• What determines how successful a receiver will be in interpreting an incoming signal?
– Signal‐to‐noise ratio (or better Eb/N0)
– Data rate
– Bandwidth
• An increase in data rate increases bit error rate
• An increase in SNR decreases bit error rate
• An increase in bandwidth allows an increase in data rate
Importantly, another factor can be utilized to improve performance and that is the encoding scheme
Factors Used to Compare Encoding Schemes
• Signal spectrum– With lack of high‐frequency components, less bandwidth required
• Clocking– Ease of determining beginning and end of each bit position
• Signal interference and noise immunity– Certain codes exhibit superior performance in the presence of noise (usually expressed in terms of a BER)
• Cost and complexity– The higher the signal rate to achieve a given data rate, the greater the cost
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Basic Encoding Techniques
• Digital data to analog signal
– Amplitude‐shift keying (ASK)• Amplitude difference of carrier frequency
– Frequency‐shift keying (FSK)• Frequency difference near carrier frequency
– Phase‐shift keying (PSK)• Phase of carrier signal shifted
Modulation of Analog Signals for Digital Data
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Phase‐Shift Keying (PSK)
• Two‐level PSK (BPSK)
– Uses two phases to represent binary digits
tsAcos 2 f
ct
Acos 2 fct
1binary 0binary
Acos 2 f
ct
Acos 2 fct
1binary 0binary
Phase‐Shift Keying (PSK)
• Differential PSK (DPSK)
– Phase shift with reference to previous bit• Binary 0 – signal burst of same phase as previous signal burst
• Binary 1 – signal burst of opposite phase to previous signal burst
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Differential Phase‐Shift Keying
Quadrature Phase‐Shift Keying (PSK)
• Four‐level PSK (QPSK)
– Each element represents more than one bit
s(t)
Acos 2 fct
4
11
Acos 2 fct
34
Acos 2 fct
34
Acos 2 fct
4
01
00
10
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QPSK Constellation Diagram
QPSK and OQPSK Modulators
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Phase‐Shift Keying (PSK)
• Multilevel PSK– Using multiple phase angles with each angle having more than one amplitude, multiple signal elements can be achieved
• D = modulation rate, baud or symbols/sec
• R = data rate, bps
• M = number of different signal elements = 2L
• L = number of bits per signal element
M
R
L
RD
2log
Performance
• Bandwidth of modulated signal (BT)
– ASK, PSK BT = (1+r)R
– FSK BT = 2Δf+(1+r)R
• R = bit rate
• 0 < r < 1; related to how signal is filtered
• Δf = f2 – fc = fc ‐ f1
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Performance
• Bandwidth of modulated signal (BT)
– MPSK
– MFSK
• L = number of bits encoded per signal element
• M = number of different signal elements
RM
rR
L
rBT
2log
11
R
M
MrBT
2log
1
Bit Error rate (BER)
• Performance must be assessed in the presence of noise
• “Bit error probability” is probably a clearer term
– BER is not a rate in bits/sec, but rather a probability
– Commonly plotted on a log scale in the y‐axis and Eb/N0 in dB on the x‐axis
– As Eb/N0 increases, BER drops
• Curves to the lower left have better performance
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Theoretical Bit Error Rate for Various Encoding Schemes
Theoretical Bit Error Rate for Multilevel FSK, PSK, and QAM
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Quadrature Amplitude Modulation
• QAM is a combination of ASK and PSK
– Two different signals sent simultaneously on the same carrier frequency
s t I t cos2 fct Q t sin2 fct
QAM Modulator
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16‐QAM Constellation Diagram
Spread Spectrum
• Input is fed into a channel encoder – Produces analog signal with narrow bandwidth
• Signal is further modulated using sequence of digits – Spreading code or spreading sequence
– Generated by pseudonoise, or pseudo‐random number generator
• Effect of modulation is to increase bandwidth of signal to be transmitted
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General Model of Spread Spectrum Digital Communication System
Spread Spectrum
• On receiving end, digital sequence is used to demodulate the spread spectrum signal
• Signal is fed into a channel decoder to recover data
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Spread Spectrum
• What can be gained from apparent waste of spectrum?– Immunity from various kinds of noise and multipath distortion
– Can be used for hiding and encrypting signals
– Several users can independently use the same higher bandwidth with very little interference
Frequency Hoping Spread Spectrum (FHSS)
