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Lab 5: Theory

Module by: Douglas L. Jones, Swaroop Appadwedula, Matthew Berry, Mark Haun, Jake Janovetz, Michael Kramer, Dima Moussa, Daniel Sachs, Brian Wade. E-mail the authors

Summary: Quadrature phase shift keying (QPSK) is a method for transmitting digital data across an analog channel. Data bits are grouped into pairs and represented by a unique waveform, called a symbol. Data may be simulated with a pseudo-noise sequence generator.

Introduction

The quadrature phase-shift keying (QPSK) digital transmitter of Figure 1 is one of many DSP systems used in the communications industry. The following sections describe the transmitter in detail.

Quadrature phase shift keying (QPSK)

QPSK is a method for transmitting digital information across an analog channel. Data bits are grouped into pairs, and each pair is represented by a particular waveform, called a symbol, to be sent across the channel after modulating the carrier. (The receiver will demodulate the signal and look at the recovered symbol to determine which pair of bits was sent.) This requires having a unique symbol for each possible combination of data bits in a pair. Because there are four possible combinations of data bits in a pair, QPSK creates four different symbols, one for each pair, by changing the I gain and Q gain for the cosine and sine modulators in Figure 1. To transmit each pair of bits in the source data, the gains are kept constant over a fixed number of output samples known as the symbol period, T symb T symb . The symbol rate, F symb F symb , is a fraction of the board's sample rate, F s F s . For our sample rate of 44.1 kHz and a symbol period of 16, the symbol rate is F symb =4410016 F symb 44100 16 symbols per second.

The QPSK transmitter system uses both the sine and cosine at the carrier frequency to transmit two separate message signals, s I n s I n and s Q n s Q n , referred to as the in-phase and quadrature signals. Provided that a coherent receiver system is employed, both the in-phase and quadrature signals can be recovered exactly, allowing us to transmit twice the amount of signal information at the same carrier frequency as we could with a single oscillator.

Figure 1
QPSK Transmitter
QPSK Transmitter (trans.png)

Pseudo-noise generation

The input bits to the transmitter are provided by a special shift-register, called a pseudo-noise generator (PN generator), in Figure 2. A PN generator produces a sequence of bits that appears random. The PN sequence will repeat with period 2B1 2 B 1 , where B B is the width in bits of the shift register.

As shown in Figure 2, the PN generator is simply a shift-register and XOR gate. Bits 1, 5, 6, and 7 of the shift-register are XORed together and the result is shifted into the highest bit of the register. The lowest bit, which is shifted out, is the output of the PN generator.

The PN generator is a useful source of random data bits for system testing. We can use the output of a PN generator as a "typical" sequence that could be transmitted by a user. The sequence is a good data model because communications systems tend to randomize the bits transmitted for efficient use of bandwidth. PN generators have other applications in communications, notably in the Code Division Multiple Access schemes used by cellular telephones.

Figure 2
Pseudo-Noise Generator
Pseudo-Noise Generator (pn-gen.png)

Series-to-parallel conversion

The PN generator produces one output bit at a time, but each symbol the system transmits will encode two bits. Therefore, we require the series-to-parallel conversion to group the output bits from the PN generator into pairs of bits so that they can be mapped to a symbol.

I/Q look-up table

This block is responsible for mapping pairs of bits to in-phase and quadrature gains. Such a mapping is often described by a signal constellation. Figure 3 shows the data mapping constellation for the QPSK system. In this case the data are grouped into pairs and each pair maps to a separate in-phase ( I I) and quadrature ( Q Q) gain. These I I and Q Q gains are then used to generate the in-phase and quadrature message signals, s I n s I n and s Q n s Q n .

Figure 3
QPSK Constellation
QPSK Constellation (qpsk_const.png)

One way to implement this mapping is by using a look-up table. A pair of data bits can be interpreted as an offset into an I I/ Q Q table that stores the in-phase and quadrature gains. Note that since each I I/ Q Q mapping defines a symbol, this mapping is done at the symbol rate F symb F symb , or once for every T symb T symb DSP samples. 1

The constellation bit-assignments are such that any two adjacent constellation points differ by only one bit. This assignment is called Gray coding and helps reduce the number of bit errors made in the event of a received symbol error.

Footnotes

  1. The I I and Q Q gains of ±12 ± 1 2 have been chosen to ensure that the magnitude of the transmitted signal never exceeds 1.0.

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