the carrier and the original message.
Modulation – Basic Principles Modulating Signal V(t), at baseband(fB) Modulated Signal carrying the information of V(t), bandpass (fC) Action on carrier’s amplitude, frequency or phase Carrier (fC) fC fC
MODULATION AND MULTIPLEXING - 1 • MODULATION • THIS IS THE WAY INFORMATION IS ENCAPSULATED FOR TRANSMISSION • MULTIPLEXING • THIS IS THE WAY MORE THAN ONE LINK CAN BE CARRIED OVER A SINGLE COMMUNICATIONS CHANNEL WE WILL BE LOOKING AT MODULATION INITIALLY, BUT WHERE DO MODULATION AND MULTIPLEXING FIT INTO A SYSTEM?
MODULATION AND MULTIPLEXING - 2 Fig. 5.1 in text: (A) At uplink earth station (B) At downlink earth station
MODULATION AND MULTIPLEXING - 3 • KEY POINTS • You have to multiplex before modulating on the transmit side (that is, you have to get all of the output signals together prior to modulating onto a carrier) • You have to demodulate before demultiplexing on the receive side (that is, before you can separate - i.e. demultiplex - the incoming signals, you have to demodulate the carrier to obtain the transmitted information)
ANALOG TELEPHONY - 1 • Baseband voice signal • 300 - 3400 Hz (CCITT, now called ITU-T) • 300 - 3100 Hz (Bell)We will use the ITU-T definition
ANALOG TELEPHONY - 2 • KEY POINT • THE NUMBER OF VOICE CHANNELS A SATELLITE TRANSPONDER CAN CARRY VARIES INVERSELY WITH THE AVERAGE POWER LEVEL PER CHANNEL Simple Example NOTE:A pessimistic choice (power level set too high) will lower capacity estimate; An optimistic choice (power level set too low) can reduce quality of signals
CHANNEL LOADING EXAMPLE - 1 A 25 W transponder is designed to carry 250 two-way telephone channels (giving 500 channels at RF). Q1. How much power is available for each telephone channel? Answer: Power per channel = (25) / (500) = 50 mW Q2. If the amplifier requires to be backed off 3 dB to preserve linearity, what is the power available per telephone channel now? Answer: Power per channel = (25/2) / (500) = 25 mW Q2. What is the power per channel in the second case if 1000 RF channels are carried? Answer: Power per channel = (25 mW) / 2 = 12.5 mW
SATELLITE ANALOG • Satellite transponders are bandwidth limited • A flexible scheme is therefore required for loading analog voice channels • earth stations may transmit in multiples of 12 voice channels (from 12 to 1872) NOTE: There is very little analog (FM) voice traffic over satellites now. The bulk of the high capacity traffic is carried over optical fibers. The majority of voice capacity is in small digital carriers called IDR (Intermediate Digital Rate)
FREQUENCY MODULATION - 1 • DEFINITION“Frequency modulation results when the deviation, f, of the instantaneous frequency, f, from the carrier frequency fc is directly proportional to the instantaneous amplitude of the modulating voltage”. LET’S LOOK AT THIS PICTORIALLY
FREQUENCY MODULATION - 1 Input voltage Transfer characteristic Vmax Instantaneous Input Voltage Range of Input Voltage, v(t) Instantaneous Output Frequency Vmin f Output Frequency NOTE: In this example, fmin = the carrier frequency, fc Range of Output Frequency f min f max
FREQUENCY MODULATION - 2 Schematic representation of a sinusoidal modulating signal, vp, on a carrier signal, frequency fc NOTE: instantaneous frequency increases with increase in modulating voltage, and vice versa
FREQUENCY MODULATION - 3 The Frequency Modulated output signal, , will be as follows: c = 2fc = carrier radian frequency Maximum angular frequency deviation of the modulator (5.2) Maximum value of input modulating radian frequency
CARSON’S RULE - 1 Carson’s rule states that the transmission bandwidth, BT, is given by: Where B is the bandwidth of the modulating signal which, for a sinusoidal modulating signal, is the highest modulating frequency, fmod.
