4.3 Quadrature Phase Shift Keying (QPSK)
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
- The QPSK signal for the first constellation above is simply:
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:
- QPSK can be differentially encoded as in the case of DSPK to allow
- PSD and Bandwidth of QPSK:
PSD in this case for rectangular pulses will be similar to PSK
where symbol duration has
to replace the bit period :
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
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
- 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.
- 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:
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 ) and we will only present the block diagram of the baseband
differential detector here.