1. Modulation and Coding Trade-offs
Kiran Thapaliya

2. Minimum Shift Keying
Minimum shift keying (MSK) can be viewed as either a special case of continuous-phase frequency shift keying (CPFSK) or a special case of OQPSK with sinusoidal symbol weighting or a special case of OQPSK with sinusoidal symbol weighting.
When viewed as CPFSK, the MSK wave form can be expressed as:
Where f0 is the carrier frequency, represents the bipolar data being transmitted at a rate R=1/T, and xk is a phase constant which is valid over the kth binary data interval.

3. The tone spacing in MSK is thus one half that employed for non-coherently demodulated orthogonal FSK, giving rise to the name minimum shift keying.
When viewed as special case of OQPSK, MSK waveform can be viewed as
Where dI(t) and dQ(t) have the same in-phase and quadrature data stream interpretation.
The above equation is sometimes referred to as pre-coded MSK.

4. In conclusion: The waveform s(t) has constant envelope
There is phase continuity in the RF carrier at the bit transition
The waveform s(t) can be regarded as FSK waveform with signaling frequencies f0+1/4T and f0-1/4T

6. Quadrature Amplitude Modulation
Quadrature amplitude modulation can be considered a logical extension of QPSK.
QAM signaling can also be viewed as a combination of amplitude shift keying(ASK) and phase shift keying (PSK), giving rise to the alternative name amplitude phase keying (APK).
Can be viewed as amplitude shift keying in two dimensions, giving rise to the name quadrature amplitude shift keying (QASK).

7. Both modulated signal occupy the same band.
Two baseband signals can be separated by synchronous detection using two local carriers in phase quadrature.

8. QAM Probability of Bit Error
For a rectangular constellation, a Gaussian channel, and matched filter reception, the bit error probability for M-QAM, where M=2k and k is even is
Where
represents the number of amplitude levels in one dimension.

9. Bandwidth-power Trade off

10. Modulation and Coding for Band limited Channels
There has been considerable interest in techniques that can be provide coding gain for band-limited channels.
The motivation is to enable the reliable transmission of higher data rates over voice grade channels.
The greatest interest is in the following three separate coding research areas:
Optimum signal constellation boundaries.(choosing a closely packed signal subset from any regular array or lattice of candidate points)
Higher density lattice structures (adding improvement to the signal subset choice by starting with the densest possible lattice for the space)
Trellis coded modulation(combined modulation and coding techniques for obtaining coding gain for band-limited channels)

11. Commercial Telephone Modems
The typical telephone channel is characterized by a high signal to noise ratio (SNR) of approximately 30dB and a bandwidth of approximately 3kHZ.

14. Signal Constellation Boundaries
Several researchers have examined large numbers of possible QAM signal constellations in a search for designs that result in the best error performance for a given signal-to noise ratio.
The constellation rule known as the Campopiano-Glazer construction rule that yields optimum signal set performance can be summarized as:
From an infinite array of points closely packed in a regular array or lattice, select a closed packed subset of 2k points as a signal constellation.
The k=6 constellation was used in the Paradyne 14.4kbit/s modem. Compared with a square, the performance improvement resulting from a circular boundary is only a modes 0.2 dB.

17. Higher Dimensional Signal Constellations
For any particular information rate and channel noise process that is independent and identically distributed in two dimensions, signaling in a two dimensional space can provide the same error performance with less average power than signaling in a one-dimensional pulse amplitude(PAM) space.
This is accomplished by choosing signaling on a two dimensional lattice from within a circular rather than a rectangular boundary.
Going to a higher number N dimensions, and choosing points on an n-dimensional lattice from within an N-sphere rather than an N-cube, further energy savings are possible.

18. The goal of this constellation shaping is to make the required energy of signal points from the N-sphere less than that from N-cube.
Such reduction in required energy for a given error performance is referred to as a shaping gain

19. Higher-Density Lattice Structures
In two dimensional signal space, the densest lattice is the hexagonal lattice.
Using a hexagonal lattice instead of rectangular lattice, 0.6dB average energy can be saved.
The k=6 constellation was used in the Codex SP14.4 modem

21. Combined Gain: N-Sphere Mapping and Dense Lattice
It is possible to combine the benefits of the Campopiano-Glazer boundary construction in N dimensions with the gain from the densest lattice in N space.
The resulting gain is a combination of N-sphere versus N-cube boundary gain of Table 9.6 and lattice packing density gain of Table 9.7.

23. Question
What are the properties of MSK modulation?