• Signal is broadcast over seemingly random series of radio frequencies– A number of channels allocated for the FH signal
– Width of each channel corresponds to bandwidth of input signal
• Signal hops from frequency to frequency at fixed intervals– Transmitter operates in one channel at a time
– Bits are transmitted using some encoding scheme
– At each successive interval, a new carrier frequency is selected
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Frequency Hopping Example
Frequency Hopping Spread Spectrum System
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Frequency Hoping Spread Spectrum
• Channel sequence dictated by spreading code
• Receiver, hopping between frequencies in synchronization with transmitter, picks up message
• Advantages– Eavesdroppers hear only unintelligible blips
– Attempts to jam signal on one frequency succeed only at knocking out a few bits
FHSS Using MFSK
• MFSK signal is translated to a new frequency every Tcseconds by modulating the MFSK signal with the FHSS carrier signal
• For data rate of R:– duration of a bit: T = 1/R seconds
– duration of signal element: Ts = LT seconds
• Tc ≥ Ts ‐ slow‐frequency‐hop spread spectrum
• Tc < Ts ‐ fast‐frequency‐hop spread spectrum
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Slow‐Frequency‐Hop Spread Spectrum Using MFSK 1M = 4, k = 22
Frequency‐Hop Spread Spectrum Using MFSK 1M = 4, k = 22
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FHSS Performance Considerations
• Large number of frequencies used
• Results in a system that is quite resistant to jamming
– Jammer must jam all frequencies
– With fixed power, this reduces the jamming power in any one frequency band
SPREAD SPECTRUM – a little history FYI
Spread Spectrum is now usually associated with digital communications using radio. (Note that wireless = radio for this course as we are talking about basic technologies, not commercial offerings.)
Spread Spectrum techniques can be employed for analog communications over guided media, although most spread spectrum systems are via radio.
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SPREAD SPECTRUM
The general concept of many communications schemes—including SS—is simple but profound: we can trade bandwidth for noise reduction. We are familiar with this concept by the use of 200 kHz channels for FM broadcasting 15 kHz stereo audio and for that matter using digital techniques to require a 64 kbps link for a 3 kHz telephone call.
The original use of the SS techniques was to make eavesdropping and/or locating military radio communications extremely difficult. But the immunity to other similar signals noise as well as to single frequency (non‐spread signal) interference was immediately manifest.
The original refinement of these techniques was to completely obscured the existence of the communications to conventional narrow band receivers.
Three Basic Spread Spectrum Techniques and Purposes
SPREAD SPECTRUM TECHNIQUE
PRIMARY PRACTICAL ATTRIBUTES
1. Frequency Hopping Unable to be received other than by intended recipients Effectively eliminates single frequency interference and/or jammingReciprocal from outlook of single channel usersUsed with analog and digital communicationsSignals are not completely occult (hidden).
2. Direct Sequence Encrypts digital data at very high level Significant noise reduction from other spectrum users, including discrete channels as well as other DSCC users.Also reciprocal to channelized radio signals
3. Code Division Multiple Access
Specific type of DSSS scheme widely usedspecifically for multiplexing multiple users rather than for encryption or for noise reduction
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SPREAD SPECTRUM TECHNIQUES ‐ Frequency Hopping Spread Spectrum (FHSS)
This is a very old technique dating back to the 1940s (WW II) and earlier but said to be invented by movie star Hedy Lamarr*.
FHSS is applicable to analog radio communications and groups of bits of digital data, even one bit—or less—at a time modulating a radio carrier.
The transmitter and receiver simply jump (hop) in synchronism between a number of different narrow band frequency—conventional AM or FM—channels.
The channel occupancy of the result can be over many channels or even entire frequency bands, e.g. the 3 – 30 MHz short wave band.
The participating transmitter and receiver need to have the exact correct sequence of frequencies and be synchronized; other receivers tuned to single channels can detect only occasional very small segments of the communications‐‐rendering eavesdropping virtually impossible.
The existence of the communications may be discerned due to the detection of "blips" of RF energy on any given channel.
