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Telecommunications Engineering Topic 4: Spread Spectrum and CDMA

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## Telecommunications Engineering Topic 4: Spread Spectrum and CDMA

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**Telecommunications EngineeringTopic 4: Spread Spectrum and**CDMA James K Beard, Ph.D. jkbeard@temple.edu http://astro.temple.edu/~jkbeard/ Topic 4**Attendance**Topic 4**Essentials**• Text: Simon Haykin and Michael Moher, Modern Wireless Communications • SystemView • Use the full version in E&A 603A for your term project • Web Site • URL http://astro.temple.edu/~jkbeard/ • Content includes slides for EE320 and EE521 • SystemView page • A few links • Office Hours • E&A 349 • Hours Tuesday afternoons 3:00 PM to 4:30 PM • MWF 10:30 AM to 11:30 AM • Others by appointment; ask by email Topic 4**Topics**• Today we explore the third tool • FDMA, uses separate channels for each user • TDMA, uses time multiplexing to time multiplex the channel between users • Now, CDMA with spread spectrum enables multiple simultaneous users of the channel • Direct-sequence modulation • Spreading codes • Code synchronization Topic 4**Direct Sequence Modulation**• We begin with BPSK or QPSK • We replace the simple pulse shape • Each “pulse” is a more complex wide band pulse • The bandwidth of the resulting signal is that of the new wide band pulse • Spectrum of new signal is given by the convolution theorem Topic 4**Base Performance Equations**Topic 4**Performance in Noise**• Base equation (Hayken & Moher equations (5.12) page 263, (E.11) page 518) • Adding spreading function -- Eb and N0 are invariant through matched filter Topic 4**Performance in Interference**• Consider a tone as interference • In base coded signal • Matched filter spreads tone over channel • Tone energy becomes part of noise floor • In spread spectrum signal • Matched filter spreads tone over channel • Effective additional noise reduced by spreading factor Topic 4**Spreading Codes and CDMA**• Common method is to use a code for each pulse in a signal • This is the spreading code • CDMA is achieved when the spreading code is one of an orthogonal set for each user of the channel Topic 4**Spreading Codes and CDMA**• Use a coded pulse for each bit in the message • The coded pulse is the symbol-shaping function • Make the code one of an orthogonal set for each user of the same broadened channel • Result • BER performance is unchanged for each user • Users of other spreading codes look like the noise floor Topic 4**The Symbol-Shaping Function**Topic 4**Walsh-Hadamard Sequences**• A simple way to formulate orthogonal code sequences • Based on recursive augmentation of Walsh-Hadamard matrices Topic 4**Properties of Walsh-Hadamard Sequences**• Matrices are symmetrical • Matrices are self-orthogonal • Each matrix has rows or columns are a sequence of orthogonal sequences of length 2k • Cross-correlation properties • Excellent for zero lag • Poor for other lags Topic 4**Maximal-Length Sequences**• Bit sequence is essentially random • Pseudo-random noise (PRN) code • Codes Construction • Shift registers with feedback • Recursive modulo-2 polynomial arithmetic • PRN codes are then selected for good cross-correlation properties Topic 4**Desirable PRN Code Properties**• Maximal length – 2m codes before repeating • Balance – equal number of (+1) and (-1) pulses • Closed on circular shifts • Contain shorter subsequences • Good autocorrelation properties Topic 4**Galois Field Vector Extensions of Order 2m**• Polynomials modulo 2 of order m-1 • Arithmetic is done modulo a generating polynomial of the form • Proper selection of generating polynomial • Sequence of powers produces all 2m elements • Set is closed on multiplication Topic 4**An Important Isomorphism**• Shift registers with feedback • Bits in shift register are isomorphic with polynomial coefficients • Shift is isomorphic with multiplication by x • Modulo the generating