Digital Modulation Interview Questions

Q1. What is the difference between ASK, FSK, and PSK modulation?

ASK (amplitude shift keying) varies carrier amplitude, FSK (frequency shift keying) varies carrier frequency, and PSK (phase shift keying) varies carrier phase to encode digital bits, each offering different bandwidth-power tradeoffs. Binary ASK with two levels 0 and A_c transmits 1 bit per symbol but is extremely sensitive to amplitude noise — it is used mainly in short-range optical fiber links and IR remotes. BPSK and BFSK are more robust in noisy channels, which is why 2G GSM uses GMSK (a shaped FSK) for cellular voice and LTE uses higher-order PSK and QAM for data.

Follow-up: Which of ASK, FSK, and PSK has the best BER performance at the same SNR?

Q2. What is BPSK and what is its bit error rate performance?

Binary phase shift keying (BPSK) encodes one bit per symbol using two phases 0° and 180°, achieving the minimum bit error rate of any binary modulation scheme: BER = Q(√(2Eb/N0)), where Eb/N0 is the energy per bit to noise spectral density ratio. At Eb/N0 = 10 dB, the BPSK BER is Q(√20) ≈ 3.9×10⁻⁶, which is why GPS signal processing uses BPSK — reliable data is recovered at very low SNR after despreading. BPSK's outstanding BER performance comes from the maximum possible Euclidean distance between its two constellation points, and no other binary scheme can outperform it in AWGN.

Follow-up: How does the BER of BPSK compare to QPSK at the same Eb/N0?

Q3. What is QPSK and how does it improve spectral efficiency over BPSK?

QPSK encodes 2 bits per symbol by using four equally-spaced phase states (0°, 90°, 180°, 270°), doubling the spectral efficiency (bits/s/Hz) compared to BPSK with identical BER performance at the same Eb/N0. A 3G WCDMA downlink uses QPSK at chip rate 3.84 Mcps to achieve a bandwidth efficiency of 2 bits/s/Hz, carrying 7.68 Mbps in a 3.84 MHz bandwidth. QPSK and BPSK have exactly the same BER versus Eb/N0 curve because splitting the signal space into two independent BPSK dimensions preserves the minimum Euclidean distance.

Follow-up: What is the difference between Gray coding and natural coding in QPSK, and why does Gray coding matter?

Q4. What is QAM and how does it increase data rate?

Quadrature amplitude modulation (QAM) varies both amplitude and phase simultaneously, packing M = 2k symbols into a 2D constellation, achieving k bits per symbol and thus k× higher spectral efficiency than BPSK at the cost of requiring higher SNR. 64-QAM (used in 4G LTE) encodes 6 bits per symbol using a 8×8 constellation grid, enabling peak data rates of 150 Mbps in a 20 MHz LTE channel. The tradeoff is that higher-order QAM requires smaller minimum symbol spacing for the same average power, demanding higher SNR — 256-QAM requires about 8 dB more SNR than 16-QAM for the same BER.

Follow-up: Why is 256-QAM used in 5G NR but was not practical in earlier cellular systems?

Q5. What is the Q-function and how is it used in BER calculations?

The Q-function Q(x) = (1/2)erfc(x/√2) gives the tail probability of a standard normal distribution above x, and it directly gives the BER for coherently detected digital modulation schemes in AWGN. For BPSK, BER = Q(√(2Eb/N0)): at Eb/N0 = 7 dB (linear 5), BER = Q(√10) = Q(3.16) ≈ 7.8×10⁻⁴. The Q-function is monotonically decreasing, so increasing Eb/N0 always reduces BER, and the steep slope of Q(x) for x > 2 means a 3 dB improvement in SNR can reduce BER by several orders of magnitude.

Follow-up: What is the complementary error function (erfc) and how does it relate to Q?

Q6. What is minimum shift keying (MSK) and why is it used?

MSK is a special case of CPFSK (continuous phase FSK) where the frequency deviation is exactly half the bit rate (modulation index h = 0.5), producing a phase change of exactly ±90° per bit and a continuous-phase signal with no abrupt phase jumps that would broaden the spectrum. GSM cellular uses GMSK (Gaussian MSK), which further filters the MSK pulse with a Gaussian low-pass filter to reduce spectral sidelobes, fitting the signal into the 200 kHz GSM channel with minimal adjacent-channel interference. MSK has the same BER as BPSK while occupying a better-contained spectrum than general FSK, making it ideal for spectrum-efficient narrowband frequency-planning systems.

Follow-up: What is the phase continuity property of MSK and why does it reduce spectral sidelobes?

Q7. What is differential PSK (DPSK) and when is it preferred over coherent PSK?

DPSK encodes each bit as a phase change relative to the previous symbol rather than an absolute phase, allowing demodulation by comparing the phase of adjacent symbols without requiring a phase-synchronised local oscillator at the receiver. Bluetooth classic uses π/4-DQPSK (a form of differential QPSK) because portable devices with fast frequency-hopping cannot afford the latency of carrier phase recovery circuits for each 625 µs time slot. The tradeoff is a BER penalty of about 3 dB compared to coherent PSK because the noise in the reference symbol adds to the noise in the current symbol during differential detection.

Follow-up: What is the BER penalty of DPSK versus coherent BPSK at high SNR?

Q8. What is OFDM and why is it used in 4G/5G?

OFDM (Orthogonal Frequency Division Multiplexing) splits the data stream across hundreds or thousands of narrowband subcarriers spaced at 1/T Hz (where T is the symbol duration), making each subcarrier experience flat fading and eliminating intersymbol interference with a cyclic prefix guard interval. LTE uses OFDM with 15 kHz subcarrier spacing and up to 1200 active subcarriers in a 20 MHz channel, mapping each subcarrier independently with QPSK to 256-QAM based on the channel conditions measured by pilot tones. OFDM's robustness against multipath fading is why it replaced CDMA in 4G and is the foundation of 802.11 Wi-Fi from 802.11a onwards.

