# What is QAM or Quadrature Amplitude Modulation?

#### Editorial Team - everything RF

Jul 19, 2022

Quadrature Amplitude Modulation or QAM is a digital modulation scheme where data is transmitted over the channel by varying both the amplitude and phase of the high-frequency carrier signal. The transmitted signal is represented in a constellation plot that contains two axes namely the in-phase and Quadrature. The in-phase and Quadrature axis are separated from each other by a phase of 90˚. Therefore, these two axes are orthogonal to each other.

In the QAM scheme, two or more bits are grouped together to form a symbol that lies in the constellation plot. Each symbol, also called state, has a unique amplitude and phase level that provides distinction across different points in the constellation. Since, the modulation scheme uses binary data, the number of possible bits that can be transmitted can be given by the following equation:

where N represents the number of bits and M is the number of possible combinations corresponding to any given number of N bits i.e the number of constellation points. Since the value of 2N is also an integer, the total number of bits that can be transmitted is given by,

QAM Modulation is also known as M-ary QAM where M can be the number of bits represented in the constellation diagram. Some examples include 16-QAM, 32-QAM, 64-QAM, 256-QAM, 1024-QAM, and 4096-QAM. Each one supporting higher data rates and constellation points based on equation 1.

Specific Cases of M-ary QAM Modulation Schemes

16-QAM: The 16-QAM is a specific case of M-ary QAM scheme in which a carrier wave of fixed frequency can exist in one of sixteen different states in the constellation plot. Each symbol consists of four bits out of 16 different possible combinations ranging from 0000 to 1111. The total number of bits that can be accomodated in a symbol for 16-QAM is 4. Since, this scheme uses binary data to perform modulation and demodulation, the number of combinations possible with four bits is 24 i.e. 16. Or equivalently, the number of bits that can be accomodated as per equation 2 is log2 16 = 4. Click here to learn more about 16-QAM.

64-QAM: The 64-QAM is a specific case of M-ary QAM scheme in which a carrier wave of fixed frequency can exist in one of sixty four different states in the constellation plot. Each symbol consists of six bits out of 64 different possible combinations ranging from 000000 to 111111. Therefore, the number of bits that can be accomodated in a symbol is 6. Since, this scheme uses binary data to perform modulation and demodulation, the number of combinations possible with six bits is 26 i.e. 64. Or equivalently, the number of bits that can be accomodated as per equation 2 is log2 64 = 6. Click here to learn more about 64-QAM.

256-QAM: The 256-QAM is a specific case of M-ary QAM scheme in which a carrier wave of fixed frequency can exist in one of 256 different states in the constellation plot. Each symbol consists of 8 bits out of 256 different possible combinations ranging from 00000000 to 11111111. Thus, the total number of bits that can be accomodated in a symbol for 64-QAM is 6. Since, this scheme uses binary data to perform modulation and demodulation, the number of combinations possible with eight bits is 28 i.e. 256. Or equivalently, the number of bits that can be accomodated as per equation 2 is log2 256 = 8. Click here to learn more about 256-QAM.

1024-QAM: The 1024-QAM is a specific case of M-ary QAM scheme in which a carrier wave of fixed frequency can exist in one of 1024 different states in the constellation plot. Each symbol consists of 10 bits out of 1024 different possible combinations. Thus, the total number of bits that can be accomodated in a symbol is 10. Since, this scheme uses binary data to perform modulation and demodulation like the relatively lower order QAMs (from 16 to 256), the number of combinations possible with ten bits is 210 i.e. 1024. Or equivalently, the number of bits that can be accomodated as per equation 2 is log2 1024 = 10. Click here to learn more about 1024-QAM.

4096-QAM: The 4096-QAM is a specific case of M-ary QAM scheme in which a carrier wave of fixed frequency can exist in one of 4096 different states in the constellation plot. Each symbol consists of 12 bits out of 4096 different possible combinations. The total number of bits that can be used to modulate the carrier wave is 12. Since, this scheme uses binary data to perform modulation and demodulation like other relatively lower order QAMs (from 16 to 256), the number of combinations possible with 12 bits is 212 i.e. 4096. Or equivalently, the number of bits that can be accomodated as per equation 2 is log2 4096 = 12. Click here to learn more about 4096-QAM.

