--- title: "Noise performance of DSB-SC and SSB-SC" subject: "Communication Systems" chapter: 9 key: "semester_6/communication_systems:noise-dsbsc-ssbsc" source: https://www.bctengineer.com/q/semester_6/communication_systems/noise-dsbsc-ssbsc site: BCT Engineering --- # Noise performance of DSB-SC and SSB-SC Communication Systems · Chapter 9: Noise in Communication Systems - Asked in: 2071 Shrawan (CS II), 6 marks - Video: [Noise Performance in DSBSC Receiver](https://www.youtube.com/watch?v=dDreOUA0ABQ) — N. Vini Antony Grace - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/communication_systems/noise-dsbsc-ssbsc - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-9 ## Question With necessary derivations, compare the noise performance of DSB-SC and SSB-SC modulations in analog communication system. ## Short answer DSB-SC has detection gain 2; SSB-SC has gain 1, but both achieve figure of merit 1. For the same transmitted power, they provide identical output SNR because SSB’s halved input noise compensates for the lack of sideband coherent addition. SSB, however, uses half the bandwidth. ## Answer **Receiver model.** The received signal $s(t)$ plus white noise ($N_0/2$) passes through a band-pass (IF) filter of bandwidth $B_T$, then a demodulator and a low-pass filter of bandwidth $W$ (message bandwidth). ```text s(t) + +-------+ +-------+ +-----+ ---->(+)-->| BPF |--->| demod |-->| LPF |--> y(t) ^ | B_T | | | | W | w(t) +-------+ +-------+ +-----+ ``` The filtered noise is narrowband and is written in in-phase/quadrature form $$ n(t)=n_c(t)\cos\omega_ct-n_s(t)\sin\omega_ct $$ where $n_c$ and $n_s$ are low-pass, each with the same power as $n(t)$: $\overline{n_c^2}=\overline{n_s^2}=\overline{n^2}=N_0B_T$. **Definitions.** Message power $P=\overline{m^2(t)}$. - Input SNR $\text{SNR}_i=\dfrac{\text{received signal power}}{\text{noise power in } B_T}$ - Output SNR $\text{SNR}_o=\dfrac{\text{message power at output}}{\text{noise power at output}}$ - **Detection gain** $\gamma_d=\dfrac{\text{SNR}_o}{\text{SNR}_i}$; **figure of merit** $=\dfrac{\text{SNR}_o}{\text{SNR}_{ref}}$, where $\text{SNR}_{ref}$ is the channel SNR measured in the message band $W$ (baseband reference). Both show how much the demodulator improves or worsens SNR. **DSB-SC (coherent detection).** $s(t)=A_cm(t)\cos\omega_ct$, $B_T=2W$. - Signal power $=\frac{A_c^2P}{2}$; noise in $2W$ $=2N_0W$, so $\text{SNR}_i=\dfrac{A_c^2P}{4N_0W}$. - Multiply $x(t)=s(t)+n(t)$ by $\cos\omega_ct$ and low-pass filter: $$ y(t)=\frac{A_c}{2}m(t)+\frac12n_c(t) $$ - $\text{SNR}_o=\dfrac{A_c^2P/4}{2N_0W/4}=\dfrac{A_c^2P}{2N_0W}$ $$ \gamma_{DSB\text{-}SC}=\frac{\text{SNR}_o}{\text{SNR}_i}=2 $$ The quadrature noise $n_s$ is rejected by coherent detection, giving a 3 dB gain. With baseband reference $\text{SNR}_{ref}=\frac{A_c^2P}{2N_0W}$, figure of merit $=1$. **SSB-SC (coherent detection).