polynomial is isomorphic to multiple-tap feedback • Shift registers with feedback can produce a Galois field in sequence of powers of x • These codes are also called m-sequences Topic 4**Gold Codes**• R. Gold, optimal binary sequences for spread spectrum multiplexing, IEEE Trans. Inform. Theory, Vol. IT-14, pp. 154-156, 1968. • Based on summing the output of two m-sequence generators Topic 4**Code Synchronization**• Two phases • Recover timing • Recover phase • Timing must be recovered first • To recover timing • Use code bits known to be 1’s • Matched filter for symbol-shaping function • Step timing in increments of Tc until match is found Topic 4**Assignment**• Read 5.2, 5.3, 5.5, 5.7, 5.11, 5.15 • Do problem 5.7 p. 273 • Next time • Power control • Frequency hopping • An example Topic 4**Chinese Remainder Theorem**• Over numbers from 0 to 2.3.5=30 • The method works when N has no repeated prime factors • Arithmetic advantages? Topic 4**A Finite Field**• Integers mod a prime • A reciprocal of a positive integer always exists • Addition, subtraction, multiplication, division, all defined and commutative Topic 4**Power Control and CDMA**• The near-far problem • The spreading loss will vary up to 70 dB over the coverage area • Code rejection factors are usually less than this • Result is that interference can occur between closely-spaced handsets or near base stations • Solution is power control • Reduce handset power to make received power constant Topic 4**Frequency Hopping**• Definition: Changing from channel to channel at regular intervals • Mitigates these problems • The near-far problem between handsets • Narrow band interference • But, non-coherent detection is necessary • Advantages also include • Full and best use of available spectrum for QoS • Can be combined with spread spectrum (FH-SS) Topic 4**EE320 March 28**Topic 4**Topics**• Term Project • Problem 5.1 p. 262 • Problem 5.17 p. 299 • Theme Example: WCDMA Topic 4**The Term Project**• Continue with the start that you turned in with the first quiz backup • Input • Frequency sweep 1000 Hz to 3500 Hz • Noise to obtain 20 dB SNR • Sampling to obtain good performance • Do NOT pitch your beginning and pick up the ADC to bitstream modules as a template • Sample and encode/decode as instructed • Measure BER vs. Eb/N0 as instructed • Compare hard decoding with soft decoding Topic 4**Problem 5.1 p. 262**• What is the equation for the spectrum of the spreading sequence given by Eq. (5.5) p. 261? • The chips c(q) are +1 or -1 and the chip shape gc(t) is Topic 4**Use the Convolution Theorem**• The spreading sequence is • The Fourier transform of each term in the sum is Topic 4**Problem 5.17 p. 299**• Do you expect FEC codes to have a greater or lesser benefit in Rayleigh-fading channels? Discuss your answer • Rayleigh fading channels have higher BER than otherwise similar Gaussian channels – more opportunity for improvement • Interleavers are necessary to make sure that dfree or fewer bits are exposed in a coherency interval Topic 4**WCDMA (1 of 3)**• From Theme Example 4 pp.323-328 • Cell phone technology generations • First: analog cell phones • Second: TDMA, IS-95, GSM • Third: Universal Mobile Terrestrial Telecommunications systems (UMTS) • WCDMA is a UMTS Topic 4**WCDMA (2 of 3)**• Functional differences • Simultaneous voice and data transmission • Other data such as real-time TV • Performance improvements • Three times the bandwidth • Four times the maximum spreading factor • Optional turbo codes Topic 4**WCDMA (3 of 3)**• Other differences • Multiple simultaneous CDMA downlink • Downlink power control • Asynchronous base stations • Bottom line • Broadband or ISDN in a cell phone • Near-far problems mitigated • Higher density of base stations and users Topic 4**Problem 5.19 page 305 (1 of 3)**Define the cellular spectral efficiency nu, in bits/second/Hz/cell; this is the total number of bits/second/Hz transmitted by all users in a cell. For a QPSK base modulation, assume that the