Comparison of QAM Modulation Schemes

 Modulation Scheme Bits/Symbol Data Rate Incremental Capacity Gain BPSK 1 QPSK / 4-QAM 2 8-QAM 3 50% 16-QAM 4 33% 32-QAM 5 25% 64-QAM 6 20% 128-QAM 7 17% 256-QAM 8 14% 512-QAM 9 13% 1024-QAM 10 11% 2048-QAM 11 10% 4096-QAM 12 9.77%

In general for a fixed channel size, increasing the order of the QAM scheme increases the link capacity. However, as we go up in complexity over a point the incremental capacity gains start to decrease. For instance, when moving towards 4096-QAM from 1024-QAM, a capacity gain of roughly 11% can be obtained whereas when moving from 16-QAM to 64-QAM the gain is 25%. The able above gives details about the data rates supported by each QAM scheme.

Lower Order QAMs vs. Higher Order QAMs

As observed in the table above, higher QAM modulation schemes result in higher signal bandwidths and data rates. However, as we go up in the M-ary QAM modulation scheme, the spacing between two constellation points decreases to maintain the mean constellation energy constant for a fixed square grid. As a result, there is a higher chance of two points (noisy) overlapping with each other, thereby resulting in ambiguity in distinguishing one point from the other. This causes an increase in noise and interference which lowers the Signal-to-Noise Ratio (SNR) and an increases in Bit Error Rate (BER). Therefore, in noisy environments, lower order QAM schemes can be used to improve the SNR,  reduce BER, as well as increase the probability of detecting the signals with low bit errors.

Multipath interference resulting from signal reflection from various objects in the channel can cause a delay in the arrival of symbols. As a result, intersymbol interference (ISI) will occur and will be more critical for higher-order QAM schemes.

Another important consideration is the hardware complexity. As we go up in the M-ary QAM scheme, the constellation size increases and the point-to-point constellation distance decreases. This makes the detection at the receiver more challenging than lower-order QAMs. A robust signal processing algorithm can be used to intelligently separate different constellation points in the presence of noise. However, the hardware cost and complexity required to support the ever-increasing constellation size will also proportionally increase.

To choose an optimal QAM modulation scheme, parameters such as carrier-to-interference ratio, carrier-to-noise ratio, threshold-to-noise ratio, type of channel, and the order of QAM are particularly important to analyze the performance of different M-ary QAMs schemes and to determine the right balance between them under a given scenario.

Applications of M-ary QAM Schemes

M-ary QAM schemes are used in a variety of applications. In the US, digital cable TV uses 64-QAM and 256-QAM. In the UK, 64-QAM is used for digital terrestrial television while 256-QAM is used for Freeview-HD systems.

Very dense constellation schemes such as 1024-QAM and 4096-QAM are used to achieve high levels of spectral efficiency in homeplug powerline Ethernet devices and can deliver data rates up to 500 Mbps. 1024-QAM scheme is particularly utilized for ultra high microwave backhaul systems. If other signal processing techniques such as adaptive equalization and channel coding are used along side 1024-QAM, a gigabit level capacity can be easily achieved over the given channel bandwidth.

What is a QAM Modulator and how does it work?

A basic QAM modulator circuit consists of a mixer, local oscillator, a 90˚ phase shifter, and a summer block located close to the output port (see figure above). The signal input is fed to I and Q parts of the circuit. A local oscillator generates a clean sinusoidal signal of a fixed amplitude and frequency. The mixer circuit multiplies the incoming signal with the oscillator signal to generate a high frequency carrier signal. While the in-phase signal is a simple mixing of incoming signal and oscillator signal, the Quadrature waveform is formed by shifting the oscillator signal by phase of 90˚, upon which mixing with the data signal is carried out. The resulting two waveforms, the in-phase and Quadrature, are added at the summer circuit to create a QAM modulated signal.

What is a QAM Demodulator and how does it work?

In the QAM demodulation process, a balun is used to split the incoming modulated signal to allow extraction of the in-phase and quadrature components of the signal. The signals can be coherently extracted since the two components are orthogonal to each other. A low-pass filter can be used to filter out the in-phase and quadrature signals separately. To extract the in-phase signal, the received signal is first multiplied with a cosine signal and then passed through a low-pass filter. A sine wave is multipled with received waveform and then passed through the lowpass filter to extract the quadrature component.