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represents, and thus receiver is able to recover the original data. A convenient way to represent

PSK schemes is on a constellation diagram, seen in Figure 1 below.

Figure 1 - Constellation Diagram of QPSK

Figure 1 represents the possible symbols that may be selected by a given modulation

scheme as points in the complex plane for Quadrature PSK (QPSK), which is a variant of PSK

modulation that uses 4 different values of the phase to transmit data. Variations of PSK can be

found in numerous communications standards from 802.11 wireless standards (OFDM with

QPSK) to cell phones (CDMA), digital television and modems (QAM) [10]. Binary PSK

(BPSK), the simplest form of PSK, uses two phases which are separated by 180 degrees. Since

BPSK is only able to modulate at one bit per symbol, it is unsuitable for high data-rate

applications when bandwidth is limited. However, this modulation is considered the most robust

of all the PSKs since it takes the highest level of noise, jamming, or distortion, when coupled

with a correlation detector or matched filter, to make the demodulator reach an incorrect decision

(QPSK has the same BER, but requires twice the energy since two bits are transmitted). Because

BPSK does best in probability of error, it is the de facto standard in testing performance of

spread spectrum systems and modulation techniques. Generally speaking, the transmission of a

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