E2 · Published 6 October 2026 · By The Ham Desk

Digital Modulation, Coding and Spread Spectrum

This is the theory behind every weak-signal mode on the bands. It explains how bits become symbols, why a constellation with more points carries more data and needs a better signal, and how coding and spreading let a signal be recovered from below the noise.

Band none
Study time 19
Level Stretch
questions 10

Waveform and antenna diagram for Signal Processing and Digital Communications — Signal Processing and Digital Communications — waveform overlay and radiation pattern

Pre-flight briefing

Turning bits into symbols

A digital modulation scheme maps groups of bits onto distinct states of a carrier. In binary phase shift keying there are two states, 180 degrees apart, carrying one bit each. Quadrature phase shift keying uses four states and carries two bits per symbol; 16-QAM uses sixteen amplitude and phase combinations for four bits; 64-QAM carries six. Doubling the number of points doubles the data rate in the same bandwidth, but it also halves the distance between neighbouring points, so the same amount of noise is more likely to push a received symbol across a boundary into the wrong decision.

That trade is visible on a constellation diagram, which plots each received symbol's amplitude and phase as a point on a two-dimensional grid. Noise appears as a fuzzy cloud around each ideal point; the ratio of the distance between points to the size of that cloud decides the error rate. It is why a marginal HF path uses a robust scheme with few points and a good path can use many.

The efficiency of any scheme is bounded from above by the Shannon limit, which relates the error-free capacity of a channel to its bandwidth and signal-to-noise ratio. It says that capacity grows only linearly with bandwidth but logarithmically with signal-to-noise ratio - so beyond a point, more power buys much less than more spectrum does. This is the theoretical reason the higher bands, with their wider channels, are attractive for data.

Coding: paying redundancy to buy reliability

Forward error correction adds redundant bits to the data so that the receiver can detect and repair errors without asking for a retransmission. Convolutional coding with Viterbi decoding suits streams of bits corrupted by random noise; Reed-Solomon coding handles bursts of errors and is standard in satellite and storage applications. The improvement over an uncoded system at the same error rate is the coding gain, typically several decibels.

Interleaving complements coding. A deep fade or an impulse wipes out a continuous run of bits, and most codes handle scattered errors far better than clustered ones, so the transmitter shuffles the bit order and the receiver restores it - turning one long burst into many short, correctable ones. The cost is latency, because the interleaver must fill before it can empty.

Automatic repeat request takes the opposite approach: it detects an error and asks for the frame again. ARQ needs a return path and its throughput falls as the channel worsens, which is why weak-signal modes on HF generally use forward error correction instead.

Spread spectrum

Spread spectrum deliberately occupies far more bandwidth than the data requires, and in exchange gains resistance to interference and the ability to share a band. In direct sequence spread spectrum the data is multiplied by a fast pseudo-random code, so the transmitted energy is spread thinly across a wide band; the receiver multiplies by the same code and collapses the wanted signal back into its original narrow band while any narrowband interferer is spread out and diluted. The ratio of the spread bandwidth to the data bandwidth is the processing gain, and it is the number of decibels by which the system can tolerate an interferer stronger than the signal.

Frequency hopping spread spectrum takes the other route: the carrier jumps among many frequencies according to a pseudo-random sequence, so an interferer occupying any single frequency only affects the fraction of time the hop lands there. The two techniques are often combined. Because both depend on the receiver knowing the code or the hop sequence, they are also a form of selective access rather than encryption.

Orthogonal frequency division multiplexing is a different idea that also uses a wide band: instead of one high-rate carrier, it transmits many low-rate subcarriers simultaneously, each narrow enough that a frequency-selective fade affects only some of them. A guard interval absorbs the echoes of multipath so the subcarriers remain orthogonal, which is why OFDM is the standard for terrestrial digital broadcasting and for high-speed data over difficult paths.

Terms you must be able to define
Term	What the examiner wants to hear
Constellation diagram	A plot of a digital signal's amplitude and phase states, with noise visible as a cloud around each point.
Forward error correction	Adding redundant bits so the receiver can correct errors without a retransmission.
Interleaving	Shuffling bit order so that burst errors are spread out into correctable single errors.
Processing gain	The ratio of spread bandwidth to data bandwidth, expressed in dB of interference tolerance.
OFDM	Orthogonal frequency division multiplexing: many narrow, closely spaced subcarriers transmitted together.

Question deck 10 questions

E2B01 Core

What does a constellation diagram display?

E2B02 Core

How many bits does each symbol of a 16-QAM signal carry?

E2B03 Core

What is the principal advantage of QPSK over BPSK?

