# 512 QAM vs 1024 QAM vs 2048 QAM vs 4096 QAM modulation types

QAM stands for Quadrature Amplitude Modulation. Each symbol in the QAM constellation represent unique amplitude and phase. Hence they can be distinguished from the other points at the receiver. Let us understand QAM modulation process at transmitter and receiver in the wireless baseband (i.e. Physical layer) chain. We will take example of 64-QAM to illustrate the concept.

Fig:1, 64-QAM Mapping and Demapping

• As shown in the figure-1, **64-QAM** or any other modulation is applied on the input binary bits.

• The QAM modulation converts input bits into complex symbols which represent bits by variation in
amplitude/phase of the time domain waveform. The 64QAM converts 6 bits into one symbol at transmitter.

• The bits to symbols conversion take place at the transmitter while reverse (i.e. symbols to bits)
take place at the receiver. At receiver, one symbol gives 6 bits as output of demapper.

• Figure depicts position of QAM mapper and QAM demapper in the baseband transmitter and
receiver respectively. The demapping is done after front end synchronization i.e. after channel and other impairments are
corrected from the received impaired baseband symbols.

• Data Mapping or modulation process is done before the RF upconversion (U/C) in the transmitter and PA.
Due to this, higher order modulation necessitates use of highly linear PA (Power Amplifier) at the transmit end.

## 64-QAM Mapping Process

Fig:2, 64-QAM Mapping Process

In 64-QAM, the number 64 refers to 2^6.

Here 6 represents number of bits/symbol which is 6 in 64-QAM.

Similarly it can be applied to other modulation types such as
512-QAM, 1024-QAM, 2048-QAM and 4096-QAM as described below.

Following table mentions 64-QAM encoding rule. Check the encoding rule in the respective wireless standard. KMOD value for 64-QAM is 1/SQRT(42).

Input bits (b5, b4, b3) |
I-Out |
Input bits (b2, b1, b0) |
Q-Out |
---|---|---|---|

011 | 7 | 011 | 7 |

010 | 5 | 010 | 5 |

000 | 3 | 000 | 3 |

001 | 1 | 001 | 1 |

101 | -1 | 101 | -1 |

100 | -3 | 100 | -3 |

110 | -5 | 110 | -5 |

111 | -7 | 111 | -7 |

QAM mapper Input parameters : Binary Bits

QAM mapper Output parameters : complex data

The 64-QAM mapper takes binary input and generates complex data symbols as
output. It uses above mentioned encoding table to do the conversion process.
Before the coversion process, data is grouped into 6 bits pair.
Here, (b5, b4, b3) determines the I value and (b2, b1, b0) determines the Q value.

Example: Binary Input: (b5,b4,b3,b2,b1,b0) = (011011)

Complex Output: (1/SQRT(42))* (7+j*7)

As we know in digital modulation, baseband is separated into in phase(I) and quadrature phase(Q) components. The combination of I and Q is known as baseband modulating signal. It is also referred as IQ diagram. The constellation diagram represent all the possible modulated symbols which will be used by modulation technique to map the information bits. This different symbols are represented in the complex plane with their amplitude and phase informations. The figures below depict 512 QAM constellation diagram and 1024 QAM constellation diagram.

## 512-QAM modulation

The figure-3 depicts 512-QAM constellation diagram. About 16 points do not exist in each of the four quadrants to make total 512 points with 128 points in each quadrant in this modulation type. It is possible to have 9 bits per symbol in 512-QAM also. 512QAM increases capacity by 50% compare to 64-QAM modulation type.

## 1024-QAM modulation

The figure depicts **1024-QAM** constellation diagram.

Number of bits per symbol: 10

Symbol rate: 1/10 of bit rate

Increase in capacity compare to 64-QAM: About 66.66%

## 2048-QAM modulation

Following are the characteristics of **2048-QAM** modulation.

Number of bits per symbol: 11

Symbol rate: 1/11 of bit rate

Increase in capacity compare to 64-QAM: About 83.33%

Total constellation points in one quadrant: 512

## 4096-QAM modulation

Following are the characteristics of **4096-QAM** modulation.

Number of bits per symbol: 12

Symbol rate: 1/12 of bit rate

Increase in capacity compare to 64-QAM: About 100%

Total constellation points in one quadrant: 1024

Following table compares 512 QAM modulation vs 1024 QAM modulation vs 2048 QAM modulation vs 4096 QAM modulation types and derives difference between 512-QAM, 1024-QAM, 2048-QAM and 4096-QAM modulation techniques.

Specifications |
512 QAM |
1024 QAM |
2048 QAM |
4096 QAM |
---|---|---|---|---|

Number of bits per symbol | 9 | 10 | 11 | 12 |

Symbol rate | 1/9 th of bit rate | 1/10 th of bit rate | 1/11 th of bit rate | 1/12 th of bit rate |

Total points in constellation diagram | 512 | 1024 | 2048 | 4096 |

Increase in capacity compare to 64-QAM | 50 % | 66.66 % | 83.33 % | 100 % |

Let us understand advantages and disadvantages of QAM over other modulation types.

## Advantages of QAM over other modulation types

Following are the advantages of QAM modulation:

• Helps achieve high data rate as more number of bits are carried by one
carrier. Due to this it has become popular in modern wireless communication system such as
WiMAX, LTE, LTE-Advanced etc. It is also used in latest WLAN technologies such as 802.11n 802.11 ac, 802.11 ad etc.

## Disadvantages of QAM over other modulation types

Following are the disadvantages of QAM modulation:

• Though data rate has been increased by mapping more than 1 bits on single carrier,
it requires high SNR in order to decode the bits at the receiver.

• Need higly linear PA (Power Amplifier) at the Transmitter.

• In addition to high SNR, higher modulation techniques need
very robust front end algorithms (time, frequency and channel) to decode the symbols without
any error.

## What is Difference between 16QAM, 64QAM, 256QAM, BPSK, QPSK, OQPSK

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## MATLAB CODE

BPSK QPSK 16QAM 64QAM modulation matlab code

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