ENSC327 Communications Systems 24: Ch. 9: Noise in Analog Systems. Jie Liang School of Engineering Science Simon Fraser University
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1 ENSC327 Communications Systems 24: Ch. 9: Noise in Analog Systems Jie Liang School of Engineering Science Simon Fraser University 1
2 Chapter 9 Noise in Analog Comm. Chap 9 studies noise performance of various analog modulations Various SNRs in a system: Pre-detection SNR Post-detection SNR Reference SNR (also known as Channel SNR) Figure of Merit SNR in DSB SNR in AM SNR in SSB SNR in FM Main Conclusions: DSB and SSB have the same noise performance as the baseband comm system. AM has worse noise performance, but has simpler receiver (envelope detector ) FM has much better noise performance, at the price of the increased bandwidth. 2
3 Receiver Model Channel model: additive white Gaussian noise with psd N0/2. Receiver model: ideal band-pass filter and ideal demodulator. Noise w(t) Bandwidth: BT The BPF is usually a part of a mixer, e.g., in superhet receiver. The output freq of the BPF is the intermediate frequency (IF) (455kHz in AM, 10.7MHz in FM). It s denoted as fc in Chap 9. The bandwidth BT of the BPF is the bandwidth of the modulated signal (2W in AM and DSB, W in SSB, 2(D+1)W in FM. W is msg. bandwidth). The noise after the BPF is thus narrowband noise (Chap 8): 3
4 9.3 Band-pass System Structures Mixer is usually used to translate the IF frequency to the RF frequency, or vice versa. The IF frequency is denoted as fc in Chap. 9. fc fc 4
5 Pre-detection SNR N 0 /2 S N (f) BT w(t) At the input to the demodulator: x(t)s(t)+n(t), The bandwidth of x(t): The power of the narrowband noise is: Pre-detection Signal to Noise Ratio (SNR) at the demodulator input (after bandpass filter): SNR pre power of modulated signal power of the narrowband noise 5
6 Post-detection SNR w(t) The output of the demodulator: recovered message with noise. The bandwidth of the output signal is usually the bandwidth of the message signal m(t), denoted as W. The output noise psd depends on the modulation scheme. Post-detection Signal to Noise Ratio : SNR post Recovered message power Output noise power. This is the SNR perceived by the users. 6
7 Reference SNR To compare noise performances of different modulation systems, we need a reference baseband transmission model, which transmits the message directly without any modulation. For fair comparison, the transmitted power should be the same as that in a bandpass modulation system. The bandwidth of the LPF at the receiver equals to the message bandwidth The reference SNR is defined as: Channel noise SNR ref Average power of modulated signal Average noise power in the message bandwidth 7
8 Figure of Merit The reference SNR can be used to normalize the post-detection SNR of different methods, so that we can compare them: Figure of Merit Postdetection SNR Reference SNR It shows whether a modulation system has better noise performance than the baseband reference system or not. 8
9 Chapter 9 Noise in Analog Comm. Various SNRs in a system: Pre-detection SNR Post-detection SNR Reference SNR (also known as Channel SNR) Figure of Merit SNR in DSB SNR in AM SNR in SSB SNR in FM 9
10 9.4 SNR in DSB-SC The modulated DSB-SC signal at the transmitter: s( t) A m( t)cos(2π f t+ θ ) c θ is a uniform random variable in [0, 2π], but is fixed during the transmission (The reason for including θ is that the time origins of m(t) and cos(2πfct) are independent). A linear DSB-SC receiver using coherent demodulation: c Superhet receiver: Note the two filters generally have different bandwidths (BW): The BPF s bandwidth is The LPF s bandwidth is 10
11 Pre-detection SNR of DSB-SC SNR DSB pre Ac 2 In DSB, BT is 2W, where W is the message bandwidth. Proof: The pre-detection SNR is defined as: SNR pre 2 0 P B power of modulated signal power of the narrowband noise T. 11
12 Post-detection SNR of DSB-SC The post-detection SNR is defined as: SNR post Recovered message power Output noise power. The signal after the bandpass filter: x ( t) s( t) + n( t). n(t) is narrowband noise with psd N0/2 and bandwidth BT. Assuming θ 0: 12
