Qpsk, Oqpsk, Cpm Probability of Error for Awgn and Flat Fading Channels [4]

This article discusses QPSK, OQPSK, π/4 DQPSK and the trade offs involved. Later we discuss various CPM schemes and their relative bandwidth efficiencies. Probability of Bit error is discussed for various schemes assuming an AWGN channel. A model is devised, ignoring any changes in phase, to determine the error probabilities for flat fading channels. The article ends with a brief discussion of non-coherent detection. 1 QPSK and Offset QPSK Signaling QPSK or Quadrature Phase Shift Keying, involves the splitting of a data stream mk(t) = m0,m1,m2, . . ., into an in-phase stream mI(t) = m0,m2,m4, . . . and a quadrature stream mQ(t) = m1,m3,m5, . . .. Both the streams have half the bit rate of the data stream mk(t), and modulate the cosine and sine functions of a carrier wave simultaneously. As a result, phase changes across intervals of 2Tb, where Tb is the time interval of a single bit (the mk(t)s). The phase transitions can be as large as ±π as shown in Figure 1. Sudden phase reversals of ±π can throw the amplifiers into saturation. As shown in Figure 2 [1], the phase reversals of ±π cause the envelope to go to zero momentarily. This may make us susceptible to non-linearities in amplifier circuitry. The above may be prevented using linear amplifiers but they are more expensive and power consuming. A solution to the above mentioned problem is the use of OQPSK. ∗Taught by Dr. Narayan Mandayam, Rutgers University. Figure 1: The figure shows a QPSK constellation. The dark black lines show all possible phase changes. Figure 2: The figure shows a QPSK waveform. As is seen across the dotted line corresponding to a phase shift of π, the envelope reduces to zero temporarily. OQPSK modulation is such that phase transitions about the origin are avoided. The scheme is used in IS-95 handsets. In OQPSK the pulse streams mI(t) = m0,m2,m4, . . . and mQ(t) = m1,m3,m5, . . . are offset in alignment, in other words are staggered, by one bit period (half a symbol period). Figure 3 [2], shows the