*A most fascinating story.
1. Frequency Hopping Spread Spectrum was invented during WW II by movie star Hedy Lamarr.
Hedy Lamarr, 1913‐2000
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THE INVENTION OF FREQUENCY HOPPING STREAD SPECTRUM
The invention of spread spectrum is quite a story involving Nazis, a future Hollywood star, attempted murders, a number of druggings (more than one), a brothel (perhaps more than one), a Hollywood mogul (decidedly one), a player piano, and a piano player (a particular one).
Original spread spectrum scheme used perforated paper reels similar to those used in player pianos to control secure synchronous transmitter and receiver frequency hopping. Besides preventing eavesdropping, frequency hopping minimized detection by enemy direction finders to locate clandestine transmitters.
Picture: millikansbend.org
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Two pages of drawings from Lamarr (name on patent is Markey, the name of Hedy’s 2nd
of 6 husbands) and Antheil's patent*.
Note the player‐piano‐like slotted paper on the second sheet at right below.
FREQUENCY HOPPING SPREAD SPECTRUM Points to Remember
Single frequency jamming and/or multipath distortion that occurs only on a few of the channels used have only minimal effects on the bit error rates. This takes a little explaining. The idea is that only syllables are lost for voice transmission where humans can “fill in the missing data”, hopefully correctly. For digital transmission, error correcting can apply. Bits do get lost unless retransmissions and/or FEC is used.
The hopping sequence must be “pseudo random” otherwise interference would be periodic and decodable. This is very important for digital transmission employing FHSS.
Pseudo Random means complicated enough to have a very long periodicity (if at all) and with statistics that appear to mimic those of true random distributions.
The effect of FHSS is to minimize interference or detection of the transmitting location. That a “hopper” is near‐by can often be determined.
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FHSS Continued…
When used with digital communications, the pseudo random hopping sequence will ensure that the bit errors will occur in what appears to be a random way. This is more easily handled by error correction operating at the data link or higher layers.
BERs will be low if enough "good" channels are employed in the sequence: bad if many of the channels are in use.
Frequency Hopping is also a multiplex and encryption technique.
Background noise (for analog signals) or BER (for digital transmission) increase as the number of users increase. The general result of many users is similar to having a high random noise within the “channel”.
If the occupancy time of any given in‐use channel is very low‐‐a fraction of a second‐‐intelligible communications can still occur or BER is tolerable when FEC schemes are used.
FHSS is widely used for 2.4 GHz cordless telephones and was part of the original IEEE 802 wireless LAN standard.
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Direct Sequence Spread Spectrum (DSSS)
• Each bit in original signal is represented by multiple bits in the transmitted signal
• Spreading code spreads signal across a wider frequency band – Spread is in direct proportion to number of bits used
• One technique combines digital information stream with the spreading code bit stream using exclusive‐OR (Figure 9.6)
Example of Direct Sequence Spread Spectrum
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Direct Sequence Spread Spectrum System
DSSS Using BPSK
• Multiply BPSK signal,
sd(t) = A d(t) cos( fct)
by c(t) [takes values +1, ‐1] to get
s(t) = A d(t)c(t) cos( fct)• A = amplitude of signal
• fc = carrier frequency
• d(t) = discrete function [+1, ‐1]
• At receiver, incoming signal multiplied by c(t)– Since, c(t) x c(t) = 1, incoming signal is recovered
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Example of Direct Sequence Spread Spectrum Using BPSK
Approximate Spectrum of Direct Sequence Spread Spectrum Signal
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Code‐Division Multiple Access (CDMA)
• Basic Principles of CDMA
– D = rate of data signal
– Break each bit into k chips• Chips are a user‐specific fixed pattern
– Chip data rate of new channel = kD
CDMA Example
• If k=6 and code is a sequence of 1s and ‐1s– For a ‘1’ bit, A sends code as chip pattern
• <c1, c2, c3, c4, c5, c6>
– For a ‘0’ bit, A sends complement of code• <‐c1, ‐c2, ‐c3, ‐c4, ‐c5, ‐c6>
• Receiver knows sender’s code and performs electronic decode function
