QAM Demodulation With Low Power Signal

Hello All

Lets assume we're using 64QAM with unit average power and gray encoding.

The modulated representation corresponding to symbols :

1 => -0.923 + 0.659i

2 => -0.923 + 0.132i

.

.

45 => 0.659 - 0.659i

.

.

The received symbols can be found as

rx_symbols = H * tx_symbols;

My question rises here, the received symbols are:

-8.005 e-05 + 5.717 e-05i

-8.005e-05 + 1.143e-05i

.

.

.

5.717e-05 - 5.717e-05i

.

.

How can I demodulate them ?

Using qamdemod with unit average power results high errors since it requires higher amplitude symbols as in given above (modulated symbols)

demodulated_symbols = qamdemod(rx_symbols ,M,"UnitAveragePower",true);

instead I tried :

rx_symbols = rx_symbols ./mean(abs(rx_symbols ));

This operation amplified average power to be 1 but if there are low amount of symbols to take mean, it becomes biased and again results errors.

For example, this normalization resulted 1.8% symbol error rate for 30 symbols received but 30% symbol error rate for 3 symbols received.

**Real Question :**

**What is the proper way to demodulate received low power signal ?**

in MATLAB forums, they do not change signal power, instead they change noise power to adjust SNR, but I need to change signal power while keeping thermal noise constant (as in real life)

Answer 1

[Abhimenyu]

Hi Can,

I understand that you are using 64QAM on your low powered signals and want to demodulate them, and this can be achieved in two ways:

The first method is as follows:

• Step 1: Normalize the received symbols to have average power of 1.

rx_symbols_normalized = rx_symbols ./ sqrt(mean(abs(rx_symbols).^2)); 

• Step 2: Use the “qamdemod” function to demodulate the normalized symbols.

demodulated_symbols = qamdemod(rx_symbols_normalized, M, 'UnitAveragePower', true); % “M” is to be taken 64 

Normalizing the symbols ensures correct demodulation regardless of the received signal power.

The following second method is a more classic approach:

• Step 1: Calculate the Euclidian distance between each received symbol and the 64 constellation points of 64QAM modulation scheme through the following formula:

distance = abs(rx_symbol - constellation_point);

• Step 2: Find the constellation point and its index, with minimum distance for each received symbol
• Step 3: Map the index of the minimum distance to the corresponding symbol in the 64QAM constellation while minimizing the bit errors. You can use gray encoding table for 64QAM.
• Step 4: Repeat the above steps for all the symbols.

Please, refer to the following links to learn more about QAM technique and “qamdemod” function respectively:

• https://www.mathworks.com/help/comm/gs/examine-16-qam-using-matlab.html
• https://www.mathworks.com/help/comm/ref/qamdemod.html

I hope this helps!

Thank you,

Abhimenyu.