M-ary Modulation PDF

M-ary modulation Multilevel modulation M-ary phase shift keying (M-PSK), where M=2n is the number of phase values (different symbols), where n - infomation quantity in bits carried by single symbol (single radiopulse). The following modulations are used: 8-PSK, 16-PSK, 32-PSK,... ì 2E...

M-ary modulation Multilevel modulation M-ary phase shift keying (M-PSK), where M=2n is the number of phase values (different symbols), where n - infomation quantity in bits carried by single symbol (single radiopulse). The following modulations are used: 8-PSK, 16-PSK, 32-PSK,... ì 2E 2p ï cos[ 2pf c t + (m - 1)], 0 £ t < Ts , m = 1,2,...M s i (t ) = í Ts M ï î0, kitur otherwise M-PSK modulation Q 011 010 m=1…8 001 110 I 000 111 100 101 8-PSK constellation diagram using Gray code Error performance of M-PSK modulation é E æp öù SER MFM » erfc ê sin ç ÷ ú , M ³ 4. E - symbol enery ë N0 èM øû é log 2 (M )E b æ p öù SER MFM » erfc ê sin ç ÷ú, M ³ 4 Eb - bit energy êë N0 è M øúû Minimal M-PSK signal/noise ratio value for BER < 10-6: M 2 4 8 16 32 64 Minimal Eb /N0, dB 10,5 10,5 14 18,5 23,4 28,5 Modulation spectral 1 2 3 4 5 8 efficiency, bps/Hz Multilevel quadrature amplitude modulation (M-QAM) Q 0000 0100 1100 1000 2 1 m=1…16 1101 1001 0001 0101 I -2 -1 1 2 0011 0111 1111 1011 -1 -2 0010 0110 1110 1010 16-QAM modulation constellation Error performance of M-QAM modulation when is even when is odd Minimal M-QAM signal/noise ratio value for BER < 10-6: M 2 4 8 16 32 64 Minimal Eb /N0, dB 10,5 10,5 10,5 14,5 17,4 18,8 Modulation spectral 1 2 3 4 5 8 efficiency, bps/Hz M-PSK and M-QAM modulator Digital signal QB (t) Q(t) Code/ analog m(t) Serial-to- parallel Coding device 900 Σ Code/ analog I(t) Digital signal IB (t) Baseband M-PSK or M-QAM modulator RF modulator Carrier generator The Q and I signals can be digitally multiplied by the carrier and then code- to-analog conversion can be performed. In this case, a radio modulator is no longer required -- it is sufficient to change the frequency. Fourbit 16-QAM coding table Fourbit I Q Fourbit I Q 0000 -2 2 1000 2 2 0001 -2 1 1001 2 1 0010 -2 -2 1010 2 -2 0011 -2 -1 1011 2 -1 0100 -1 2 1100 1 2 0101 -1 1 1101 1 1 0110 -1 -2 1110 1 -2 0111 -1 -1 Q 1111 1 -1 0000 0100 1100 1000 2 1 m=1…16 0001 0101 1101 1001 I -2 -1 1 2 0011 0111 1111 1011 -1 -2 0010 0110 1110 1010 OFDM modulation [ S. S. Haykin, Introduction to analog and digital communications, Wiley, 2007 ]  Sequential bitrate R data OFDM modulation (binary bioplar signal) Serial-to-parallel converter I1 Q1 I2 Q2 Subcarrier symbols IN-1 QN-1 IN QN Rate R/2N 1st M-QPSK 2nd M-QPSK N-1-th M-QPSK N-th M-QPSK modulator modulator modulator modulator Modulated subcarrier f2=(m+2)R/2N symbols fN-1=(m+N-1)R/2N f1=(m+1)R/2N fN=(m+N)R/2N S(f) Σ f0 f1 f2 f3... fN f Modulated signal S(t)- n nR high RF symbol fn = f0 + = f0 + , n = 1,2,3...N. Ts 2N Orthogonality of OFDM subcarriers n nR Subcarriers are defined as: fn = f0 + = f0 + , n = 1,2,3...N. Ts 2N Such definition means coherent modulation for all Ts n subcarriers ( f0 is 1/Ts m-th harmonic), since: = Ts ( f 0 + ) = m + n Tn Ts Modulated subcarrier symbols are orthogonal. Let f0 =0: Ts 2E 2E ò cos[ 2pf k t + ( 2i + 1) p ] cos[ 2pf j t + ( 2l + 1) p ]dt = 0 Ts 4 Ts 4 E Ts = ò cos[ 2p ( f k - f j )t + (i - l ) p ]dt + Ts 0 2 E Ts + ò cos[ 2p ( f k + f j )t + (i + l + 1) p ]dt = Ts 0 2 E Ts = ò cos[ 2p ( k - j ) t + (i - l ) p ]dt + Ts 0 Ts 2 E Ts + ò cos[ 2p ( k + j ) t + (i + l + 1) p ]dt = Ts 0 Ts 2 E Ts E Ts = cos[( i - l ) p ]ò cos[ 2p ( k - j ) t ]dt - sin[( i - l ) p ]ò sin[ 2p ( k - j ) t ]dt + Ts 2 0 Ts Ts 2 0 Ts E Ts E Ts + cos[( i + l + 1) p ]ò cos[ 2p ( k + j ) t ]dt - sin[( i + l + 1) p ]ò sin[ 2p ( k + j )] t dt = 0, Ts 2 0 Ts Ts 2 0 Ts OFDM spectrum FDMA spectrum OFDM spectrum Saved bandwidth N æ æ æ R öö æ æ R ööö High-frequency S (t ) = å çç I n cosçç 2pt ç f 0 + n ÷ ÷÷ + Qn sinçç 2pt ç f 0 + n ÷ ÷÷ ÷÷ symbol: n =1 è è è 2N ø ø è è 2N ø ø ø N æ æ nR ö æ nR ö ö Low-frequency S (t ) = å çç I n cosç 2pt 1 ÷ + Qn sin ç 2pt ÷ ÷÷ symbol: n =1 è è 2N ø è 2N ø ø OFDM modulation Sequential bitrate R data Serial-to-parellel converter I1 Q1 I2 Q2 Subcarrier IN-1 QN-1 IN QN symbols ? Low-frequency symbol S1(t) 0 Hz Carrier fc=f0 Frequency converter f11 f21 f31... fN1 f High-frequency symbol S(t) OFDM modulation Lets use complex numbers and complex amplitudes: d n = I n - iQn , C n = cos(2pf n t ) + i sin(2pf n t ) = exp(i 2pf n t ). Here: dn – complex subcarrier symbol, Cn- subcarrier. We can notice, that: æ N ö æ N ö æ N nR ö S (t ) = Reç å d n C n ÷ = Reç å d n exp(i 2pf nt ) ÷ = Reç å d n exp(i 2p 1 t) ÷ è n =1 ø è n =1 ø è n =1 2N ø IDFT (IFFT) N kn X ( k ) = å x n exp(i 2p ) k=1,2,3… result: n =1 N. If we insert into equation discrete time values t=kΔT, whereΔT=2/R The same (sampling period corresponds to input dibit duration), we will get: æ N nRk 2 ö æ N nk ö S (t ) = Reç å d n exp(i 2p 1 ) ÷ = Reç å d n exp(i 2p ) ÷ è n =1 2 NR ø è n =1 N ø  OFDM modulator parallel Serial to quadrature coding M-QAM I Q I DAC DAC Complex data Cyclic Cyclic Complex data prefix prefix Parallel to serial [K. D. Wong, Fundamentals of wireless communication engineering technologies, 2012] Guard band and intrasymbol interference Δt Subcarrier oscilogram with inserted guard interval. Transient oscillations are visible at the beginning and end of the signal. Δt > TCP. But TCP must be larger than the channel time spread parameter, which in urban conditions can reach several μs. Requires - 10lg(NC) S/I, dB 40 Only for adjacent subcarriers 0 1% 10% 100% fD /Δf Cyclic prefix duration 1. TCP > time spread parameter 2. Because the temporal spreading parameter depends on the geographic environment of the communication channel, it should be possible to adapt TCP to the channel. 3. It must be possible to increase the TCP in order to create single frequency network (SFN) Peak-to-Average Power Ratio (PAPR) OFDM and multiple access (OFDMA) Subcarrier sets can be used for multiple users To/from 1st user Localized and distributed subcarrier sets To/from 2nd user To/from 3rd user Important for uplink direction: 1. Mobile transmissions should be synchronized such that signals would reach base station at the same time 2. Adjust mobile transmitter powers to make equal received power at base station [ W. Stallings and C. Beard, Wireless communication networks and systems, 2016 ] Exercise: LTE 20 MHz OFDM modulation Find data bitrates for LTE 20 MHz 32-QAM system with above parameters: subcarrier spacing 15 kHz, total number of FFT subcarriers 2048. Consider two cases: (a) with normal cyclic prefix 4.7μs and (b) with extended cyclic prefix 16.7μs.