• User A code = <1, –1, –1, 1, –1, 1>– To send a 1 bit = <1, –1, –1, 1, –1, 1>
– To send a 0 bit = <–1, 1, 1, –1, 1, –1>
• User B code = <1, 1, –1, – 1, 1, 1>– To send a 1 bit = <1, 1, –1, –1, 1, 1>
• Receiver receiving with A’s code– (A’s code) x (received chip pattern)
• User A ‘1’ bit: 6 ‐> 1• User A ‘0’ bit: ‐6 ‐> 0• User B ‘1’ bit: 0 ‐> unwanted signal ignored
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CDMA in a DSSS Environment
Rake receiver (“digital multipath”)
• RAKE receiver– Multiple versions of a signal arrive more than one
chip interval apart
– RAKE receiver attempts to recover signals from multiple paths and combine them
• This method achieves better performance than simply recovering dominant signal and treating remaining signals as noise
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Principle of RAKE Receiver
Categories of Spreading Sequences
• Spreading Sequence Categories – PN sequences
– Orthogonal codes
• For FHSS systems– PN sequences most common
• For DSSS systems not employing CDMA– PN sequences most common
• For DSSS CDMA systems– PN sequences
– Orthogonal codes
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PN Sequences
• PN generator produces periodic sequence that appears to be random
• PN Sequences – Generated by an algorithm using initial seed
– Sequence isn’t statistically random but will pass many test of randomness
– Sequences referred to as pseudorandom numbers or pseudonoise sequences
– Unless algorithm and seed are known, the sequence is impractical to predict
Required Textbook: Antennas and Propagation for Wireless Communication Systems, by Simon R. Saunders and Alejandro Aragon‐Zavala, ISBN 978‐0‐470‐84879‐1; March 2007 (2nd edition).
Optional References:Wireless Communications and Networks, by William Stallings, ISBN 0‐13‐040864‐6, 2002 (1st edition);
Wireless Communication Networks and Systems, by Corey Beard & William Stallings (1st edition); all material copyright 2016
Wireless Communications Principles and Practice, by Theodore S. Rappaport, ISBN 0‐13‐042232‐0 (2nd edition)
Additional reference materials
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Required Textbook: Antennas and Propagation for Wireless Communication Systems, by Simon R. Saunders and Alejandro Aragon‐Zavala, ISBN 978‐0‐470‐84879‐1; March 2007 (2nd edition).
Optional References:Wireless Communications and Networks, by William Stallings, ISBN 0‐13‐040864‐6, 2002 (1st edition);
Wireless Communication Networks and Systems, by Corey Beard & William Stallings (1st edition); all material copyright 2016
Wireless Communications Principles and Practice, by Theodore S. Rappaport, ISBN 0‐13‐042232‐0 (2nd edition)
Acknowledgements:
Additional reference materials
OSI 7‐layer model
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Coping with Data Transmission Errors
• Error detection codes– Detects the presence of an error
• Automatic repeat request (ARQ) protocols– Block of data with error is discarded
– Transmitter retransmits that block of data
• Error correction codes, or forward correction codes (FEC)– Designed to detect and correct errors
Error Detection Probabilities
• Definitions• Pb : Probability of single bit error (BER)
• P1 : Probability that a frame arrives with no bit errors
• P2 : While using error detection, the probability that a frame arrives with one or more undetected errors
• P3 : While using error detection, the probability that a frame arrives with one or more detected bit errors but no undetected bit errors
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Error Detection Probabilities
• Definitions• Pb : Probability of single bit error (BER)
• P1 : Probability that a frame arrives with no bit errors
• P2 : While using error detection, the probability that a frame arrives with one or more undetected errors
• P3 : While using error detection, the probability that a frame arrives with one or more detected bit errors but no undetected bit errors
Error Detection Process
• Transmitter– For a given frame, an error‐detecting code (check bits) is calculated from data bits
– Check bits are appended to data bits
• Receiver– Separates incoming frame into data bits and check bits
– Calculates check bits from received data bits
– Compares calculated check bits against received check bits
– Detected error occurs if mismatch
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Error Detection Process
• Transmitter– For a given frame, an error‐detecting code (check bits) is calculated from data bits
– Check bits are appended to data bits