CARSON’S RULE - 2 A. Single-frequency sinusoid: Approximate value for required bandwidth B: (5.5) Modulating frequency Maximum frequency deviation B. Real signal (practical case): Approximate value for required bandwidth B: (5.6) Maximum modulating frequency
FM IMPROVEMENT • FM modulation is relatively inefficient with the use of transmission spectrum • A small baseband bandwidth is converted into a large RF bandwidth • FM demodulation and detection converts the wide RF bandwidth occupied into a small baseband bandwidth occupied • Ratio of RF to baseband bandwidths gives an improvement in signal to noise ratio which leads to the so-called FM IMPROVEMENT
DIGITAL COMMUNICATIONS -1 §5.4 in Chapter 5 + updated material • Many signals originate in digital form • data from computers • data from digital fixed and mobile systems • digitized information (e.g. voice) • World-wide network is moving towards all-digital system • Computers can only handle digital signals
Why Digital Transmission? • Robustness • Generally less susceptible to degradations • But...when it does degrade tends to fail quickly • Adaptiveness • Can easily combine a mix of signal information • Data, voice, video, multiple user signals • Compatibility - with digital storage, etc. • Security - not easily received except by recipient
DIGITAL COMMUNICATIONS -2 • At baseband, send V (volts) to represent a logical 1 and 0 • At RF - digitally modulate the carrier • ASK Amplitude Shift Keying • FSK Frequency Shift Keying • PSK Phase Shift Keying • Binary forms of these areOOK, BFSK, and BPSK, respectively Let’s first look at basic Digital Communications from the book by COUCH (7th. Edition)
DIGITAL COMMUNICATIONS -3 NOTE: from Couch
DIGITAL COMMUNICATIONS - 4 From Couch, Fig. 3-15
DIGITAL COMMUNICATIONS - 5 From Couch, Fig. 3-13
DIGITAL COMMUNICATIONS - 5 • Analog-to-Digital recap; we have: • Sampled at 2 times highest frequency • Stored the sampled value • Compared stored value with a quantized level • Selected the nearest quantized level • Turned the selected quantized level into a digital value using the selected number of bits • We now need to generate a line code Line Codes are serial bit streams that are used to drive the digital modulator
LINE CODES - 1 Couch Fig. 3-15 Usually used in digital circuits Always have net zero voltage
LINE CODES - 2 • SELECTION OF LINE CODE BASED ON • NEED TO HAVE SYNCHRONIZATION (OR OTHERWISE) • NEED TO HAVE A NET ZERO VOLTAGE (OR OTHERWISE) • NEED TO PREVENT STRING OF SAME VOLTAGE LEVEL SIGNALS • SPECTRAL EFFICIENCY SOME TYPICAL SPECTRA
TYPICAL SPECTRA Couch Fig. 2-6
PULSE SPECTRA A random train of ones and zeroes has a spectrum (power spectral density) of (5.40) X = fTb, Tb = bit period, and f = frequency in Hz Max value of Tb at f = 0 G(f) extends to f = Filtering affects the pulse shape
EFFECT OF FILTERING - 1 Fig. 5.8 in text
EFFECT OF FILTERING - 2 • Rectangular pulses (i.e. infinite rise and fall times of the pulse edges) need an infinite bandwidth to retain the rectangular shape • Communications systems are always band-limited, so • send a SHAPED PULSE • Attempt to MATCH the filter to the spectrum of the energy transmitted Before FILTERS, let’s look at Inter-Symbol Interference
INTER-SYMBOL INTERFERENCE • Sending pulses through a band-limited channel causes “smearing” of the pulse in time • “Smearing” causes the tail of one pulse to extend into the next (later) pulse period • Parts of two pulses existing in the same pulse period causes Inter-Symbol Interference (ISI) • ISI reduces the amplitude of the wanted pulse and reduces noise immunity Example of ISI
ISI - contd. - 1 Form Couch, Fig. 3-23
ISI - contd. - 2 • To avoid ISI, you can SHAPE the pulse so that there is zero energy in adjacent pulses • Use NRZ; pulse lasts the full bit period • Use Polar Signaling (+V & -V); average value is zero if equal number of 1’s and 0’s • Communications links are usually AC coupled so you should avoid a DC voltage component • Then use a NYQUIST filter Nyquist Filter???
