The document discusses various digital modulation formats including BPSK, QPSK, OQPSK, and π/4 QPSK. BPSK carries only 1 bit per symbol and has low bandwidth efficiency. QPSK carries 2 bits per symbol but has issues with zero crossing during transitions of 2 bits. OQPSK addresses this with a delay between in-phase and quadrature components to avoid 180 degree phase shifts. π/4 QPSK provides further improvements with phase shifts of up to 135 degrees, allowing for non-coherent detection and better performance in noisy environments. DQPSK first performs differential encoding before QPSK modulation to minimize transitions.

1. MODULATION
FORMATS
- BPSK, QPSK,
OQPSK,Pi/4 QPSK

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3. Modulation:
Modulation is the process of encoding information from a message source in a manner suitable for transmission.
Qualities of Modulation Formats:
 Spectral Efficiency:
 This must be as HIGH as possible
 This is achieved by using Higher order modulation formats.
 This allows higher data bits to be transmitted with each symbol.
 Adjacent Channel Interference:
 This must be as LOW as possible.
 This entails that the power spectrum of the signal should not roll outside the desired band.
 This is achieved by proper filtering mechanisms.
 Sensitivity with respect to noise:
 This must be as LOW as Possible.
 This is achieved by using lower order Modulation formats.
 Robustness with respect to delay and Doppler dispersion:
 This must be as LARGE as Possible.
 To achieve this Filtering must be as minimum as possible.
 Waveform must be easy to generate
 To use class C Amplifiers , then modulation formats with constant envelop must be used
 To use class A or B amplifiers, then modulation formats with envelop distortions can be used.

4. Choice of Digital Modulation
• Several factors that influence the choice of a digital modulation scheme. A desired
modulation scheme provides,
 Low bit error rates at low received signal to noise ratios
 Performs well in multipath and fading conditions
 Occupies a minimum of bandwidth
 Easy and cost effective to implement
• Existing modulation formats do not simultaneously satisfy all of these requirements.
Hence trade-offs were made when selecting a digital modulation schemes.
• The performance of the modulation formats are decided by
 Power efficiency:
This parameter describes the ability of modulation format to preserve the
fidelity of digital messages at low power levels.
 Bandwidth efficiency:
This parameter describes the ability of modulation format to accommodate
data within a limited bandwidth.

5. Binary Phase Shift Keying (BPSK)
In Binary Phase Shift Keying (BPSK), the phase of the carrier signal is varied between two possible states m1 and m2
corresponding to binary 1 and binary 0. These two waveforms will have 180o phase shift.
Considering the Energy per bit Eb,
𝐸 𝑏 =
1
2
𝐴 𝑐
2
𝑇𝑏
The Most Generalised Eqn. is Given by:
Then, Amplitude Ac is given by
𝐴 𝑐 =
2 𝐸 𝑏
𝑇𝑏

6. Power Spectral Density of BPSK
Power Spectral Density of BPSK:
PSD of any band pass signal is given by,
g(t) for BPSK is given by
The power spectral density of BPSK is given by
The PSD frp the BPSK signal at RF can be evaluated by translating the
baseband spectrum to the carrier frequency using the relation shown
above, Hence the PSD of a BPSK signal at RF is given by
Null to Null Bandwidth:
The simpler and most widely accepted measure
of bandwidth is equal to the width of the main
spectral lobe.
BW = (f+Rb) – (f-Rb) = 2Rb
Where Rb = Bit Rate

7. Quadrature Phase Shift Keying (QPSK)
 There are certain drawbacks with BPSK, it can carry only 1 bit in a symbol.
 This makes the BPSK not suitable for High data rates. Also BPSK is not spectrum Efficient.
 Quadrature Phase Shift Keying has twice the bandwidth efficiency of BPSK, since 2 bits are transmitted in a single
modulation symbol.
 The phase of the carrier takes 1 of 4 equally spaced values, such as 0,Pi/2, pi, and 3Pi/2 where each value carries
unique message bits.
 The equations for QPSK is given by

8. PSD of QPSK
Bandwidth:
BW = (fc + Rb /2) - (fc - Rb /2)
= Rb

9. Comparison of BPSK and QPSK
Constellation Diagram:
 No. of Points in constellation diagram is inversely proportional to the spectrum occupancy. i.e., More
the number of points lesser the bandwidth occupancy (Spectrum Efficient)
 Distance between the points on constellation diagram directly replicates the Error Probability of the
modulation format.
BW = (f+Rb) – (f-Rb) = 2Rb
BW = (fc + Rb /2) - (fc - Rb /2)
= Rb

10. OQPSK – Offset QPSK or Staggered QPSK
Drawbacks of QPSK are:
Where there is a 2 bit change in the input sequence, the transition in the state crosses
the origin of the constellation diagram for a particular period of time.
 This causes NON LINEARITY effects in the systems.
 Because of this effect the systems attracts the Side Lobes.
 Also the Linear Amplifiers that are used in the system cannot amplify the signals
to optimal levels.
These drawback of QPSK is mainly because of the 180o transition. This can be eliminated by introducing an Offset
between the in phase and quadrature components will eliminate the 180o phase shift. Instead it will be 90o phase
shift.
 Other than the offset all others things are as similar to the
QPSK
 The phase shifts are delayed to half a symbol period that
ensures 180o phase shift never occurs in the input sequence.
 This avoids the problem of zero crossing there by effective
amplification is achieved.
 However, this is not spectrum efficient as compared to the
QPSK.
 But, OQPSK is proved to perform better than QPSK in the
presence of phase jitter due to noisy reference signals at the
receiver.

11. π/4 QPSK
• π/4 QPSK is a compromise of QPSK and OQPSK.
• This modulation format allows a maximum phase shift to +/- 135o .
Which further improves the performance of the modulation scheme.
• The most important feature of Pi/4 QPSK is that it offers non coherent
method of detection.
• This technique performs better in the presence of Multipath spread and
Fading.

12. Differential QPSK
• DPSK → Differential Phase Shift Keying
• Non-coherent Rx can be used
• easy & cheap to build
• no need for coherent reference signal from Tx
• Bit information determined by transition between two phase states
• incoming bit = 1 → signal phase stays the same as previous bit
• incoming bit = 0 → phase switches state

13. Summary
• Binary Phase Shift Keying
Carries only 1 bit at a time
Not bandwidth efficient
• Quadrature Phase Shift Keying
Problem of zero crossing when 2 bit change is detected
Non linearity effects due to 180o phase shift
Offset QPSK
Inserting a offset reduces the phase shift to 90o there by improving the effective amplification
of signals with linear amplifiers
• Pi/4 QPSK
Compromise between the QPSK and OQPSK
More points on Constellation Diagram thereby better spectrum efficient
Since more points on constellation diagram distance between the points is also less there for
performs better in noisy environments also. Better Error probability
• DQPSK
Further improvements in modulation qualities
First Differential encoding is performed and then QPSK is performed.
Minimizes the amount of transition during modulation.
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