Software-defined Radio
using Xilinx

QPSK Wireless Communication Systems

    QPSK (or 4PSK) is a modulation scheme that encodes data based on the phase angle between two waveforms. The two waveforms are represented as an in-phase component, I(t), and an out-of-phase component, Q(t). This information is modulated with a carrier signal and transmitted. The mathematical representation of the transmitted signal, s(t), is

s(t) = I(t)cos(2πfot) - Q(t)sin(2πfot)            

     = cos(2πfot + ϕ(t)),                                                     (1)

where I, Q є {1/√2, -1/√2}. Here fo  denotes the carrier frequency and the vectors I and Q carry one bit information each. ϕ(t) denotes the phase of the transmitted signal s(t)

    Once received, the signal is demodulated and the data can be extracted. The data can be represented as a constellation on an x-y plane in terms of symbols. The possible decoded symbols will be at 45 degrees, 135 degrees, 225 degrees, and 315 degrees as shown in Fig 1. Each of these constellation points, or symbols, represents two bits of information that are decoded based on their position in the constellation. The term quadrature is used to describe this method of modulation because the data is represented based on the quadrant the symbol is located in. In higher order phase-shift keying modulation schemes, such as 8PSK or 16PSK, the constellation becomes more crowded in order to represent more symbols. Although the bits-per-symbol ratio has increased, the degree of accuracy needed for accurate transmission is also heightened, requiring a more complex demodulation scheme.

Fig. 1.  QPSK constellation grid.

    When making a QPSK communication system wireless, several problems are encountered. Those include multi-path effect, carrier synchronization, and phase ambiguity. For more information regarding each of these imperfections please follow the links provided.