Follow-up: What is the cyclic prefix in OFDM and how long must it be?

Q9. What is spectral efficiency and how is it measured?

Spectral efficiency η = R_b/B (bits/s/Hz) is the data rate achievable per unit bandwidth, bounded by the Shannon capacity limit η_max = log₂(1 + SNR) bits/s/Hz for AWGN channels. An LTE-Advanced carrier aggregating 100 MHz of spectrum achieving a peak downlink rate of 1 Gbps has a spectral efficiency of 10 bits/s/Hz, approaching 256-QAM 4×4 MIMO's theoretical limit of about 32 bits/s/Hz. Modulation order directly determines spectral efficiency: BPSK gives 1 bit/s/Hz, QPSK 2 bits/s/Hz, 16-QAM 4 bits/s/Hz, and 64-QAM 6 bits/s/Hz in the absence of coding overhead.

Follow-up: What does the Shannon-Hartley theorem state about the relationship between bandwidth, SNR, and capacity?

Q10. What is the Gray code mapping in QAM and why is it used?

Gray code mapping assigns constellation points so that adjacent symbols differ by only one bit, meaning the most likely symbol errors (to adjacent points at high SNR) cause only a single bit error rather than multiple bit errors. In 16-QAM with Gray coding, a symbol error in the worst case causes 1 bit error out of 4 bits, giving BER ≈ SER/4 at high SNR — without Gray coding, symbol errors could affect up to 4 bits, multiplying the BER by up to 4×. Every practical QAM system from Wi-Fi to 5G NR uses Gray-coded constellation mapping for this reason.

Follow-up: How does the BER-versus-SER relationship change in higher-order QAM with Gray coding?

Q11. What is intersymbol interference (ISI) and how is it caused?

ISI occurs when the response of a channel to one symbol extends in time and overlaps with the response to adjacent symbols, causing the receiver to see a combination of the desired symbol and 'echoes' of preceding symbols. A multipath wireless channel with a delay spread of 5 µs causes ISI for any digital system with symbol rate faster than about 200 kbps, because each symbol lasts less than 5 µs and the delayed echoes bleed into the next symbol. ISI is mitigated by reducing the symbol rate (lower data rate), using equalization at the receiver, or using OFDM with a cyclic prefix longer than the delay spread.

Follow-up: What is the Nyquist criterion for zero ISI and how does it determine the minimum signaling bandwidth?

Q12. What is coherent detection and how does it differ from non-coherent detection?

Coherent detection uses a locally generated carrier that is perfectly synchronized in phase with the received carrier, multiplying the received signal by the synchronized carrier to extract the baseband message; non-coherent detection does not require phase synchronization and relies on envelope or differential phase methods. BPSK and QAM require coherent detection because their information is encoded in the absolute phase — a receiver that loses phase lock cannot decode them. Non-coherent BFSK and DPSK work without a phase reference but pay a 2–3 dB SNR penalty compared to their coherent counterparts, making them suitable for low-complexity or fast-hopping applications.

Follow-up: What is carrier phase recovery and how is it implemented in a digital receiver?

Q13. What is constellation diagram and what does it reveal about a modulated signal?

A constellation diagram plots the in-phase (I) and quadrature (Q) components of received symbols as points in the complex plane, and its shape reveals modulation format, noise level, phase error, amplitude imbalance, and nonlinear distortion. A clean 64-QAM constellation has 64 tight clusters arranged in an 8×8 grid; if the clusters are large (noisy), the SNR is insufficient; if the grid is rotated, there is carrier phase error; if it is compressed in one dimension, there is IQ amplitude imbalance. Signal analyzers on 5G NR test benches display the constellation diagram in real time to diagnose transmitter impairments during development.

Follow-up: What IQ impairment causes a 16-QAM constellation to appear sheared or non-rectangular?

Q14. What is the Nyquist rate and how does it relate to digital modulation bandwidth?

The Nyquist rate is the minimum bandwidth required to transmit symbols at rate Rs without ISI: BW_min = Rs/2 Hz (double sideband), achieved only with the ideal (sinc) Nyquist filter. A 10 Mbps BPSK signal has Rs = 10 Msymbols/s and requires a minimum bandwidth of 5 MHz, while 10 Mbps with 16-QAM (4 bits/symbol) requires Rs = 2.5 Msymbols/s and only 1.25 MHz minimum bandwidth. In practice, raised-cosine filters with rolloff factor α are used instead of ideal sinc filters, occupying BW = Rs(1+α)/2, where α = 0.25–0.35 is typical in cellular systems.

Follow-up: What is the raised-cosine filter and why is it preferred over the ideal Nyquist (sinc) filter?

Q15. What is PAPR (Peak-to-Average Power Ratio) and why is it a problem in OFDM?

PAPR is the ratio of the peak instantaneous power to the average power of a signal, and OFDM has high PAPR (theoretically up to N for N subcarriers) because all subcarriers can add constructively to create brief but large amplitude peaks. An 802.11n Wi-Fi OFDM signal with 64 subcarriers has a worst-case PAPR of about 18 dB, meaning the power amplifier must be backed off to accommodate peaks without clipping, dramatically reducing efficiency — a typical Wi-Fi PA operates at only 20–30% efficiency because of PAPR constraints. PAPR reduction techniques like clipping and filtering, SeLected Mapping (SLM), and tone reservation are used in 5G NR to allow higher average output power from the same PA.

Follow-up: How does clipping-and-filtering for PAPR reduction affect the BER and spectral regrowth of an OFDM signal?