NYQUIST FILTER - 1 • Bit Period is Tb • Sampling of the signal is usually at intervals of Tb • Thus, if we could generate pulses that are at a one-time maximum at t = Tb and zero at each succeeding interval of Tb (i.e. t = 2Tb, 3Tb, ….. , NTb then we would have no ISI • This is called a NYQUIST filter
NYQUIST FILTER - 2 Sampling instant is CRITICAL Impulse at this point t 0 Tb 2Tb 3Tb 4Tb
NYQUIST FILTER - 3 NOTE: At each sampling interval, there is only one pulse contribution - the others being at zero level Fig. 5.9 in text
NYQUIST FILTER - 4 • Arranging to sample at EXACTLY the right instant is the “Zero ISI” technique, first proposed by Nyquist in 1928 • Networks which produce the required time waveforms are called “Nyquist Filters”. None exist in practice, but you can get reasonably close
NYQUIST FILTER - 5 • Noise into receiver must be held to a minimum • Place half of Nyquist filter at transmit end of link, half at receive end, so that the individual filter transfer function H(f) is given byVr(f)NYQUIST = H(f) H(f)Filter is a “Square Root Raised Cosine Filter” H(f)matches pulse characteristic, hence it is called a “matched filter” Matched Filter
MATCHED FILTER - 1 f f Roll-off factor = = (f / f0) where f0 = 6 dB bandwidth B = absolute bandwidth (here shown for = 0.5) and B = f + f0 f1 = start of ‘roll-off’ of the filter characteristic 6 dB f1 f0 B Fig. 5.10 in text
MATCHED FILTER - 2 • A Raised Cosine Filter gives a Matched Filter response • The “Roll-Off Factor”, , determines bandwidth of Raised Cosine Low Pass Filter (LPF) • Gives zero ISI when the output is sampled at correct time, with sampling rate of Rb (i.e. at a sampling interval of Tb) BUT how much bandwidth is required for a given transmission rate???
BANDWIDTH REQUIRED - 1 • Bandwidth required depends on whether the signal is at BASEBAND or at PASSBAND • Bandwidth needed to send baseband digital signal using a Nyquist LPF isBandwidth = (1/2)Rb(1 + ) • Bandwidth needed to send passband digital signal using a Nyquist Bandpass filter isbandwidth = Rb(1 + ) NOTE: It is the Symbol Rate that is key to bandwidth, not the Bit Rate
BANDWIDTH REQUIRED - 2 • SYMBOL RATE is the number of digital symbols sent per second • BIT RATE is the number of digital bits sent per second • Different modulation schemes will “pack” different numbers of Bits in a single Symbol • BPSK has 1 bit per symbol • QPSK has 2 bits per symbol
BANDWIDTH REQUIRED - 3 • OCCUPIED BANDWIDTH, B, for a signal is given by B = Rs ( 1 + ) where Rs is the symbol rate and is the filter roll-off factor • NOISE BANDWIDTH, BN, for a channel will not be affected by the roll-off factor of filter. Thus BN = Rs
BANDWIDTH EXAMPLE - 1 • GIVEN: • Bit rate 512 kbit/s • QPSK modulation • Filter roll-off, , is = 0.3 • FIND: Occupied Bandwidth, B, and Noise Bandwidth, BN • SOLUTION: Symbol Rate = Rs = (1/2) (512 103) = 256 103 2 bits per symbol Number of bits/s
BANDWIDTH EXAMPLE - 2 • Occupied Bandwidth, B, isB = Rs (1 + ) = 256 103 ( 1 + 0.3) = 332.8 kHz • Noise Bandwidth, BN, isBN = Rs = 256 kHz • Now what happens if you have FEC? Example with FEC