• It has twice the bandwidth efficiency of BPSK as mentioned above. The phase of the carrier takes on 1 of 4 equally spaced values as shown below:

• The QPSK signal for the first constellation above is simply:

(4.15)

where the symbol duration: , the bit period.

• From the constellation diagram we see that the distance between adjacent samples is and since each symbol corresponds to 2-bits then . The distance in QPSK then becomes .
• Substituting the above into the generic probability equation we obtain the BER for QPSK:

(4.16)

• QPSK can be differentially encoded as in the case of DSPK to allow non-coherent detection.

PSD in this case for rectangular pulses will be similar to PSK where symbol duration has to replace the bit period :

(4.17)

As it can be seen from the figure below, the null-to-null bandwidth is equal to the bit rate , which is half of that of a BPSK signal as desired.

• QPSK Transmitter and Receivers:

• First unipolar binary messages are converted into bipolar NRZ sequence.
• Next, the bit stream is split into in-phase (even) and quadrature (odd) bit streams each with a bit rate .
• Two orthogonal carriers separately modulate two binary sequences.
• They are summed to produce a QPSK signal.
• Finally, the bandpass filter at the output prevents the spillover of signal energy into adjacent channels and also removes the out-of-band spurious signals generated during the modulation process. In most wireless and other RF implementations, pulse shaping is done at the baseband to provide proper RF filtering at the output.

• Front-end BPF removes the out-of-band noise and the interchannel interference and each part of the filter output is coherently demodulated.
• The decision circuits very similar to BPSK systems process the outputs of demodulators.

• Offset QPSK (OQPSK):

This modified QPSK system is designed to combat the following ill of QPSK systems: The amplitude of a QPSK signal is ideally constant. However, they are normally pulse-shaped for efficiency and then they loose the constant envelope property. Occasional phase shift of can cause the signal envelope to have a Z.C. Any kind of hard-limiting or non-linear amplification of the Z.C. brings back the filtered sidelobes since the fidelity of the signal at small voltage levels is lost in transmission. To prevent the regeneration of sidelobes and spectral spreading, it is imperative that only linear amplifiers, which are costly and very inefficient, are used for amplifying QPSK signals. If the in-phase and quadrature bit streams of QPSK signals are offset in their relative alignment by one-bit period (half-symbol rate), then this modified version of QPSK is called an Offset QPSK (OQPSK) and it results in more efficient amplification process.

• Since the transition instants of are offset, at any given time only one bit stream can change values and maximum phase-shift is only , which eliminates Z.C.
• Obviously, there will be some ISI caused especially at the phase transition points. But the envelope variations are much less and non-linear amplifiers do not generate H.F. sidelobes.
• Spectrum and BER of OQPSK are identical to those of QPSK and it is very attractive for wireless communications due to their improved performance even if there is phase jitter.

p/4 Shifted QPSK offers a compromise between OQPSK and QPSK in terms of the allowed maximum phase transitions.

• It may be demodulated in a coherent or non-coherent fashion.
• Maximum phase change is limited to and hence, it preserves the constant envelope property better than bandlimited QPSK.
• But it is more susceptible to envelope variations than OQPSK.
• Non-coherent detection capability is an extremely attractive feature for simplifying receiver design.
• In the presence of multipath spread and fading, it is observed to perform better than others do.
• Very often they are differentially encoded to facilitate the implementation and they are called p/4 DQPSK.
• Constellations:

• In-phase and quadrature pulses, over the time interval are determined by their previous values as well as , which itself is a function of , which is a function of the current input symbols

. That is:

and the following table gives the phase shifts:

• The transmitter block diagram is shown below, where the in-phase and quadrature bit streams are separately modulated by two carriers which are in quadrature with one another and the p/4- QPSK waveform is given by:

(4.21)

where:

(4.22)

(4.23)

• Both

are passed through Raised-Cosine roll-off pulse shaping filters before modulation to reduce the bandwidth occupancy.

There are various types of detection techniques used for these signals, including "baseband differential detection, IF differential detection, and FM discriminator detection." Simulations show that all 3 receiver configurations offer similar BER, although there are implementation issues, which are specific to each technique. (Details of these are neatly presented in Rappaport [11]) and we will only present the block diagram of the baseband differential detector here.