Frequency Hopping Spread Spectrum


The use of a PN sequence to modulate a phase shift keyed signal allows immediate spreading of the transmission bandwidth in Direct sequence spread spectrum systems (DS-SS). A different technique that can be used is the frequency hopping spread spectrum (FH-SS) system. The transmitted signal's spectrum is spread sequentially in FH-SS by randomly hopping the data modulated carrier from one frequency to the next.

Thus, a Frequency-hopped Spread Spectrum (FH-SS) system is a type of spread spectrum in which the carrier hops from one frequency to another at random.

Basic Principle

The available channel bandwidth in an FH-SS communication system is split into a large number of contiguous frequency slots. The transmitted signal occupies one or more of the available frequency slots at each signalling period. The frequency slots in each signalling interval are chosen pseudorandomly from a PN generator's output. Figure 1 shows a specific FH pattern in the time-frequency plane.

Figure 1: Example of a Frequency - Hopped (FH) Pattern

Reason for employing M-ary FSK modulation

M-ary frequency shift keying is a popular modulation scheme for FH systems (MFSK). The combination is simply referred to as FH/MFSK. Although PSK modulation performs better than FSK in the AWGN channel, maintaining phase coherence in 

 Although PSK modulation performs better than FSK in the AWGN channel, maintaining phase coherence in

(i) The synthesis of frequencies employed in the hopping pattern 

(ii) the signal's propagation through the channel as it hops from one frequency to another over a large bandwidth.

With FH spread spectrum transmissions, FSK modulation with non-coherent detection is typically used.

Types of Frequency hopping

We consider the rate at which the hops occur since frequency hopping does not cover the complete spread spectrum instantaneously. Frequency-hopping may be broadly classified into two types (both of which are technology-independent). They are namely:

1) Slow-frequency hopping

2) Fast-frequency hopping

Slow-frequency hopping:

We have a slow-hopped signal in the FH system if the hopping is performed at the symbol rate. As a result, with slow-frequency hopping, the MFSK signal's symbol rate Rs is an integer multiple of the hop rate Rh, implying that various symbols are transmitted per each frequency hop.

Frequency hopping example:

An example of frequency hopping is shown in Figure 2.

Figure 2: Example of Frequency Hopping

• The input binary sequence data rate is: Rb=150bits/s

• The modulation is 8-ary FSK.

• Then the symbol rate is Rs=๐‘…๐‘/๐‘˜ = 150/log28 = 50 bits/s

• The symbol interval is Ts = 1/๐‘…๐‘  = 1/50 = 20ms

• The frequency is hopped once per symbol. Thus the hopping rate is given as Rh=50hops/s.

• The abscissa (x-axis) of the figure's time-bandwidth plane represents time, while the ordinate (y-axis) denotes hopping bandwidth.

• There is an 8-ary FSK symbol-to-tone mapping available. The data band's non-fixed centre frequency is designated as f0.

• The tone separation is ฮ”f = 1/๐‘‡๐‘  =1/20๐‘š๐‘ = 50Hz.

• At the top, there is a normal binary data sequence. The bits are grouped three at a time to generate symbols since the modulation is 8-ary FSK.

• According to symbol-to-tone assignment, a single-sideband tone (offset from f0) would be transmitted.

• f0 hops to a new position in the hopping bandwidth for each new symbol. f0+25Hz assignment is done for the first symbol in the data sequence 011. f0 is shown with a dashed line and the symbol tone f0+25Hz is shown with a solid line in the figure.

• Likewise, f0 - 125Hz assignment is done for the second symbol 110. For the third symbol 001, f0 + 125Hz assignment is done. The centre frequency f0 hops to a new position for each symbol.

Frequency hopping with diversity:

Robustness is the capacity of a sent signal to withstand channel impairments such as noise, jamming, fading, and so on in communication. A signal containing many duplicate copies, each delivered on a different frequency, has a better chance of surviving than a single signal of the same type.

Multiple broadcasts of the same signal at various frequencies that are spaced apart in time are referred to as diversity. The higher the signal's variety, the more resistant it is to random interference.

