# Reading — EP for Communications

By the end of this lesson you should be able to:

1. Explain why a **narrowband link** is easy to find, intercept, and jam.
2. Describe **DSSS** and **FHSS** as two routes to a spread-spectrum signal.
3. Compute **processing gain** and relate it to a survivable J/S and to bit-error rate.
4. Explain how a signal can ride **below the noise floor**, and why that is **LPD**.

## A link is a target too

EP in L15 protected the **radar**: emit less, spread the waveform, hop the carrier, and police the side-lobes. Those same instincts protect the other thing the fight depends on — our **links**. A datalink only helps if the message actually arrives, and a plain **narrowband** signal makes stopping it trivial.

The problem is concentration. All of a narrowband signal's energy sits in one small slice of spectrum, which makes it **easy to find** — a wideband receiver sees a tall spike at a known frequency and immediately has something to intercept. It is also **easy to deny**: a jammer aims its entire output at that one band and overwhelms the receiver. The energy is parked in one place, so both the eavesdropper and the jammer know exactly where to point.

The intuitive fix — **encryption** — does not solve this. Encryption hides the *content* of the message; it does nothing to the *signal* that carries it. The spike is still there, still narrow, still tall. The enemy cannot read your traffic, but they can still drown it out, and a denied channel carries no traffic at all to read.

:::{admonition} Key Concept
:class: key-concept

Encryption protects the **message**; it does nothing for the **signal**. You can encrypt every bit you send and still be silenced — a jammer denies the *channel*, not the plaintext. Surviving a jammer is a problem about the signal's shape in the spectrum, not about what the bits mean.
:::

## Spread spectrum: smear it into noise

The way out is to stop concentrating the energy. **Spread spectrum** takes the signal and **smears** it across a band far wider than the data actually needs, using a code that both ends share — a "key" that drives the spreading.

Three things follow. The code spreads the energy until the signal looks like **noise** — a low, flat hump instead of a spike. Because no single slice of spectrum now carries much power, the signal is **hard to find** and **hard to jam**: there is no tall feature to lock onto, and a jammer's power, spread across a band it must cover, is diluted. And critically, only a receiver holding the **same code** can pull the signal back together. To everyone else it stays buried in the noise.

There are two ways to do the smearing: spread in **code** (direct-sequence, DSSS) or spread in **frequency** (frequency-hopping, FHSS). They look different on a spectrum analyzer but buy the same thing.

## Processing gain, quantitatively

The payoff of spreading is captured by one number — the **processing gain**, $G_p$. It is the ratio of the spread bandwidth to the data bandwidth, expressed in dB:

$$
G_p = 10\log_{10}\frac{B_{\text{spread}}}{B_{\text{data}}} = 10\log_{10} N_{\text{chips}},
$$

where $N_{\text{chips}}$ is the number of code **chips per data bit** (each chip is one symbol of the fast spreading code). Spreading the bandwidth by a factor of $N$ uses $N$ chips per bit and yields $10\log_{10} N$ dB of gain. Typical systems run **10–60 dB**.

The numbers are blunt. A code at $1000$ chips per bit gives

$$
G_p = 10\log_{10}(1000) = 30 \text{ dB},
$$

while a modest $64$-chip code gives $10\log_{10}(64) \approx 18$ dB. Every factor-of-ten in chip rate is another 10 dB.

Why the gain helps is the heart of the lesson. At the receiver, multiplying by the **same** code that spread the signal **despreads** it. The wanted signal's chips line up and add coherently, so it **collapses back to narrowband** — concentrated again, tall again. The **jammer**, which is *uncorrelated* with the code, experiences that same multiplication as a *spreading* operation: it gets smeared across the full spread band. Despreading therefore does two things at once — it **concentrates the signal** and **spreads the jammer**:

- **Before despreading:** the signal is a wide, low hump; the jammer is a tall narrowband spike sitting well above it.
- **After despreading:** the signal is a tall narrowband spike; the jammer is a wide, low hump.

That reversal is exactly $G_p$ worth of relief. The jammer-to-signal ratio that matters after the receiver is roughly the input J/S *minus* the processing gain:

$$
(\text{J/S})_{\text{after}} \approx (\text{J/S})_{\text{in}} - G_p.
$$

So the link survives even when the jammer is **louder than the signal** at the antenna — when J/S is *positive* — as long as $G_p$ exceeds that deficit with margin to spare. With $G_p = 30$ dB against a jammer $20$ dB above the signal, the post-despread margin is about $30 - 20 = 10$ dB, comfortably positive: the link closes. The jammer never loses a single watt; the code wins anyway.