spectral efficiency of a single CDMA user is 1/Q bits/second/Hz, where Q is the length of the spreading code. Suppose the receiver requires a specified SINR. Using Eq. (5.85) page 304, develop an expression for nu that depends on the received I0/N0, SINR, and f. Whay does the result not depend explicitly on Q? How does it depend implicitly on Q? Topic 4**Problem 5.19 page 309 (2 of 3)**• The spectral efficiency for • K users in the cell • Each transmitting 2/Q bits/second/Hz • From Eq. (5.85) page 304 Topic 4**Problem 5.19 page 309 (3 of 3)**• Rolling up these two equations gives nu as • The spreading factor Q influences • The interference factor f • The interference to noise ratio I0/N0 Topic 4**Theme Example 1: IS-95**• Section 5.12 Page 311 • Wireless cellular generations • Analog systems • Initial digital systems – GSM, IS-54, IS-95 • Integrated voice and data systems • Cell bands • Uplink 869-894 MHz, downlink 24 MHz lower • Uplink 1930-1990 MHz, downlink 80 MHz lower Topic 4**IS-95 Specifications and Usage**• Most CDMA cell phones use the IS-95 standard • Data rate is 9.6 kbps • Mainly voice • Some data, trend is increasing amounts • Direct sequence spread to 1.2288 megachips per second • Channel bandwidth is 1.25 MHz • Emerging standard based on IS-95 is CDMA2000 Topic 4**Channel Protocol of IS-95**• Making an IS-95 call – the Mobile Terminal • Searches for Pilot channel and synchronizes with it • Locks to the Sync channel that is synchronized with the Pilot channel, and gets system information (spreading code) of the access and paging channels • Sends a request to set up a call to the Access channel • Listens to Paging channel for traffic channel assignment • Transmits up assigned uplink channel, receives on assigned downlink channel Topic 4**Channel Protocol of IS-95**• Receiving an IS-95 call – the Base Station • Transmits a short message on the paging channel • Accepts Mobile Terminal request for call • Differences • Request for call has the phone number to initiate a call • Paging channel has Mobile Terminal phone number in the paging message Topic 4**What The Pilot Channel Is**• Shared by all users of the base station • Transmitted at higher power than the data channels – about 20% of total power • Unmodulated signal – no CDMA here • Provides fast synch and reliable channel tracking to support coherent demodulation and robust CDMA • Mobile terminal • Tracks the pilot channel of the current cell • Searches for other pilot channels • Switches cells when another pilot signal is stronger • Transparent to the user Topic 4**The Four Downlink Channels**• Separated by use of Walsh-Hadamard codes of length 64 • Pilot used Walsh #0 • Sync uses Walsh #32 • Paging using Walsh #1 • Traffic uses one of the other codes • See Figure 5.29 page 314 Topic 4**The Traffic Channel**• Multiplexed with control bits for power control • Rate ½ FEC encoded and interleaved • Scrambling with long code sequence follows interleaving (42 bits) • Block diagram in Figure 5.30 page 315 Topic 4**Problem 5.2 Page 263**Filtering with an integrate-and-dump filter is equivalent to convolving with a rectangular pulse of length T. Show, by using Parseval’s theorem, that the noise bandwidth of an integrate-and-dump is 1/T. Topic 4**Parseval’s Theorem**• For Fourier transform pair see Table A.2 p. 482 • For Parseval’s theorem see Eq. (A.36) p. 491 Topic 4**Noise Bandwidth**• Definition: ratio of • The variance of the output of a transfer function to a white noise with two-sided power spectral density N0/2 • The power spectral density N0 • Equation Topic 4**Power Control: The Near-Far Problem**• Haykin & Moher Section 5.7 pp. 294-297 • Received signal from K CDMA transmitters is, from Eq. (5.38) p. 279 Topic 4**SINR of First User**• More detail in 5.4.1 pages 279-283 Topic 4**FEC Coding and CDMA**• Haykin & Moher Section 5.8 pp. 297-299 • Direct Sequence Spread Spectrum (DS-SS) spreads spectrum without added redundancy • Use of FEC spreads spectrum and adds redundancy Topic 4