Quadrature Tensor Amplitude Modulation
One of the greatest successes in digital communications has been the discovery of M-Ary Quadrature Amplitude Modulation schemes for encoding digital symbols, mapping to binary bit sequences, as a 2D constellation of IQ Amplitude and Phase.
By incorporating into the symbol equation a previous state for at least half of the pulses we can extend the set of symbols represented per pulse.
In quadrature amplitude modulation (QAM), the effective representation of current symbols relies heavily on the analysis of previous amplitude and phase inputs. This approach enhances the robustness of the modulation scheme, particularly in environments with noise and interference.
To determine the current QAM symbol representation, we can regard the previous amplitude and phase inputs as variables. Assume we have a series of received symbols, where each symbol can be expressed in terms of its amplitude (A) and phase (φ). The previous symbols can be represented as:
( S_{n-1} = A_{n-1} e^{j \phi_{n-1}} )
( S_{n-2} = A_{n-2} e^{j \phi_{n-2}} )
These past symbols provide context for interpreting the current symbol ( S_n ).
To compute the current QAM symbol, we can define a state transition model using the amplitude and phase of the preceding symbols. The relationship could be modeled as follows:
Amplitude Prediction: Estimate the amplitude ( A_n ) based on an average or weighted amplitude of previous symbols. For example: [ A_n = \alpha A_{n-1} + (1 - \alpha) A_{n-2} ] where ( \alpha ) is a weighting factor between 0 and 1.
Phase Prediction: Similarly, the phase ( \phi_n ) can be estimated by considering the differences in phase between the last two symbols. A simple model could utilize a circular averaging method, expressed as: [ \phi_n = \phi_{n-1} + \beta (\phi_{n-1} - \phi_{n-2}) ] where ( \beta ) is a factor that governs the influence of the previous phase difference.
Symbol Formation: By combining the predicted amplitude and phase, the current symbol can be formulated as: [ S_n = A_n e^{j \phi_n} ]
These equations serve as a basis for symbol representation; however, refining the model may involve additional elements such as error correction and adaptive filtering techniques. The goal remains to minimize distortions and improve accuracy when transitioning between symbols, utilizing the inherent relationships between past and current inputs.
In summary, leveraging previous amplitude and phase inputs to predict the current QAM symbol effectively enhances the signal integrity in communication systems, promoting more reliable data transmission.