• Receiver– Separates incoming frame into data bits and check bits
– Calculates check bits from received data bits
– Compares calculated check bits against received check bits
– Detected error occurs if mismatch
Parity Check
• Parity bit appended to a block of data
• Even parity– Added bit ensures an even number of 1s
• Odd parity– Added bit ensures an odd number of 1s
• Example, 7‐bit character [1110001]– Even parity [11100010]
– Odd parity [11100011]
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Cyclic Redundancy Check (CRC)
• Transmitter– For a k‐bit block, transmitter generates an (n‐k)‐bit frame check sequence (FCS)
– Resulting frame of n bits is exactly divisible by predetermined number
• Receiver– Divides incoming frame by predetermined number
– If no remainder, assumes no error
Wireless Transmission Errors
• Error detection requires retransmission
• Detection inadequate for wireless applications
– Error rate on wireless link can be high, results in a large number of retransmissions
– Long propagation delay compared to transmission time
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Block Error Correction Codes
• Transmitter– Forward error correction (FEC) encoder maps each k‐bit block into an n‐bit block codeword
– Codeword is transmitted; (analog transmission for wireless communications systems)
• Receiver– Incoming signal is demodulated
– Block passed through an FEC decoder
Forward Error Correction Process
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FEC Decoder Outcomes
• No errors present– Codeword produced by decoder matches original codeword
• Decoder detects and corrects bit errors
• Decoder detects but cannot correct bit errors; reports uncorrectable error
• Decoder incorrectly corrects bit errors– Error pattern looks like a different block of data was sent
• Decoder detects no bit errors, though errors are present
Block Code Principles
• Hamming distance – for 2 n‐bit binary sequences, the number of different bits– E.g., v1=011011; v2=110001; d(v1, v2)=3
• Redundancy – ratio of redundant bits to data bits
• Code rate – ratio of data bits to total bits
• Coding gain – the reduction in the required Eb/N0 to achieve a specified BER of an error‐correcting coded system
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10.6 How Coding Improves System Performance
Hamming code
• Designed to correct single bit errors
• Family of (n, k) block error‐correcting codes with parameters:– Block length: n = 2m – 1
• Reasons for breaking up a block of data before transmitting:– Limited buffer size of receiver
– Retransmission of PDU due to error requires smaller amounts of data to be retransmitted
– On shared medium, larger PDUs occupy medium for extended period, causing delays at other sending stations
Error Control
• Mechanisms to detect and correct transmission errors
• Types of errors:
– Lost PDU : a PDU fails to arrive
– Damaged PDU : PDU arrives with errors
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10.17 Model of PDU Transmission
Error Control Requirements
• Error detection– Receiver detects errors and discards PDUs
• Positive acknowledgement– Destination returns acknowledgment of received, error‐free PDUs
• Retransmission after timeout– Source retransmits unacknowledged PDU
• Negative acknowledgement and retransmission– Destination returns negative acknowledgment to PDUs in error
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Go‐back‐N ARQ
• Acknowledgments
– RR = receive ready (no errors occur)
– REJ = reject (error detected)
• Contingencies
– Damaged PDU
– Damaged RR
– Damaged REJ
Go‐back‐N ARQ
• Acknowledgments
– RR = receive ready (no errors occur)
– REJ = reject (error detected)
• Contingencies
– Damaged PDU
– Damaged RR
– Damaged REJ
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HYBRID ARQ
• Hybrid Automatic Repeat Request (HARQ)
– Neither FEC or ARQ is adequate in practical situations
• FEC may add unnecessary redundancy
• ARQ may cause excessive delays from retransmissions
– HARQ is widely used
– Uses combination of FEC and ARQ
Required Textbook: Antennas and Propagation for Wireless Communication Systems, by Simon R. Saunders and Alejandro Aragon‐Zavala, ISBN 978‐0‐470‐84879‐1; March 2007 (2nd edition).
Optional References:Wireless Communications and Networks, by William Stallings, ISBN 0‐13‐040864‐6, 2002 (1st edition);
Wireless Communication Networks and Systems, by Corey Beard & William Stallings (1st edition); all material copyright 2016
Wireless Communications Principles and Practice, by Theodore S. Rappaport, ISBN 0‐13‐042232‐0 (2nd edition)