13 Post-detection SNR of DSB-SC Bandwidth W After multiplying with the carrier: After low-pass filter with bandwidth W, the output is Only in-phase noise appears after LPF! 13
14 Post-detection SNR of DSB-SC Bandwidth W 14
15 Post-detection SNR of DSB-SC Pre-detection SNR: Post-detection SNR: To get Figure of Merit, we need the reference SNR: DSB SNR ref Post SNR Figure of Merit Ref SNR 15
16 Post-detection SNR of DSB-SC Example: Problem 9.2 DSB with 17 watts/hz, Find the post-detection SNR. Solution: W 4kHz [ ] 2 ( t) dbm fc 200kHz, E s 80 16
17 Chapter 9 Noise in Analog Comm. Various SNRs in a system: Pre-detection SNR Post-detection SNR Reference SNR (also known as Channel SNR) Figure of Merit SNR in DSB SNR in AM SNR in SSB SNR in FM 17
18 9.5 Noise in AM with Envelope Detector Modulated signal in AM: s( t) A[ 1+ k m( t) ] cos(2πf t) AM Receiver: mixer followed by an envelope detector c a c The BW of the BPF is After the BPF, 18
19 Pre-detection SNR in AM Power of modulated signal: Power of the noise after the BPF: AM Pre-detection SNR: SNR pre 19
20 Post-detection SNR in AM The result after BPF can be written as where the envelope is When the SNR is high, DC term Ac can be removed by a capacitor, so final output is: 20
21 Post-detection SNR of AM The envelope detector output The recovered message power is AM Post-detection SNR: 21
22 Figure of Merit of AM SNR AM post 2 A c k a P 2 W 0 2 To get Figure of Merit, we need the reference SNR: AM SNR ref Figure of Merit Post SNR Ref SNR [ 1+ k m( t) ] cos(2πf ), s( t) A t c a To avoid over-modulation, we need c 22
23 Figure of Merit of AM AM Figure of Merit Post SNR Ref SNR The noise performance of AM is worse than the DSB-SC, because at least half of the power is spent on the carrier. The benefit we get is the simpler envelope detector. 23
24 Chapter 9 Noise in Analog Comm. Various SNRs in a system: Pre-detection SNR Post-detection SNR Reference SNR (also known as Channel SNR) Figure of Merit SNR in DSB SNR in AM SNR in SSB SNR in FM 24
25 9.6 Pre-detection SNR in SSB A 2 c SSB signal: s( t) ( m( t)cos( 2πf t) m mˆ ( t)sin( 2πf t) ) To get the power of SSB signal, we need the following facts: 1. m(t) and its Hilbert transform are orthogonal: E ( m ( t ) m ˆ ( t ) ) 0. This is because Hilbert transform rotates the signal by 90 o. Example: 2. m(t) and its Hilbert transform have the same power. Proof: c c 25
26 Pre-detection SNR in SSB Proof: Pre-detection SNR of SSB: SNR SSB pre 2 A c P 4 W 0. 26
27 Post-detection SNR in SSB SSB signal: Ac s( t) c m 2 ( m( t)cos( 2πf t) mˆ ( t)sin( 2πf t) ) SSB signal can be demodulated by coherent method too. Using narrowband representation of the noise, the received signal is (use LSB as example): c After multiplying with the carrier and LPF: 27
28 Post-detection SNR in SSB W -fc SN(f) 0 /2 fc f 28
29 Post-detection SNR in SSB ni(t) has the same power as n(t) output noise power of ni(t)/2 is: Post-detection SNR in SSB SSB SNR post SSB Reference SNR in SSB: SNR ref Post SNR Figure of Merit: SSB Figure of Merit Ref SNR The noise performance of SSB is the same as DSB and baseband system. 29
30 Post-detection SNR of DSB-SC Example: Problem 9.5 SSB with Find the post-detection SNR. Solution: [ ] 2 ( t) dbm watts/hz, W 4kHz, E s
31 Chapter 9 Noise in Analog Comm. Various SNRs in a system: Pre-detection SNR Post-detection SNR Reference SNR (also known as Channel SNR) Figure of Merit SNR in DSB SNR in AM SNR in SSB SNR in FM 31
32 Noise in FM (Not covered in the final exam) s( t) A c cos(2πf c t + 2πk f t 0 m( τ ) dτ ) It can be shown that the figure of merit of FM modulation is Figure of merit Performance depends on the bandwidth of the modulated signal! This is different from DSB, AM, and SSB. An increase in the bandwidth BT can significantly improve the noise performance of FM system. 3 4 B T W 2. 32
33 Chapter 9 Noise in Analog Comm. Main Conclusions: DSB and SSB have the same noise performance as the baseband comm system. AM has worse noise performance, but has simpler receiver (envelope detector ) FM has much better noise performance, at the price of the increased bandwidth. 33
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