**Slow Frequency Hopping Block Diagram**

**Slow-frequency Hopping:**

We have a slow-hopped signal in the FH system when the hopping is done at the symbol rate. As a result, the symbol rate Rs of the MFSK signal is an integer multiple of the hop rate Rh when using slow-frequency hopping, indicating that many symbols are transmitted on each frequency hop.

**Transmitter:**

The block diagram of a slow-frequency hopping FH-MFSK transmitter is shown in Figure 1.

The incoming binary data is first sent via an M-ary FSK modulator. A Mixer receives the resultant M-ary FSK modulated signal. The Mixer is made up of a multiplier and a bandpass filter (BPF).

**Figure 1: FH-MFSK
Transmitter**

A digital frequency synthesizer provides the other input to the mixing block. A PN code generator controls the frequency synthesizer. As a result, a carrier created by the frequency synthesizer modulates the M-ary FSK modulated signal once again. The sum and difference frequencies are produced by the Mixer in two outputs. Only the sum frequency signal, which is the FH-MFSK signal, is selected by the bandpass filter that follows the mixer. Then the signal is transmitted.

• M symbols can be transmitted using the M-ary FSK system,
where M=2^{K}. The number of bits in the input binary data that make up
one symbol is denoted by k.

• Each of these M symbols will be assigned a different frequency by the M-ary FSK modulator.

• The frequency hop is the output of the synthesizer at a specific point in time.

• The PN generator's output bits vary at random. As a result, the synthesizer's output frequency will fluctuate at random.

• To create the transmitted signal, each frequency hop is combined with the MFSK signal.

• If the number of consecutive bits at the PN generator's
output is n, the total number of frequency hops is 2^{n}.

• The sum of all frequency hops determines the entire bandwidth of the transmitted FH-MFSK signal. As a result, the transmitted FH-MFSK signal has an extremely wide bandwidth, on the order of a few GHz.

**Receiver:**

A block diagram of a slow-frequency hopping FH-MFSK receiver is shown in Figure 2.

**Figure 2: FH-MFSK
Receiver**

• The received signal is sent into the Mixer as an input. The digital frequency synthesizer provides the mixer with the other input.

• A PN code generator powers the frequency synthesizer. The PN code generator at the transmitter is synced with this generator.

• As a result, the frequency hops generated at the synthesizer output will be the same as those produced at the transmitter.

• The sum and difference frequencies are produced by the mixer in two outputs. Only the difference frequency, which is the MFSK signal, is selected by the bandpass filter. As a result, the frequency hopping is eliminated by the mixer.

• After then, the MFSK signal is sent into a non-coherent MFSK detector. For non-coherent MFSK detection, a bank of M non-coherent matching filters is utilized.

Each matching filter corresponds to one of the MFSK signal's tones. By selecting the greatest filter output, an approximation of the original symbol sent may be derived.

• For an FH/MFSK system,

(i) The chip rate, R_{c} = max (R_{h}, R_{s})
------------------- (1)

where Rh is the hop rate and Rs is the symbol rate

(ii) The transmission of several symbols per hop characterizes a slow FH/MFSK system. As a result, in a sluggish FH/MFSK system, each symbol is referred to as a chip.

(iii) We can relate all rates as

Rc = Rs = ๐
_{๐}/๐
≥ R_{h} ----------------- (2)

where k = log_{2}๐

(iv) Processing gain, PG = Bandwidth of Spread signal / Bandwidth of unspread signal

Let f_{s} be the symbol frequency and 2^{n}
be the number of frequency hops

Then, Processing gain, PG = 2๐๐_{๐ }/๐_{๐ }
= 2n -------------- (3)

(v) Probability of error, P_{e} = ½ ๐^{−}^{๐๐}๐
_{๐}/2
---------------- (4)