PN CODE GENERATION (cont d) ALi Linear n-stage t ShiftRegister output tsequence Modulo-2 Adder h hn-1 h hn-2 h h2 h h1 X n-1 X n-2 X 1 X 0 Output Note: hi=1 represents a closed circuit; hi=0 represents an open circuit 12
PN CODE GENERATION (cont d) Maximal llength ths Sequence (m-sequence) The longest sequences that can be generated by a given shift register of a given length 2 n -1 chips n is the number of stages in the shift registers Containing 2 n-1-1 zeros and 2 n-1 ones per period regardless of the initial condition A modulo-2 addition with a phase-shifted replica of itself results in another replica of a phase shift different from either of the originals. 13
EXAMPLE n-stage Linear Shift Register S1 S2 S3 S4 Output X 2 X0 X 4 X 3 X 1 h(x) : the n-th-order polynomial with feedback coeff. (h 0, h 1,,h n ) h(x) = h 0 h 1 x h 2 x 2 h n x n h 0 = h n = 1. h(x) = 1 x 1 x 4 When h(x) is an irreducible (not factorable) primitive polynomial of degree n, then all sequences generated by h(x) have a max. period of 2 n -1. 14
EXAMPLE (cont d) Shift and Adder Property 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 100110101111000 0 1 1 0 1 0 1 1 1 1 0 0 0 3 chips delayed 1 0 0 0 1 0 0 1 1 0 1 0 1 1 1 14 chips delayed Distribution of Runs for a 2 4-1 Chip Sequence Run Length Ones Zeros Number of Chips Included 1 2 2 1 2 1 2 = 4 2 1 1 1 2 1 2 = 4 3 0 1 0 31 1 3 = 3 4 1 0 1 4 0 4 = 4 Total Number of Chips 15 15
AUTOCORRELATION To be a good PN sequence {a i } a i is independent of a j for any i j If a i = a in, (N : period) N Normalized Autocorrelation R c N 1 1, k = 0, ± N, ± 2N,... ( k) = 1 Ci Ci k = 1 N =, otherwise i 0 N 1 R c (k) -N 0 N k 16
BS SEPARATION BY PN OFFSET N PN Sequence PN Sequence BS 1 BS 2 Offset PN Sequence PN Sequence BS 3 BS 4 Autocorrelation by shifting PN seq. a b c d t Finding the offset value of c Synchronized to BS 3 t 17
PN OFFSET GENERATION CDMA 0 0 1 1 0 1 1 1 1 0 0 0 1 1 1 1 Pattern = 1001011 0 1 0 0 1 1 0 0 1 0 1 1 18
PN OFFSET GENERATION (cont d) CDMA Masking 0 1 1 1 1 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 Pattern 1 1 1 = 1001011 Offset = 110 1 1 0 0 1 1 0 1 0 1 1 1 0 1 1 0 0 1 0 1 1 0 1 0 1 19
MODULATION AND CODING (2G) Modulation Chip rate Nominal data rate Filtered bandwidth Channel coding Interleaving Quadrature Phase-Shift Keying 1.2288 Mcps 9600 bps 1.25 MHz Convolutional coding with Viterbi decoding With 20-ms span 20
DL PHYSICAL CHANNELS Pilot channel (2G) 4-6dB higher than a traffic channel Determination of handoff based on its strength Channel estimation, demodulation Sync channel Frame sync. Time information Paging gchannel Traffic channel 21
UL PHYSICAL CHANNELS Access channel Responding to pages (2G) Making call originations Processing other messages between MS and BS Traffic channel 22
CAPACITY Processing Gain G p RF bandwidth = = The information Bit Rate W R Typically, 20 60 db Quantifying the degree of Robustness to interference 23
CAPACITY (cont d) Signal to noise ratio E / N = b o S/ R ( N W α( N 1) S)/ W t S : received signal power at the BS from a mobile station N t : noise spectral density W : tx bandwidth N : number of users in the cell α : voice activity Power limited Soft capacity S = Nt W W / R ( α N E / N0 1) E b 24
CAPACITY (cont d) CAPACITY (cont d) IfS t i fi it th t ti li k it If S goes to infinity, the asymptotic link capacity is given by S 0 1 1 / / b W R N E N α = 1 / W R 0 1 1 capacity) / ( / u b p W R N E N G α = 0 / p b E N α = 1 /N E W/R 0 b α 1 N 25
NEAR-FAR EFFECT Ideal Near-Far Effect P T1 P T1 P T 2 P T 2 MS1 MS1 MS2 MS2 d/2 d P P R1 P R2 1.25 MHz f P R1 C = I = P P P R 2 R1 R2 = 1 P P = 1.25 MHz P R 2 16 R1 d f P P C I 1 R 2 = P 4 R1 R1 = = ( d /( 2d )) 1 16 P R1 P R 2 P R 2 1 = 16 26
