Frequency Hopping Spread Spectrum

Frequency Hopping Spread Spectrum (FHSS) is a spread spectrum technique in which the carrier frequency changes in a pseudorandom pattern at regular intervals, hopping across a wide set of sub-bands. Unlike DSSS which spreads continuously in frequency, FHSS spreads statistically over time. FHSS is used in Bluetooth, military radios, and certain military satellite links because it provides strong anti-jam and anti-intercept protection without requiring a very high chip rate.

Core Concept Explanation

In FHSS, the total available spread bandwidth W is divided into N non-overlapping sub-bands, each of bandwidth approximately equal to the instantaneous signal bandwidth. At each hop period Th, the PN code generator produces a new code word that drives a frequency synthesizer to select one of the N sub-bands as the carrier for that hop. The data modulation (typically FSK) is applied within each sub-band independently. Because the carrier moves pseudorandomly, a narrowband jammer targeting one frequency can disrupt at most a few hops before the signal has moved elsewhere.

The distinction between **slow FHSS** and **fast FHSS** is fundamental. In slow FHSS, the hop rate Rh is lower than the data rate Rb — multiple data bits are transmitted on each frequency before hopping. In fast FHSS, the hop rate exceeds the data rate — the carrier hops multiple times within a single bit duration. Fast FHSS provides significantly better anti-jam performance because a jammer must follow the hop pattern in real time, which is practically infeasible without knowing the PN code.

The **processing gain of FHSS** is defined as the ratio of the total spread bandwidth W to the instantaneous signal bandwidth Binst. If there are N hop slots, PG equals N. This is different from DSSS where PG is the chip-to-bit rate ratio. A wider spread bandwidth with more hop frequencies gives a higher processing gain and better jam resistance.

Mathematical Expression

Let the total spread bandwidth be W Hz divided into N equal sub-bands each of width Binst = W/N. The hop period is Th seconds. For slow FHSS, Th is greater than the bit period Tb, meaning Rh is less than Rb. For fast FHSS, Th is less than Tb. The processing gain equals W divided by Binst, which equals N. The probability that a follower jammer successfully hits a given hop is 1/N in the absence of dwell time information, making jamming effectiveness inversely proportional to N.

In Bluetooth, the system hops across 79 channels each 1 MHz wide in the 2.4 GHz ISM band, giving N = 79 and a hop rate of 1600 hops per second (hop period of 625 microseconds). Each hop uses frequency shift keying. The rapid hopping across 79 channels gives effective coexistence with other ISM band devices and robustness against narrowband interference from Wi-Fi or microwave ovens.

Given:
Total spread bandwidth W = 79 MHz
Number of hop channels N = 79
Instantaneous channel bandwidth Binst = 1 MHz
Hop rate Rh = 1600 hops/sec
Data rate Rb = 1 Mbps (Bluetooth 1.0 basic rate)

Why this formula applies:
FHSS processing gain = total BW / instantaneous BW = N.
Hopping classification: compare Rh with Rb.

Formula:
PG = W / Binst = N
Hop period Th = 1 / Rh
Slow FHSS if Rh < Rb; Fast FHSS if Rh > Rb

Substitution:
PG = 79 MHz / 1 MHz = 79
Th = 1 / 1600 = 625 µs
Rb = 1 Mbps → Tb = 1 µs
Rh = 1600 hops/sec, Rb = 1,000,000 bps → Rh < Rb

Calculation:
PG = 79 (about 19 dB)
Th = 625 µs; Tb = 1 µs
Since Rh (1600) < Rb (1,000,000): Slow FHSS

Final Answer:
Bluetooth uses Slow FHSS with PG = 79 (≈19 dB); 625 bits transmitted per hop period.

Practical Understanding

Bluetooth uses FHSS specifically to coexist with other 2.4 GHz ISM band devices. Since Wi-Fi occupies only a few fixed channels within the same band, the Bluetooth hop pattern ensures that only a small fraction of hops land on a busy Wi-Fi channel, and frequency error correction coding recovers from these occasional collisions. This design avoids the need for coordination between unrelated devices sharing the ISM band.

Military frequency hopping radios may hop thousands of times per second. The PN hop sequence must be shared between the transmitter and all intended receivers through a secure key management system. A follower jammer, which listens to detect the current frequency and then jams it, faces the limitation that the signal has already hopped before the jam signal arrives — particularly in fast FHSS. This inherent time delay makes fast FHSS highly resistant to follower jamming.

Exam Tip: For FHSS problems, PG = N (number of hop channels) = W/Binst, not Rc/Rb. Slow FHSS has Rh < Rb (multiple bits per hop). Fast FHSS has Rh > Rb (multiple hops per bit). Bluetooth is slow FHSS — this specific fact appears in objective questions.

Mechanism: Follower Jamming and Fast Hopping Defense

• FHSS divides total bandwidth W into N sub-bands. PN code selects one sub-band per hop period Th.
• Slow FHSS: Rh less than Rb. Multiple bits per hop. More vulnerable to partial-band and follower jamming.
• Fast FHSS: Rh greater than Rb. Multiple hops per bit. Signal hops away before jammer can respond.
• Processing gain PG = N = W/Binst. Unlike DSSS, PG is not Rc/Rb.
• Bluetooth: 79 channels, 1600 hops/sec, slow FHSS. Provides ISM band coexistence, not maximum anti-jam.

Quick Revision

• FHSS hops carrier pseudorandomly across N sub-bands. PG = N = W/Binst.
• Slow FHSS: Rh < Rb (more bits per hop). Fast FHSS: Rh > Rb (more hops per bit).
• Fast FHSS resists follower jamming; slow FHSS is simpler and sufficient for coexistence applications.
• Bluetooth: slow FHSS, 79 channels, 1600 hops/sec, 625 µs hop period, 1 Mbps data rate.
• FHSS PG formula is different from DSSS: PG = N, not Rc/Rb.
• Follower jammer is defeated by fast FHSS because hop period is shorter than jammer detect-retune-transmit cycle.
• Trap: FHSS does not use chip rate — it uses hop rate. Do not apply DSSS formulas to FHSS processing gain questions.