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• EE 6331, Spring, 2009 Advanced Telecommunication Zhu Han Department of Electrical and Computer Engineering Class 22 Apr. 16 th , 2009
• Outline
• Review
• Convolutional code
• Encoder
• Decoder: Viterbi decoding
• Turbo Code
• LDPC Code
• TCM modulation
• CDMA
• OFDM
• 2G-3G-4G
• Exam2 until this class
• Project 2 due on the exam
ECE6331
• Example
• Convolutional encoder, k = 1, n = 2, L=2
• Convolutional encoder is a finite state machine (FSM) processing information bits in a serial manner
• Thus the generated code is a function of input and the state of the FSM
• In this ( n,k,L ) = (2,1,2) encoder each message bit influences a span of C= n(L+1)=6 successive output bits = constraint length C
• Thus, for generation of n -bit output, we require n shift registers in k = 1 convolutional encoders
ECE6331
• Generator sequences ECE6331
• Representing convolutional codes compactly: code trellis and state diagram ECE6331 Shift register states Input state ‘1’ indicated by dashed line Code trellis State diagram
• Distance for some convolutional codes
• Lower the coding rate, larger the L, then larger the distance
ECE6331
• Puncture Code
• A sequence of coded bits is punctured by deleting some of the bits in the sequence according to some fixed rule.
• The resulting coding rate is increased. So a lower rate code can be extended to a sequence of higher rate codes.
ECE6331
• ECE6331 Note also the Hamming distances! The largest metric, verify that you get the same result!
• The Viterbi algorithm
• Problem of optimum decoding is to find the minimum distance path from the initial state back to initial state (below from S 0 to S 0 ). The minimum distance is the sum of all path metrics that is maximized by the correct path
• Exhaustive maximum likelihood method must search all the paths in phase trellis (2 k paths emerging/ entering from 2 L+1 states for an ( n,k,L ) code)
• The Viterbi algorithm gets its efficiency via concentrating into survivor paths of the trellis
ECE6331 Received code sequence Decoder’s output sequence for the m :th path
• The maximum likelihood path ECE6331 The decoded ML code sequence is 11 10 10 11 00 00 00 whose Hamming distance to the received sequence is 4 and the respective decoded sequence is 1 1 0 0 0 0 0 (why?). Note that this is the minimum distance path. (Black circles denote the deleted branches, dashed lines: '1' was applied) Smaller accumulated metric selected First depth with two entries to the node After register length L +1=3 branch pattern begins to repeat (Branch Hamming distances in parenthesis) 1 1
• Parallel Concatenated Codes
• Instead of concatenating in serial, codes can also be concatenated in parallel.
• The original turbo code is a parallel concatenation of two recursive systematic convolutional (RSC) codes.
• systematic : one of the outputs is the input.
ECE6331 Encoder #1 Encoder #2 Interleaver MUX Input Parity Output Systematic Output
• Iterative Decoding
• There is one decoder for each elementary encoder.
• Each decoder estimates the a posteriori probability (APP) of each data bit.
• The APP’s are used as a priori information by the other decoder.
• Decoding continues for a set number of iterations.
• Performance generally improves from iteration to iteration, but follows a law of diminishing returns.
ECE6331 Decoder #1 Decoder #2 DeMUX Interleaver Interleaver Deinterleaver systematic data parity data APP APP hard bit decisions
• Performance as a Function of Number of Iterations
• K=5, r=1/2, L=65,536
ECE6331
• LDPC Introduction
• Low Density Parity Check (LDPC)
• History of LDPC codes
• Proposed by Gallager in his 1960 MIT Ph. D. dissertation
• Rediscovered by MacKay and Richardson/Urbanke in 1999
• Features of LDPC codes
• Performance approaching Shannon limit
• Good block error correcting performance
• Suitable for parallel implementation
• LDPC do not require a long interleaver
• LDPC’s error floor occurs at a lower BER
• LDPC decoding is not trellis based
ECE6331
• Pro and Con
• Near Capacity Performance .. Shannon’s Limit
• Some LDPC Codes perform better than Turbo Codes
• Trellis diagrams for Long Turbo Codes become very complex and computationally elaborate … and make my head hurt !
