Chapter 3. Digital Communication Fundamentals for Cognitive Radio
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1 Chapter 3 Digital Communication Fundamentals for Cognitive Radio 1
2 Outline Fundamental of Data Transmission Digital Modulation Techniques Probability of Bit Error Multicarrier Modulation Multicarrier Equlization Intersymbol Interference Pulse Shaping 2
3 Data Transmission Anatomy of a wireless Digital Comm Sys 3
4 Data Transmission Fundamental Limits Shannon Hartley theorem S is the total received signal power over the bandwidth (in case of a modulated signal, often denoted C, i.e. modulated carrier), measured in watt or volt; N is the total noise or interference power over the bandwidth, measured in watt or volt; and S/N is the signal-to-noise ratio (SNR) or the carrier-to-noise ratio (CNR) of the communication signal to the Gaussian noise interference expressed as a linear power ratio (not as logarithmic decibels). 4
5 Data Transmission Source of Transmission Error The linear filter channel with additive noise 5
6 Data Transmission Additive White Gaussian Noise (AWGN) White noise assumption in most situations Gaussian pdf 6
7 Data Transmission Additive White Gaussian Noise (AWGN) Histogram of AWGN superimposed on the probability density function for a Gaussian random variable of N(0,0.25) Power spectral density of AWGN with N(0,0.25) 7
8 Data Transmission Nearest neighbor detection AWGN N(0,0.01) AWGN N(0,0.25) 8
9 Digital Modulation Techniques Representation of Signals Euclidean Distance between Signals Decision Rule Power Efficiency M-ary Phase Shift Keying M-ary Quadrature Amplitude Modulation 9
10 Representation of Signals 10
11 Euclidean Distance between Signals For any two signals s i (t) and s j (t), the Euclidean Distance between them is defined as d 2 ij s t s t i ( ) j ( ) 2 dt Vector form d ij s s i j 11
12 Decision Rule Nearest neighbor rule: Determine r is if s is the closest to r i r rewritten as s r s, j waveform representation T 0 i i r s r s, j r( t) s i ( t) dt j T 0 j r( t) s i j i ( t) dt s i 12
13 Power Efficiency Measures the largest minimum signal distance achieved given lowest transmit power Energy per symbol Energy per bit Es Eb log 2 M M 1 Es P s i0 i 2 i ( t) dt 13
14 Power Efficiency Power efficiency P d 2 min E b 14
15 M-ary Phase Shift Keying 2 t si ( t) Acos( ct ), m 0,1,, M 1 m 15
16 M-ary Quadrature Amplitude Modulation 16
17 M-ary Quadrature Amplitude Modulation 17
18 M-ary Quadrature Amplitude Modulation Receiver Simple receiver structure makes M-QAM popular in digital communication systems. 18
19 Probability of Bit Error Also known as bit error rate Starting from the modulation scheme with two signal waveforms, 1( t) and ( Assuming the noise term has a Gaussian distribution n( t) ~ N(0; ) s s 2 t) 19
20 Derivation of BER Assuming s 1 ( t) was transmitted, then an error event occurs if where T T 0 0 r( t) s1( t) n( t) r( t) s1( t) dt r( t) s2 ( t) dt 20
21 Derivation of BER P(error)= Q E N 0 12 N 0 is the noise density 12 is the correlation between ( t 1 ) and Q-function defines the area under the tail of a Gaussian pdf Q( x) 1 2 x e y 2 / 2 dy s s ( t) 2 21
22 Derivation of BER When E E, s 1 s 2 Q E 1 E2 2 2N 0 12 and E therefore 2 1 E2 212 dmin P e Q d 2N 2 min 0 22
23 Upper Bound on BER At least one error occurs m j j m Therefore m Pe Q d 2 ij 2N j2 0 23
24 Lower Bound on BER The smaller d 2, the more likely an error ij happens. Therefore P e Q d 2N 2 min 0 24
25 Multicarrier modulation Advantages: Transmission agility High datarate Immunity to non-flat fading response. divide-and-conquer channel distortion Adaptive bit loading 25
26 Multicarrier modulation Disadvantages: Sensitive to narrowband noise Sensitive to amplitude clipping Sensitive to timing jitter, delay 26
27 Multicarrier Modulation Transmitter Receiver 27
28 Comparison between single carrier and multicarrier tt 28
29 OFDM Orthogonal Frequency Division Multiplexing 29
30 FB-OFDM Orthogonal Frequency Division Multiplexing with Filterbank FB-MC subcarrier spectrum employing a seuqre-root raised cosine prototype lowpass filter with a rolloff of
31 OFDM Transmitter Receiver 31
32 Multicarrier Equalization Interference in multicarrier systems 32
33 Distortion Reduction Channel coding Add redundancy to improve recovering 33
34 Distortion Reduction Channel equalization Before equalization After equalization 34
35 Distortion Reduction Channel equalization Pre-equalization requires a feedback path from the receiver 35
36 Intersymbol Interference Signal being distorted by the temporal spreading and resulting overlap of individual symbol pulses Simplified block diagram for a wireless channel 36
37 Intersymbol Interference RC-LPF filter response of combined modulation pulses when T=1, A=1 37
38 Intersymbol Interference Peak Interference/Distortion When all symbols before and after have destruct effect on the symbol on cursor 38
39 Pulse Shaping Nyquist Pulse Shaping Theory Time domain condition for zero ISI No ISI if sampling at t=kt 39
40 Nyquist Pulse Shaping Theory Nyquist-I Pulse (W=1/(2T)) 40
41 Nyquist Pulse Shaping Theory Nyquist-II Pulse (W>1/(2T)) 41
42 Nyquist Pulse Shaping Theory Frequency domain No ISI criterion H H eq eq ( ( f f ) ) C, f N k N H ( 1 2T f k T ), f 1 2T 42
43 Chapter 3 Summary Digital communication theory at the core of cognitive radio operations Mathematical tools necessary for enabling advanced features Various modulation schemes can be used for transmission under different constraints and expectations Bit Error Rate is primarily used to define performance 43
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