--- title: "Detection gain of SSB-SC vs DSB-SC" subject: "Communication Systems" chapter: 9 key: "semester_6/communication_systems:detection-gain-ssbsc-dsbsc" source: https://www.bctengineer.com/q/semester_6/communication_systems/detection-gain-ssbsc-dsbsc site: BCT Engineering --- # Detection gain of SSB-SC vs DSB-SC Communication Systems · Chapter 9: Noise in Communication Systems - Asked in: 2075 Chaitra (CS II), 8 marks; 2073 Shrawan (CS II), 3+3 marks (asked 2 times) - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/communication_systems/detection-gain-ssbsc-dsbsc - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-9 ## Question Find the detection gain for SSB-SC demodulation and compare with DSB-SC. ## Short answer For SSB-SC, the detection gain is 1 (SNR_o/SNR_i). For DSB-SC, it is 2. However, both have a figure of merit of 1 relative to baseband, meaning for equal transmitted power and noise density, they provide the same output SNR despite different bandwidths. ## 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. **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 $=1$. **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 $=1$. **Comparison:** | Quantity | DSB-SC | SSB-SC | |---|---|---| | Transmission bandwidth | $2W$ | $W$ | | Noise power at input | $2N_0W$ | $N_0W$ | | $\text{SNR}_i$ (same $A_c$) | $\frac{A_c^2P}{4N_0W}$ | $\frac{A_c^2P}{4N_0W}$ | | Detection gain $\gamma$ | 2 | 1 | | Figure of merit (baseband reference) | 1 | 1 | The DSB-SC detection gain is twice that of SSB because the two sidebands add coherently (voltage) while the noise in them adds in power. But SSB lets in only half the noise bandwidth, so for the **same transmitted power and same noise PSD, both give the same output SNR** (figure of merit 1). 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. How is detection gain defined? A. SNR_o / SNR_i B. SNR_i / SNR_o C. Message power / carrier power D. Transmission bandwidth / message bandwidth Answer: A. Detection gain is the ratio of demodulator output SNR to input SNR, showing how much the demodulator improves SNR. (Key point: Detection gain definition) 2. What is the detection gain of coherent SSB-SC? A. 2 B. 1/2 C. 1 D. 3 Answer: C. For SSB, SNR_o = A^2 P/(4 N0 W) equals SNR_i, so the gain is 1. (Key point: SSB-SC gain) 3. Why is the DSB-SC detection gain 2? A. DSB-SC uses half the bandwidth of SSB B. Coherent detection rejects the quadrature noise n_s, a 3 dB gain over SNR_i, which counts noise in 2W C. DSB-SC has twice the carrier power D. The noise power is zero after the LPF Answer: B. SNR_i uses noise in 2W, while the output keeps only the in-phase noise, so SNR_o is twice SNR_i. (Key point: DSB-SC gain) 4. For the same transmitted power and noise PSD, how do SSB-SC and DSB-SC compare in output SNR? A. DSB-SC is 3 dB better B. SSB-SC is 3 dB better C. DSB-SC is twice as good because of its larger gain D. They are equal (figure of merit 1 for both); SSB needs half the bandwidth Answer: D. SSB has smaller gain but admits half the noise, so output SNR is the same; SSB's advantage is half the bandwidth. (Key point: Overall comparison) ## Related in Communication Systems - [DSB-SC vs SSB; synchronous demodulation of DSB-SC](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adsbsc-vs-ssb-synchronous-demod) — 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 - [Detection gains of DSB-FC, DSB-SC and SSB](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adetection-gain-dsbfc-dsbsc-ssb) — Communication Systems, chapter 9 - [Phase error in coherent DSB-SC detection; AM demodulation by PLL](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aphase-error-dsbsc-am-pll) — Communication Systems, chapter 2 - [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