4.4 Quadrature Phase Shift Keying Analysis

4.4 Quadrature phase shift keying (QPSK)
Quadrature phase shift keying (QPSK) has twice the bandwidth efficiency of BPSK since two bits are transmitted in a single modulation symbol. In the phase of the carrier takes on one of four equally spaced values, such as 0, π/2,π and 3π/2, where each value of phase corresponds to a unique pair of message bits. The Quadrature phase shift keying (QPSK) signal for this set of symbol states may be defined as s_QPSK (t) =√(〖2E〗_s/T_s ) cos⁡[〖2πf〗_c t +(i-1)π/2] 0≤ t ≤T_(s ) i = 1,2,3,4
WhereT_sis symbol duration and is equal to twice the bit period.
Using trigonometric identities, the above equations can be rewritten for the interval 0≤t≤T_sas s_QPSK (t) =√(〖2E〗_s/T_s ) cos⁡[(i-1)π/2] cos⁡〖(〖2πf〗_c 〗 t)
When compared to BPSK, QPSK provides twice the spectral efficiency with exactly the same energy efficiency. In similar to BPSK, QPSK can also be differentially encoded to allow no coherent detection. The bit stream m(t) is split into two bit streams m_1 (t) and m_Q (t)(in phase and Quadrature streams) each having a bit rate of R_(s = ) R_b/2. The bit stream m_1 (t)is called “even stream” and m_Q (t)is called “odd” stream. The two modulated signals, in each of which can be considered to be a BPSK signal, are summed to produce a QPSK signal. The two binary sequences are separately modulated by two carriers ∅_1andϕ_2, which are in Quadrature. The filter at the output of the modulator confines the power spectrum of the QPSK signal within the allocated band. This is prevents spill-over of signal energy into adjacent channels and also removes out-of band spurious signals generated during the modulation process. In most implementations, pulse shaping is doing baseband to provide proper RF filtering at the transmitter