• Low Floor Error
• Decoding in the Log Domain is quite fast.
• Long time to Converge to Good Solution
• Very Long Code Word Lengths for good Decoding Efficiency
• Iterative Convergence is SLOW
• Takes ~ 1000 iterations to converge under standard conditions.
• Due to the above reason
• transmission time increases
• i.e. encoding, transmission and decoding
• Hence Large Initial Latency
• (4086,4608) LPDC codeword has a latency of almost 2 hours
ECE6331
• Trellis Coded Modulation
• Combine both encoding and modulation. (using Euclidean distance only)
• Allow parallel transition in the trellis.
• Has significant coding gain (3~4dB) without bandwidth compromise.
• Has the same complexity (same amount of computation, same decoding time and same amount of memory needed).
• Has great potential for fading channel.
• Widely used in Modem
ECE6331
• Set Partitioning
• Branches diverging from the same state must have the largest distance.
• Branches merging into the same state must have the largest distance.
• Codes should be designed to maximize the length of the shortest error event path for fading channel (equivalent to maximizing diversity).
• By satisfying the above two criterion, coding gain can be increased.
ECE6331
• Three advantages over fixed spectrum
• Spread-spectrum signals are highly resistant to noise and interference . The process of re-collecting a spread signal spreads out noise and interference, causing them to recede into the background.
• Spread-spectrum signals are difficult to intercept . A Frequency-Hop spread-spectrum signal sounds like a momentary noise burst or simply an increase in the background noise for short Frequency-Hop codes on any narrowband receiver except a Frequency-Hop spread-spectrum receiver using the exact same channel sequence as was used by the transmitter.
• Spread-spectrum transmissions can share a frequency band with many types of conventional transmissions with minimal interference . The spread-spectrum signals add minimal noise to the narrow-frequency communications, and vice versa. As a result, bandwidth can be utilized more efficiently.
ECE6331
• PN Sequence Generator
• Pseudorandom sequence
• Randomness and noise properties
• Walsh, M-sequence, Gold, Kasami, Z4
• Provide signal privacy
ECE6331
• Direct Sequence (DS)-CDMA
• It phase-modulates a sine wave pseudo-randomly with a continuous string of pseudo-noise code symbols called &quot; chips &quot;, each of which has a much shorter duration than an information bit. That is, each information bit is modulated by a sequence of much faster chips. Therefore, the chip rate is much higher than the information signal bit rate.
• It uses a signal structure in which the sequence of chips produced by the transmitter is known a priori by the receiver. The receiver can then use the same PN sequence to counteract the effect of the PN sequence on the received signal in order to reconstruct the information signal.
ECE6331
• Unique code to differentiate all users
• Sequence used for spreading have low cross-correlations
• Allow many users to occupy all the frequency/bandwidth allocations at that same time
• Processing gain is the system capacity
• How many users the system can support
ECE6331
• Source signal is multiplied by a PN signal: 6.134, 6.135
• Processing Gain:
• Polar {±1} signal representation
ECE6331
• CDMA – Multiple Users
• One user’s information is the other’s interferences
• If the interference structure can be explored, multiuser detection
• Match filter
• Decorrelator
• MMSE decodor
• Successive cancellation
• Decision feedback
ECE6331
• CDMA Example ECE6331 R A B Receiver (a base station) Transmitter (a mobile) Transmitter Codeword=010011 Codeword=101010 Data=1011… Data=0010… Data transmitted from A and B is multiplexed using CDMA and codewords. The Receiver de-multiplexes the data using dispreading.
• CDMA Example – transmission from two sources ECE6331 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 0 Transmitted A+B Signal A Data A Codeword B Data B Codeword A Signal B Signal
• CDMA Example – recovering signal A at the receiver ECE6331 0 1 0 0 A+B Signal received A Codeword at receiver Integrator Output Comparator Output Take the inverse of this to obtain A
• CDMA Example – recovering signal B at the receiver ECE6331 1 1 0 1 A+B Signal received B Codeword at receiver Integrator Output Comparator Output Take the inverse of this to obtain B
• CDMA Example – using wrong codeword at the receiver ECE6331 X 0 1 1 Noise A+B Signal received Wrong Codeword Used at receiver Integrator Output Comparator Output Wrong codeword will not be able to decode the original data!