E2B04 Core

What does forward error correction do?

E2B05 Stretch

Why is interleaving used together with error correction coding?

E2B06 Core

How does direct sequence spread spectrum make a signal resistant to interference?

E2B07 Stretch

What is processing gain in a spread spectrum system?

E2B08 Stretch

What is the essential idea of orthogonal frequency division multiplexing?

E2B09 Stretch

According to the Shannon relationship, how does channel capacity grow with bandwidth compared with signal-to-noise ratio?

E2B10 Stretch

Why does a modern digital mode often include a synchronisation sequence at the start of each transmission?

Reference sheet

The explanations for all ten questions sit on this sheet. Pick an answer on the left and the matching card lights up.

E2B01 Explanation 1

Key C — The amplitude and phase states used by a digital modulation scheme

Each point on the diagram is one symbol state, so the number of points tells you how many bits per symbol the scheme carries and their spacing tells you how much noise it can tolerate. Noise on a real signal appears as a cloud around each ideal point.

Rule Fundamentals - digital modulation

E2B02 Explanation 2

Key B — Four

Sixteen states correspond to four bits, because 2 to the fourth power is 16. QPSK's four states carry two bits and 64-QAM's sixty-four states carry six, so the bit rate in a given bandwidth rises with the number of constellation points.

Rule Fundamentals - QAM

E2B03 Explanation 3

Key A — It carries twice the data in the same bandwidth

Four states carry two bits per symbol instead of one, so the data rate doubles within the same occupied bandwidth. The cost is that the states are closer together, so a slightly better signal-to-noise ratio is needed to keep the same error rate.

Rule Fundamentals - PSK

E2B04 Explanation 4

Key D — It adds redundant bits so the receiver can correct errors without a retransmission

FEC spends bandwidth and processing to buy reliability, which is the right trade on a one-way or high-latency path where a retransmission would be impractical. The improvement over an uncoded link at the same error rate is the coding gain.

Rule Fundamentals - error correction

E2B05 Explanation 5

Key C — It spreads burst errors across time so the decoder sees many short errors instead of one uncorrectable run

Almost all coding schemes correct scattered errors far better than clustered ones, and a deep fading notch or an impulse wipes out a continuous run of bits. Interleaving scatters that run across the transmission and the receiver re-assembles it, at the cost of latency while the interleaver fills.

Rule Fundamentals - interleaving

E2B06 Explanation 6

Key B — The data is multiplied by a fast pseudo-random code, and the receiver's matching code collapses the wanted signal while spreading the interferer

Multiplying by the code spreads the wanted signal's energy across a wide band, and the receiver multiplying by the same code reverses the process. The interfering signal, which does not match the code, is spread wider still and most of its energy falls outside the receiver's narrow output filter.

Rule 47 CFR §97.311 - spread spectrum emissions

E2B07 Explanation 7

Key A — The ratio of the spread bandwidth to the data bandwidth, expressed in decibels of interference tolerance

A signal spread over 1 MHz carrying 1 kHz of data has a processing gain of 1,000, or 30 dB, which is the margin by which it can be received in the presence of an interferer 30 dB stronger than the signal. More spreading means more immunity, and more spectrum consumed.

Rule Fundamentals - processing gain

E2B08 Explanation 8

Key D — Many narrow subcarriers are transmitted together, each slow enough that a frequency-selective fade affects only some of them

Splitting a high-rate stream into many low-rate subcarriers turns a wideband channel with deep frequency-selective fades into a set of narrow channels, each of which is nearly flat. A guard interval absorbs multipath echoes so orthogonality is preserved.

Rule Fundamentals - OFDM

E2B09 Explanation 9

Key C — Linearly with bandwidth, but only logarithmically with signal-to-noise ratio

The capacity formula is bandwidth times the logarithm of one plus the signal-to-noise ratio, so doubling the bandwidth doubles capacity while doubling the power adds only a fraction of a bit per hertz. That is the fundamental reason wide channels are worth more than brute force power.

Rule Fundamentals - channel capacity

E2B10 Explanation 10

Key C — So the receiver can establish symbol timing, frequency alignment and phase before decoding the data

A digital demodulator must know where each symbol begins, what frequency offset the path has introduced and what the carrier phase is before it can make decisions. Weak-signal modes begin with a known pattern precisely so those three can be estimated, which is why an FT8 signal is only decodable if its start is captured.

Rule Fundamentals - digital synchronisation

How to use this unit

Work the ten questions in one sitting with the reference sheet covered, then uncover it and read every explanation - including the ones you got right. The wording of the real exam is different, so learn the reasoning rather than the answer letters.