POWER CONTROL Objectives Solving the near-far problem Maximizing system capacity Measures Received signal strength Received signal to interference ratio (SIR) 27
OPEN-LOOP POWER CONTROL To decide tx power based on the received signal strength No control by feedback 28
CLOSED-LOOP LOOP POWER CONTROL CDMA By the received power control bits By 1 bit: up or down By multiple bits: multi-level up/down Based on the received SIR If the received SIR is over the target SIR or not 800Hz (IS-95), 1500Hz (WCDMA) 29
OUTER-LOOP POWER CONTROL Changing the target SIR value Target SIR is varying according to the conditions such as channel, speed, etc. Adaptively following the target SIR For 1% PER (packet error rate) 1 unit itdown: for a success 99 units up: for an error 30
EXAMPLE 31
RAKE RECEIVER 32
OFDM Orthogonal Frequency Division Multiplexing
OFDM Fourier Transform Given a varying signal s(t) in the time-domain, the spectral components S(f) are obtained as follows: S( f ) = s( t) e dt j2πft And vice versa: For a fixed frequency f, the integral tells us how much of that harmonic is present in the signal s(t). s( t) j2 πftf = S( f ) e 2 df 2
OFDM Theorems Useful Theorems Time delay Frequency translation Convolution Multiplication Transforms Rectangular Constant Impulse t Π τ τ sincfτ 3
OFDM Multi-Carrier Modulation Channel impulse response t f Data on single carrier t f subch. 1 f f 0 f 0 f 1 f 2 f 3 t Multicarrier with 4 subchannels subch. 2 f 1 subch. 3 f 2 t t f subch. 4 f 3 t Time domain Frequency domain 4
OFDM Single Carrier Transmission SCM vs. MCM Symbol duration < delay (multipath) spread = BW of Tx Signal > BW of Channel Severe ISI, High complexity (Rake receiver, Equalizer) Multi-Carrier Modulation Frequency division multiplexing (for a single user) Divide a wideband channel into narrow subchannels Serial-to-Parallel conversion, Parallel transmission Low symbol rate at each subchannel Frequency selective channel Flat narrowband channel Less ISI No need for complex multi-tap tap time-domain equalizer Possibly simple 1-tap frequency domain equalizer More sensitive to frequency offset Large PAPR 5
OFDM FDM vs. OFDM (a) Conventional multicarrier FDM Saving of bandwidth (b) Orthogonal multicarrier (OFDM) By using the overlapping multi-carrier modulation, we can save almost 50% of bandwidth 6
OFDM Common to FDM & OFDM Split a high-rate data stream into a number of lower rate streams Transmitted simultaneously over a number of subcarriers Symbol duration increases for the lower rate parallel subcarriers Relative amount of dispersion is decreased 7
OFDM FDM No requirement for carrier spacing If the spacing is sufficiently large to guarantee no overlapping or negligible interference from neighboring bands Receive method - filtering f BPF f f 8
OFDM FDM-Transmit 9
OFDM OFDM T t 1/T f Transmitting sinusoidal soidal signals with an integer multiple of cycles cles (time domain) carrier spacing is exactly 1/T, where T is the symbol duration 1/T is the minimum spacing (Frequency domain) Maintaining and exploiting the orthogonality property when modulating and demodulating the signal no need for filtering but sensitive to frequency & timing offset 10
Time Domain Representation OFDM A * 1.5 1 0.5 B * 0-0.5-1 C * -1.5 0 10 20 30 40 50 60 70 80 90 100 Data symbols (T = 1) T 0 e j 2πf t k e j 2πf t j dt T, if f k = 0, if f k = f f j j = n T T T T T Asin( t)*2sin( t) dt = A Asin( t)*2sin(2t) dt = 0 { Asin( t) Bsin(2t) C sin(3t)}2sin( t) dt { Bsin(2t) C sin(3t)}2sin( t) dt = 0 = A 11
OFDM Frequency Domain Representation For blue curve, when it is at its peak value The other curves have a zero value at that point This means orthogonality in frequency domain f 1/T 2/T 3/T 4/T 5/T 12