• Near Far Problem and Power Control ECE6331
• At a receiver, the signals may come from various (multiple sources.
• The strongest signal usually captures the modulator. The other signals are considered as noise
• Each source may have different distances to the base station
• In CDMA, we want a base station to receive CDMA coded signals from various mobile users at the same time.
• Therefore the receiver power at the base station for all mobile users should be close to eacother.
• This requires power control at the mobiles.
• Power Control : Base station monitors the RSSI values from different mobiles and then sends power change commands to the mobiles over a forward channel. The mobiles then adjust their transmit power.
B M M M M p r(M)
• Frequency-hopping spread spectrum ( FHSS ) is a spread-spectrum method of transmitting radio signals by rapidly switching a carrier among many frequency channels , using a pseudorandom sequence known to both transmitter and receiver .
• Military, bluetooth
ECE6331
• FDMA/CDMA
• Available wideband spectrum is frequency divided into number narrowband radio channels. CDMA is employed inside each channel.
• DS/FHMA
• The signals are spread using spreading codes (direct sequence signals are obtained), but these signal are not transmitted over a constant carrier frequency; they are transmitted over a frequency hopping carrier frequency.
ECE6331
• Time Division CDMA (TCDMA)
• Each cell is using a different spreading code (CDMA employed between cells) that is conveyed to the mobiles in its range.
• Inside each cell (inside a CDMA channel), TDMA is employed to multiplex multiple users.
• Time Division Frequency Hopping
• At each time slot, the user is hopped to a new frequency according to a pseudo-random hopping sequence.
• Employed in severe co-interference and multi-path environments.
• Bluetooth and GSM are using this technique.
ECE6331
• Orthogonal frequency-division multiplexing
• Special form of Multi-Carrier Transmission.
• Multi-Carrier Modulation.
• Divide a high bit-rate digital stream into several low bit-rate schemes and transmit in parallel (using Sub-Carriers)
ECE6331
• Map the rate with the sub-channel condition
• Water-filling
ECE6331
• OFDM Time and Frequency Grid
• Put different users data to different time-frequency slots
ECE6331
• Guard Time and Cyclic Extension...
• A Guard time is introduced at the end of each OFDM symbol for protection against multipath.
• The Guard time is “cyclically extended” to avoid Inter-Carrier Interference (ICI) - integer number of cycles in the symbol interval.
• Guard Time > Multipath Delay Spread, to guarantee zero ISI & ICI.
ECE6331
• OFDM Transmitter and Receiver ECE6331
• Pro and Con
• Can easily be adopted to severe channel conditions without complex equalization
• Robust to narrow-band co-channel interference
• Robust to inter-symbol interference and fading caused by multipath propagation
• High spectral efficiency
• Efficient implementation by FFTs
• Low sensitivity to time synchronization errors
• Tuned sub-channel receiver filters are not required (unlike in conventional FDM )
• Facilitates Single Frequency Networks , i.e. transmitter macro-diversity .
• Sensitive to Doppler shift.
• Sensitive to frequency synchronization problems
• Inefficient transmitter power consumption, since linear power amplifier is required.
ECE6331
• OFDM Applications
• IEEE 802.11a and 802.11g Wireless LANs .
• The Digital audio broadcasting systems EUREKA 147 , Digital Radio Mondiale , HD Radio , T-DMB and ISDB-TSB .
• The terrestrial digital TV systems DVB-T , DVB-H , T-DMB and ISDB-T .
• The IEEE 802.16 or WiMax Wireless MAN standard.
• The IEEE 802.20 or Mobile Broadband Wireless Access (MBWA) standard.
• The Flash-OFDM cellular system.
• Some Ultra wideband (UWB) systems.