That surviving margin is what sets **bit-error rate (BER)**. BER is governed by the energy-per-bit to noise-density ratio $E_b/N_0$ *after* despreading, and despreading raises the effective $E_b/N_0$ by the processing gain. Drive the post-despread margin positive and the BER collapses — bits that were lost in the jammer come through clean. In the type-along demo, a jammer set **12 dB above** the signal kills a narrowband link outright; spreading the same bits with a $64$-chip code ($\approx 18$ dB of gain) and despreading drops the BER back to near zero.

## DSSS: direct sequence

**DSSS** spreads in code. Each data bit is multiplied by a fast **pseudo-noise (PN)** chip sequence — a code that looks random but is exactly reproducible at the far end.

- $N$ chips per bit spreads the bandwidth by $N$ and, by the formula above, sets the processing gain.
- The receiver multiplies the incoming waveform by the **same** PN code and integrates over each bit.
- The signal's chips line up and add; the jammer, having no correlation with the code, is spread out instead.

Same code at both ends, and the signal re-collapses while the jammer smears — which is precisely the before/after picture of processing gain.

## FHSS: frequency hopping

**FHSS** spreads in frequency. Instead of spreading energy at every instant, the carrier **hops** across many channels on a code-driven schedule.

- Transmitter and receiver hop together, so the link is continuous; an eavesdropper sees only disconnected fragments.
- A **spot jammer** cannot follow a fast hopper — it is the same lose-lose we built for the radar in L15. To touch every channel a jammer must spread its power across the whole hop set (a **partial-band** or **barrage** attack), diluting itself exactly as in the DSSS case.
- The spreading is over **time and frequency** rather than code, but the payoff is the same J/S relief.

This is where L15 connects directly: the radar's **frequency agility** was the radar-side preview of this very idea — a signal that refuses to sit still in the spectrum. FHSS is that idea pushed onto our links. DSSS and FHSS are two routes to one goal: a **moving, noise-like signal**.

## Below the noise floor — LPD

With enough processing gain, a spread signal can live not just *quietly* but **below the noise floor** entirely.

The canonical example is **GPS**: the signal arrives at the antenna *below* the thermal noise, and only correlation with the known code digs it back out. The consequence is a defensive property in its own right — if the threat cannot *find* a signal at all, it cannot intercept it and cannot jam it effectively, because it does not know where or when to put its power. This is **low probability of detection (LPD)** — the communications cousin of the **LPI** radar from L15. The slogan is the same on both sides: *you cannot jam what you cannot find.*

::::{admonition} Quick Exercise
:class: quick-exercise

A protected B-21 datalink uses DSSS. Reason about each:

1. The code runs 1000 chips per bit. What is the processing gain in dB?
2. A jammer sits 20 dB above your signal. With that gain, can the link close?
3. The enemy cannot even detect your transmission. Which EP property is that?
4. Why does encrypting the message not, by itself, defeat a jammer?

:::{admonition} Solution
:class: dropdown

1. $G_p = 10\log_{10}(1000) = 30$ dB.
2. Yes. The post-despread margin is roughly $G_p - \text{J/S} = 30 - 20 = 10$ dB — positive, with room left for the required $E_b/N_0$, so the link closes.
3. **Low probability of detection (LPD)** — the signal sits below the noise floor, so the threat never finds it.
4. Encryption hides the message *content*, not the signal's *presence* or *power*. A jammer denies the channel regardless of what is encoded — a silenced link carries no traffic at all.
:::

::::

## Wrap-Up

A narrowband link concentrates its energy in one place, which makes it easy to find and easy to jam — and encryption does not help, because it protects the message, not the signal. Spread spectrum smears the energy into a wide, noise-like band, and **processing gain** $= 10\log_{10} N_{\text{chips}}$ measures the payoff: despreading concentrates the wanted signal while spreading the jammer, so the link survives a *positive* J/S whenever $G_p$ exceeds the deficit, and the surviving margin drives the BER down. **DSSS** spreads in code, **FHSS** in frequency — the radar-side preview of which was L15's frequency agility — and with enough gain either can hide a signal below the noise floor, the essence of **LPD**. That closes EP. Next, **L17 — Electromagnetic Attack** turns to the offense: the jamming taxonomy, the J/S ratio in full, and **burn-through range**.