We may extend the frequency hopping example illustrated in Figure 2 to show the beneficial effect of diversity. A chip repeat factor of N=4 is used to introduce frequency hopping diversity. The effect of diversity is seen in Figure 3.

Figure 3: Frequency hopping with diversity (N =4)

• There are now four columns for each 20ms symbol interval, corresponding to the four distinct chips to be transmitted for each symbol.

• Each symbol is now transmitted four times. The centre frequency f0 is hopped to a new part of the hopping band for each transmission.

• The chip interval is Tc = ๐‘‡๐‘ /๐‘ = 20๐‘š๐‘ /4 = 5ms.

• The hopping rate is Rh= ๐‘…๐‘/log28 . N = 150 x 4/3 = 200 hops/s.

• To obtain orthogonality, the spacing between frequency tones must also change. Hence the tone separation is ฮ”f = 1/๐‘‡๐‘  .N =4/20๐‘š๐‘ = 200Hz.

• Thus, the resulting transmissions provide a more robust signal than those that do not have such diversity.

Fast-frequency hopping:

If there are multiple hops per symbol in the FH system, we have a fast-hopped signal. As a result, the hop rate Rh in fast-frequency hopping is an integer multiple of the MFSK symbol rate. During the transmission of a single symbol, the carrier frequency will vary or hop numerous times. Thus, each hop in a fast FH-MFSK system is a chip.

Advantages of the FH-SS system:

1. The PG ( processing gain) is higher than the DS-SS system's processing gain.

2. The distance between two points does not affect synchronisation.

3. The acquisition time for a serial search system using FH-SS is reduced.

Disadvantages of the FH-SS system:

1. The FH-SS system's bandwidth is high (in GHz).

2. Digital frequency synthesisers, which are complex and expensive, are required.

Applications of FHSS system:

1) For mobile communication, CDMA systems based on FH spread spectrum signals are particularly attractive.

2) The Wi-Fi standard for wireless local area networks (WLAN).

3) The Bluetooth WPAN (Wireless Personal Area Network) standard

Fast hopping Versus Slow hopping:

The table compares the performance of fast hopping and slow hopping systems.

SI No.

Slow frequency hopping

Fast frequency hopping


For each frequency hop, more than one symbol is transmitted.

To transmit one symbol, multiple frequency hops are needed.


Chip rate and symbol rate are equal.

The chip rate is greater than the symbol rate.


The symbol rate is larger than the hop rate.


Hop rate is bigger than Symbol rate.



One or more symbols are transmitted using the same carrier frequency.

In different hops, one symbol is transmitted over multiple carriers


If the carrier frequency in one hop is known, a jammer can detect this signal.

Since one symbol is transmitted using multiple carrier frequencies, a jammer will be unable to detect it.

The following two examples can be used to compare slow and fast hopping performance:

1) Figure 4 shows the chip as part of an FH-MFSK system.


Figure 4: Chip in the context of an FM-MFSK System

• A fast frequency hopping example is shown in Figure 4 (a). The data symbol rate is 30 symbols per second, and frequency hopping is 60 hops per second. The waveform s(t) over one symbol time (1/30s) is shown in the figure. A new frequency hop is responsible for the waveform shift in (the middle of) s(t).

• A slow frequency hopping example is shown in Figure 4 (b). Although the data symbol rate remains at 30 symbols per second, the frequency hopping rate has been lowered to 10 hops per second. The waveform s(t) is shown across three symbols (1/10s).

2) The comparison for a binary FSK system is shown in Figure 5.

• For a binary FSK system, Figure (a) shows an example of rapid frequency hopping. N=4 is the diversity. Per bit, four chips are transmitted. The hop duration is the chip duration.

Figure 5: Comparison for a binary FSK system

• Figure (b) shows an example of a binary FSK system of slow frequency hopping. In this case, three bits are transferred throughout the time of a single hop. In this case, the bit duration is the chip duration.

Sreejith Hrishikesan

Sreejith Hrishikesan is a ME post graduate and has been worked as an Assistant Professor in Electronics Department in KMP College of Engineering, Ernakulam. For Assignments and Projects, Whatsapp on 8289838099.

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