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Design Article

# Modulation roundup: error rates, noise, and capacity

## 7/6/2008 12:00 PM EDT

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The article compares various digital modulation schemes like BPSK, QPSK, PAM, 16PSK, 32PSK, 16QAM and 64QAM using the following metrics:

(a) Symbol Error Rate vs. Signal to Noise Ratio (SER vs Es/No)

(b) Symbol Error Rate vs. Bit to Noise Ratio (SER vs Eb/No)

(c) Capacity in bits per second per Hertz vs. Bit to Noise Ratio (Capacity vs Eb/No)

(d) Bit Error Rate vs. Bit to Noise Ratio (BER vs Eb/No)

Symbol Error Rate vs. Es/No
Binary Phase Shift Keying (BPSK) Modulation
In Binary Phase Shift Keying, the symbols are used for transmitting information. From the post, Bit error probability for BPSK modulation, the symbol error rate is given as,

.

Pulse Amplitude Modulation (4-PAM)
In 4-PAM modulation, the symbols are used for transmitting information. The symbol error rate for 4-PAM modulation is derived in the post, symbol error rate for 4PAM and is given as,

.

4QAM (QPSK)
In 4-QAM modulation, the symbols are used for transmitting information. The symbol error rate for 4-QAM modulation, derived in the post, symbol error rate for 4-QAM (QPSK) is given as,

16QAM
In 16QAM modulation, the symbols are used. The symbol error rate for 16QAM modulation, derived in the post, symbol error rate for 16-QAM, is given as,

16PSK
In 16PSK modulation, the alphabets is used, where . The symbol error rate for 16PSK, derived in the post, Symbol Error Rate for 16PSK is given as,

.

Note: The formula derived in this post is for a general M-PSK case. For an M-PSK scheme, the symbol error rate is,

.

M-QAM
In a general M-QAM constellation, where and is even, the alphabets used are:

, where .

From the article deriving the symbol error rate for M-QAM,

Figure: Symbol Error Rate vs Es/No (dB) in AWGN

wassouf_salahat

12/22/2008 5:51 PM EST

thatsd great keep going:)

tamdtvt

5/12/2009 1:08 PM EDT

please give me sourse code ??

DerekJC

9/4/2009 6:18 AM EDT

Good article. However, it would be useful to include some constellation plots.

dangermouse

9/16/2011 5:11 PM EDT

So if I'm setting up a RF Central Microwave system for a reality TV show and my options are QPSK, 16QAM, or 64QAM. What should I set the transmitter to, to obtain the best quality in the microwave monitor/receiver? And does anyone know about the FEC: 1/2 2/3 3/4 5/6 7/8
Guard interval: 1/32 1/16 1/8 1/4
What are my optimum settings?

Frank Eory

9/16/2011 6:13 PM EDT

The absolute most robust (error-free) settings would be QPSK, rate 1/2 FEC and 1/4 guard interval -- but that might not give you enough Mbps data capacity for what you're doing.

Step one is figure out the data rate you need to transmit. Step two, dial in the most robust parameters that are just enough to meet that data rate. Step three, cross your fingers and hope there is enough signal to noise ratio for the receiver to catch all the data with an extremely low bit error rate.

banibani

4/25/2012 12:19 PM EDT

plz help me by giving me the formula of 16-APSK bit error rate or symbol error rate.
i need only the equation of APSK bit error rate or symbol error rate.