• Power line communication (PLC).
• Point-to-point (PtP) and point-to-multipoint (PtMP) wireless applications.
ECE6331
• The IEEE 802.11a/g Standard
• Belongs to the IEEE 802.11 system of specifications for wireless LANs.
• 802.11 covers both MAC and PHY layers.
• Five different PHY layers.
• 802.11a/g belongs to the High Speed WLAN category with peak data rate of 54Mbps
• PHY Layer very similar to ETSI’s HIPERLAN Type 2
ECE6331
• Road Map ECE6331 1XRTT/3XRTT cdma2000 1999 2000 2001 2002 IS-95B 2G 2.5G 3G Phase 1 3G Phase 2 CDMA (IS 95 A) IS 95 B GSM TDMA EDGE UWC-136 GPRS W-CDMA 3X No 3X cdmaOne IS-95A 1X
• 2G: IS-95A (1995)
• Known as CDMAOne
• Chip rate at 1.25Mbps
• Convolutional codes, Viterbi Decoding
• Downlink (Base station to mobile):
• Walsh code 64-bit for channel separation
• M-sequence 2 15 for cell separation
• Uplink (Mobile to base station):
• M-sequence 2 41 for channel and user separation
ECE6331 Standard IS-95, ANSI J-STD-008 Multiple Access CDMA Uplink Frequency 869-894 MHz Downlink Frequency 824-849 MHz Channel Separation 1.25 MHz Modulation Scheme BPSK/QPSK Number of Channel 64 Channel Bit Rate 1.25 Mbps (chip rate) Speech Rate 8~13 kbps Data Rate Up to 14.4 kbps Maximum Tx Power 600 mW
• 2.5G: IS-95B (1998)
• Increased data rate for internet applications
• Up to 115 kbps (8 times that of 2G)
• Support web browser format language
• Wireless Application Protocol (WAP)
ECE6331
• 3G Technology
• Ability to receive live music, interactive web sessions, voice and data with multimedia features
• Global Standard IMT-2000
• CDMA 2000, proposed by TIA
• W-CDMA, proposed by ARIB/ETSI
• Issued by ITU (International Telecommunication Union)
• Excellent voice quality
• Data rate
• 144 kbps in high mobility
• 384 kbps in limited mobility
• 2 Mbps in door
• Frequency Band 1885-2025 MHz
• Convolutional Codes
• Turbo Codes for high data rates
ECE6331
• 3G: CDMA2000 (2000)
• CDMA 1xEV-DO
• peak data rate 2.4 Mbps
• supports mp3 transfer and video conferencing
• CDMA 1xEV-DV
• Integrated voice and high-speed data multimedia service up to 3.1 Mbps
• Channel Bandwidth:
• 1.25, 5, 10, 15 or 20 MHz
• Chip rate at 3.6864 Mbps
• Modulation Scheme
ECE6331
• Variable length orthogonal Walsh sequences for channel separation
• M-sequences 3x2 15 for cell separation (different phase shifts)
• Variable length orthogonal Walsh sequences for channel separation
• M-sequences 2 41 for user separation (different phase shifts)
ECE6331
• 3G: W-CDMA (2000)
• Stands for “wideband” CDMA
• Channel Bandwidth:
• 5, 10 or 20 MHz
• Chip rate at 4.096 Mbps
• Modulation Scheme
• Variable length orthogonal sequences for channel separation
• Gold sequences 2 18 for cell separation
• Variable length orthogonal sequences for channel separation
• Gold sequences 2 41 for user separation
ECE6331
• 4G OFDM
• 4G is being developed to accommodate the quality of service (QoS) and rate requirements set by forthcoming applications like wireless broadband access, Multimedia Messaging Service (MMS), video chat , mobile TV , HDTV content, Digital Video Broadcasting (DVB), minimal service like voice and data, and other streaming services for &quot;anytime-anywhere&quot;.
• Baseband techniques [9]
• OFDM : To exploit the frequency selective channel property
• MIMO : To attain ultra high spectral efficiency
• Turbo principle : To minimize the required SNR at the reception side