OQPSK

Offset Quadrature Phase Shift Keying (OQPSK) is a variant of standard QPSK that introduces a half-symbol time offset between the in-phase (I) and quadrature (Q) bit streams before modulation. This simple modification prevents the signal envelope from passing through zero, reducing the peak to average power ratio and making it suitable for nonlinear power amplifiers. OQPSK is an important concept in GATE and is used in CDMA systems and satellite communications.

Core Concept of OQPSK

In standard QPSK, the in-phase and quadrature bit streams are synchronized. They can both change simultaneously at symbol boundaries. When both I and Q flip together, the constellation point jumps diagonally across the origin, corresponding to a 180 degree phase transition. As the bandlimited signal passes through a nonlinear power amplifier, this 180 degree jump causes the instantaneous envelope to pass through zero, which generates spectral regrowth outside the allocated bandwidth.

OQPSK introduces a half-symbol time offset (Ts/2) between the I and Q streams. Since the symbol period Ts = 2Tb where Tb is the bit period, this offset equals exactly one bit period. With this offset applied, the I and Q streams can never change at the same instant. At any given transition moment, only one of the two streams changes, and the phase jump is limited to plus or minus 90 degrees. The signal envelope never passes through zero.

This reduction in envelope variation makes OQPSK highly suitable for use with nonlinear power amplifiers such as Class C amplifiers that are common in satellite and mobile transmitters. Less envelope variation means the amplifier can operate closer to saturation, improving power efficiency without causing severe spectral distortion.

Mathematical Expression

The baseband OQPSK signal is expressed as:

s(t) = I(t) * cos(2*pi*fc*t) - Q(t - Ts/2) * sin(2*pi*fc*t)

where I(t) and Q(t) are the NRZ pulse trains carrying the even and odd bits respectively, and the Q stream is delayed by Ts/2 relative to the I stream. The power spectrum of OQPSK is identical to that of QPSK because the offset does not change the statistical properties of the signal. Therefore, bandwidth efficiency of OQPSK = bandwidth efficiency of QPSK = 2 bits per symbol.

The BEP performance of OQPSK in AWGN is also identical to QPSK:

Pe_OQPSK = (1/2) * erfc(sqrt(Eb/N0))

This means OQPSK trades no performance penalty for its envelope advantage. It achieves the same BEP and bandwidth as QPSK while significantly reducing envelope fluctuations.

Practical Understanding

OQPSK is used in IS-95 CDMA reverse link (mobile to base station direction) because the mobile handset power amplifier operates more efficiently with a lower PAPR signal. Satellite transponders also benefit from OQPSK for similar reasons. In Bluetooth, a variant called pi/4-QPSK (which is different from OQPSK but similarly limits maximum phase change to 135 degrees) is used.

A related and more advanced scheme is Minimum Shift Keying (MSK), which can be viewed as continuous-phase OQPSK using sinusoidal pulse shaping instead of rectangular pulses. MSK has a constant envelope (no variation at all) and better spectral properties. Gaussian MSK (GMSK) is used in GSM systems.

Given:
Modulation: OQPSK with QPSK-equivalent parameters
Bit rate Rb = 2 Mbps
Eb/N0 = 8 dB

Why this formula applies:
OQPSK BEP is identical to QPSK: Pe = 0.5 * erfc(sqrt(Eb/N0))
Bandwidth is same as BPSK at half the bit rate (since 2 bits per symbol)

Formula:
Null-to-null bandwidth = 2 * Rs = Rb (for QPSK/OQPSK)
Pe = 0.5 * erfc(sqrt(Eb/N0))

Substitution:
Symbol rate Rs = Rb / 2 = 2 Mbps / 2 = 1 Msymbols/s
Null-to-null BW = 2 * Rs = 2 MHz
Eb/N0 (linear) = 10^(8/10) = 6.31
sqrt(6.31) = 2.51
erfc(2.51) approximately 0.00048

Calculation:
Pe = 0.5 * 0.00048

Final Answer:
OQPSK null-to-null bandwidth = 2 MHz for 2 Mbps bit rate
BEP = 2.4 x 10^-4 at Eb/N0 = 8 dB
Max phase jump = 90 degrees (key advantage over QPSK)

Exam Tip: GATE commonly asks whether OQPSK has different BEP or bandwidth compared to QPSK. The answer is no to both. OQPSK has identical BEP and bandwidth as QPSK. The only advantage is limiting maximum phase jump from 180 degrees to 90 degrees, which helps when using nonlinear amplifiers.

Mechanism of I-Q Offset and Phase Transitions

• I stream changes at t = 0, Ts, 2Ts, ... while Q stream changes at t = Ts/2, 3Ts/2, ... due to the Tb offset.
• Since transitions alternate between I and Q, the phasor never jumps across the origin, eliminating 180 degree transitions.
• The bandpass envelope therefore never touches zero, preventing amplifier-induced spectral spreading.
• BEP and bandwidth efficiency remain identical to QPSK because only timing is changed, not the fundamental modulation parameters.
• MSK is the continuous-phase version of OQPSK using sinusoidal pulse shaping, yielding constant envelope and better out-of-band spectral rolloff.

Quick Revision

• OQPSK offsets the Q bit stream by Ts/2 = Tb relative to the I stream.
• Maximum phase jump in OQPSK = 90 degrees (vs 180 degrees in QPSK).
• BEP of OQPSK = BEP of QPSK = 0.5 * erfc(sqrt(Eb/N0)).
• Bandwidth of OQPSK = bandwidth of QPSK. No spectral penalty.
• Main advantage: envelope does not cross zero, suitable for nonlinear Class C power amplifiers.
• Used in IS-95 CDMA reverse link. MSK is the continuous-phase generalization.
• Trap: OQPSK has the same BEP and bandwidth as QPSK. It only differs in envelope behavior and phase transitions.