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Constellation Diagrams of M-ary QAM | M-ary Modulation

QAM

Unlike M-ary PSK, where the signal is modulated with different phase-shifted versions of the carrier, QAM varies both the phase and the amplitude levels. For instance:

QAM = ASK + PSK

QAM Constellation Example
In the figure above, 2 amplitude levels and 4 phase shifts are applied, resulting in a total of 2 * 4 = 8 constellation points.

Multilevel QAM

In M-ary QAM, groups of data bits are mapped to one of M possible amplitude and phase-shifted signals. By sending a single symbol that represents multiple bits, we can theoretically achieve a data rate that is log₂(M) times higher than a binary modulation scheme (like BPSK or BASK).

Instead of only modifying the phase, frequency, or amplitude of the RF signal, the RF carrier's phase (or frequency) is also altered. Since the envelope and phase offer two degrees of freedom, M-ary modulation methods convert baseband data into four or more different RF carrier signals. We refer to four carrier signals because a symbol is made up of two or more bits, and two bits can represent four distinct signals. Such modulation schemes are called M-ary modulation.

Depending on whether the amplitude, phase, or frequency is changed, the modulation is referred to as M-ary ASK, M-ary PSK, or M-ary FSK. Because M-ary modulation techniques increase bandwidth efficiency, they are appealing for use in bandlimited channels. Since a physical channel's bandwidth is always limited, a 16-QAM system, for instance, uses the channel log₂(16) = 4 times more effectively than a BASK system.

To transfer signals in the form of symbols and to enhance the bit rate, M-ary PSK and M-ary QAM are both utilized. You can obtain multiple prior data rates if you send a symbol rather than a single bit at a time. These M-ary modulation techniques are used to multiplex data.

  • 16-QAM ==> 4N ('data rate' is 4 times as compared to binary ASK, FSK, or PSK)
  • 32-QAM ==> 5N
  • 64-QAM ==> 6N
  • 128-QAM ==> 7N
  • 256-QAM ==> 8N

Constellation Diagram of 4-QAM (Transmitted)
Fig 1: Constellation Diagram of 4-QAM (Transmitted)

Constellation Diagram of 4-QAM (Received thru noisy channel)
Fig 2: Constellation Diagram of 4-QAM (Received through a noisy channel)

(Get MATLAB Code)

MATLAB Code for BER vs SNR for M-ary QAM

BER vs SNR for M-ary QAM

(Get MATLAB Code)

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