6.1 Lab 5: theory

Frequency shift keying

Frequency Shift Keying ( FSK ) is a scheme to transmit digital information across an analogchannel. Binary data bits are grouped into blocks of a fixed size, and each block is represented by a unique carrierfrequency, called a symbol , to be sent across the channel.

The carrier frequency is kept constant over some number of samples known as the symbol period( $T_{\mathrm{symb}}$ ). The symbol rate, defined as $F_{\mathrm{symb}}$ , is a fraction of the board's sampling rate, $F_s$ . For our sampling rate of 44.1 kHz and a symbol period of 32, the symbol rate is 44.1k/32 symbols per second.

Pseudo-noise sequence generator

The input bits to the transmitter are provided by the special shift-register, called a pseudo-noise sequence generator ( PN generator ), on the left side of . A PN generator produces a sequence of bits that appears random. The PN sequence will repeat withperiod $2^B-1$ , where $B$ is the width in bits of the shift register. A more detailed diagram of the PN generator alone appears in .

As shown in , the PN generator is simply a shift-register and XOR gate. Bits 14 and 15 of theshift-register are XORed together and the result is shifted into the lowest bit of the register. This lowest bit isthe output of the PN generator.

The PN generator is a useful source of random data bits for system testing. We can simulate the bit sequence that wouldbe transmitted by a user as the random bits generated by the PN generator. Since communication systems tend to randomizethe bits seen by the transmission scheme so that bandwidth can be efficiently utilized, the PN generator is a good datamodel.

Series-to-parallel conversion

The shift-register produces one output bit at a time. Because each symbol the system transmits will encode two bits, werequire the series-to-parallel conversion to group the output bits from the shift-register into blocks of two bits so thatthey can be mapped to a symbol.

Frequency look-up table

This is responsible for mapping blocks of bits to one of four frequencies as shown in . Each possible two-bit block of data from the series-to-parallel conversionis mapped to a different carrier frequency ${}_i$

One way to implement this mapping is by using a look-up table. The two-bit data block can be interpreted as an offsetinto a frequency table where we have stored the possible transmission frequencies. Note that since each frequencymapping defines a symbol, this mapping is done at the symbol rate $F_{\mathrm{symb}}$ , or once for every $T_{\mathrm{symb}}$ DSP samples.

The symbol bit assignments are such that any two adjacent frequencies map to data blocks that differ by only one bit.This assignment is called Gray coding and helps reduce the number of bit errors made in the event of areceived symbol error.

Phase continuity

In order to minimize the bandwidth used by the transmitted signal, you should ensure that the phase of your transmittedwaveform is continuous between symbols; i.e., the beginning phase of any symbol must be equal to the ending phase of theprevious symbol. For instance, if a symbol of frequency $\frac{9\pi }{32}$ begins at phase 0, the symbol will end 31 output samples later at phase $31\frac{9\pi }{32}$ . To preserve phase continuity, the next output sample must be at phase $32\frac{9\pi }{32}$ , which is equivalent to phase $\pi$ . Therefore, the next symbol, whatever its frequency, must begin at phase $\pi$ . For each symbol, you must choose ${}_i$ in the expression $\sin ({}_{i}n+{}_i)$ to create this continuity.