Demo — Frequency Agility

Demo — Frequency Agility#

A spot jammer is only powerful if it can find the radar’s channel. Frequency agility forces the jammer into a losing choice: a strong spot that the radar simply hops around, or a barrage spread so thin it barely registers. This demo makes that trade quantitative.

The trade#

A jammer that covers \(W\) of \(N\) channels denies a fixed radar only if it happens to sit on the radar’s channel. Against an agile radar it lands a hit with probability \(W/N\). If it instead barrages all \(N\) channels, its power per channel drops by \(10\log_{10}N\) dB.

Coverage is only half the story, though: a jammer denies a channel only if it can still hold it. The jammer’s total power is fixed, so spreading it over \(W\) channels leaves \(J/S_0 - 10\log_{10}W\) in each one, and the radar burns through anything the link budget cannot sustain. Denial is gated, not graded:

\[ \text{denied fraction} = \underbrace{\bigl(J/S \ge J/S_{\max}\bigr)}_{\text{can the jammer hold a channel?}} \cdot \underbrace{\frac{W}{N}}_{\text{how often is the radar in one?}} \]

The demo carries \(J/S_0 = 28\) dB — everything in one channel — and puts \(J/S_{\max}\), the burn-through ceiling, on a slider so you can move the cliff and watch where it lands.

Interactive demo#

Open in full screen

Walkthrough#

  1. Fixed radar, narrow jammer. The demo loads with \(N = 20\) channels, a width-\(W = 4\) jammer over channels #6–#9, and the fixed radar parked on channel #2 — clear of the block, so nothing is denied. Click a channel inside the red block to park the radar there and denial jumps to 100% — a fixed radar lives or dies on one frequency.

  2. Switch to agile. Now the radar hops across all \(N\) channels. The denied fraction drops to \(W/N\) — the jammer only catches the pulses that happen to land under it.

  3. Widen the jammer. Take \(W\) from 4 up to 10 and the agile denial rises with it — but the jammer is spending power to cover more spectrum, and the per-channel J/S card counts down as it does: 22.0 dB at \(W = 4\), 19.0 dB at \(W = 8\).

  4. Walk \(W\) across the cliff. Leave the burn-through ceiling at its default 18 dB. At \(W = 10\) the card reads exactly 18.0 dB, still green, still denied — agile denial peaks at 50%, the best the jammer ever does. Click one more channel. At \(W = 11\) the card falls to 17.6 dB, turns grey and reads burned through; the jammed block in the channel map fades to a dashed outline, and P(denied) drops from 50.0% to 0.0% in a single step. Press Next pulse or Auto-hop and the tally confirms it: the radar now flies straight through the block. One extra channel of coverage cost the jammer everything. (The tie at exactly 18.0 dB counts as denied, which is what puts the cliff on the round number.)

  5. Force the barrage. Read the barrage-dilution number, and read it carefully: the readout’s \(10\log_{10}N\) — 13 dB at 20 channels — is the per-channel cost measured against a jammer that had everything in one channel. Coming off this demo’s 4-channel spot the cost is \(10\log_{10}(N/W) = 10\log_{10}(20/4) \approx 7\) dB, the number the type-along and the pre-flight use. Either way it is power the jammer simply gives away.

Key observations#

  • A jammer’s spare J/S in dB is its channel budget. It starts with \(J/S_0 = 28\) dB in one channel and needs to stay at or above the radar’s 18 dB burn-through ceiling, so it has \(28 - 18 = 10\) dB of headroom — and 10 dB is a factor of ten, which buys exactly 10 channels. Drag the burn-through slider and the budget moves with it: a radar that burns through 25 dB of J/S leaves only 3 dB of headroom, and 3 dB buys one channel.

  • Agility converts a power contest into a coverage contest — and coverage is expensive for the jammer.

  • Spot vs barrage is a dilemma, not a choice. Concentrate and be dodged; spread and be diluted.

  • More channels, more leverage. The defender’s advantage grows as \(10\log_{10}N\).

Source#

MATLAB bundle · L15_FrequencyAgility.m↓

The companion script fixes the same numbers the demo loads with — \(N = 20\) channels, a \(W = 4\) spot — and runs a 2000-pulse Monte Carlo hop draw against an 18 dB per-channel burn-through ceiling. It prints three outcomes side by side: the fixed radar parked on and fully denied, the agile radar losing only the pulses that land under the spot, and the same jammer diluted to barrage until the radar burns through everywhere.

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