** $s(t)=\frac{A_c}{2}[m(t)\cos\omega_ct\mp\hat m(t)\sin\omega_ct]$, $B_T=W$. - Signal power $=\frac{A_c^2}{4}\cdot\frac{P+P}{2}=\frac{A_c^2P}{4}$ (since $\overline{\hat m^2}=P$); noise in $W$ $=N_0W$, so $\text{SNR}_i=\dfrac{A_c^2P}{4N_0W}$. - Multiply by $\cos\omega_ct$ and low-pass filter: $$ y(t)=\frac{A_c}{4}m(t)+\frac12n_c(t) $$ - Signal power $\frac{A_c^2P}{16}$, noise power $\frac{N_0W}{4}$, so $\text{SNR}_o=\dfrac{A_c^2P}{4N_0W}$ $$ \gamma_{SSB}=\frac{\text{SNR}_o}{\text{SNR}_i}=1 $$ With baseband reference ($\text{SNR}_{ref}=\frac{A_c^2P}{4N_0W}$, same transmitted power), figure of merit $=1$. **Comparison:** | Quantity | DSB-SC | SSB-SC | |---|---|---| | Bandwidth $B_T$ | $2W$ | $W$ | | Input noise power | $2N_0W$ | $N_0W$ | | Detection gain | 2 | 1 | | Figure of merit | 1 | 1 | | Output SNR (same transmitted power) | Equal | Equal | DSB-SC has twice the detection gain because its two sidebands add coherently, but it collects twice the noise. For the same transmitted power both give identical output SNR; SSB is preferred because it needs half the bandwidth. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For coherent DSB-SC detection, what is the detection gain SNR_o/SNR_i? A. 1 B. 2 C. 3 D. 1/2 Answer: B. Output SNR is A_c^2P/(2N_0W) while input SNR is A_c^2P/(4N_0W), so the ratio is 2 (3 dB). (Key point: DSB-SC detection gain) 2. Why does coherent DSB-SC detection give a gain of 2 over the input SNR? A. The LPF removes half the message power B. The quadrature noise component n_s is rejected by the coherent detector C. The bandwidth is halved after demodulation D. The carrier is added back at the receiver Answer: B. Multiplying by cos(wc t) keeps only the in-phase noise n_c and rejects n_s, while both sidebands add coherently. (Key point: Quadrature noise rejection) 3. What are the transmission bandwidth and detection gain of coherent SSB-SC? A. B_T = 2W, gain 2 B. B_T = W, gain 2 C. B_T = W, gain 1 D. B_T = 2W, gain 1 Answer: C. SSB occupies only W, so it collects noise N_0W, and its output SNR equals its input SNR, giving gain 1. (Key point: SSB-SC detection gain) 4. For the same transmitted power, how do DSB-SC and SSB-SC compare in output SNR, and why is SSB preferred? A. DSB-SC is twice as good, so it is preferred B. SSB is twice as good because of less noise C. They are equal, and SSB needs half the bandwidth D. They are equal, and SSB needs no carrier recovery Answer: C. DSB-SC's higher detection gain is offset by collecting twice the noise, so both give the same output SNR; SSB needs half the bandwidth. (Key point: Equal output SNR for same power) ## Related in Communication Systems - [Noise performance of DSB-AM, DSB-SC and SSB-SC](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Anoise-dsbam-dsbsc-ssbsc) — Communication Systems, chapter 9 - [Compare DSB-AM, DSB-SC, SSB, VSB; SSB by phase discrimination](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Acompare-am-variants-ssb-phase) — Communication Systems, chapter 2 - [Compare DSB-AM, DSB-SC and SSB](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Acompare-dsbam-dsbsc-ssb) — Communication Systems, chapter 2 - [DSB-AM, DSB-SC and SSB spectra; synchronous detection](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adsbam-dsbsc-ssb-spectrum-synchronous) — Communication Systems, chapter 2 - [Noise performance of coherent DSB-FC detection](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adsbfc-noise-coherent-100pct) — Communication Systems, chapter 9 - [Detection gain of SSB-SC vs DSB-SC](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adetection-gain-ssbsc-dsbsc) — Communication Systems, chapter 9, asked 2× ## Related in other subjects - [Compare analog and digital communication](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Adigital-vs-analog-comparison) — Data Communication, chapter 1, asked 4×