March 2008 - DSP LOG

Comparing 16PSK vs 16QAM for symbol error rate

In two previous posts, we have derived theoretical symbol error rate for 16-QAM and 16-PSK modulation schemes. The links are:

(a) Symbol error rate for 16-PSK

(b) Symbol error rate for 16-QAM

Given that we are transmitting the same number of constellation points in both 16-PSK and 16-QAM, let us try to understand the better modulation scheme among the two, i.e. to answer the following question:

For the same signal to noise ratio $\frac{E_s}{N_0}$ , will 16-PSK or 16-QAM give a lower symbol error rate?

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Blog on DSP

I happened to visit ‘The Digital Signal Processing Blog’, maintained by Mr. Andres Kwasinski, Ph. D.

In the blog one can find details about the upcoming IEEE conferences pertaining to communication and multimedia processing.
Further, in some of the posts, author shares his thoughts on topics like fixed point arithmetic (here) and wavelets (here) etc.

Thanks,
Krishna

Symbol Error Rate for 16PSK

In this post, let us try to derive the symbol error rate for 16-PSK (16-Phase Shift Keying) modulation.

Consider a general M-PSK modulation, where the alphabets,

$alpha_{16PSK} =\sqrt{E_s}\left\{1,\ e^{\frac{j2\pi}{M}},\ e^{\frac{j4\pi}{M}},\ \ldots,\ e^{\frac{j2\pi(M-1)}{M}} \right}$ are used.

(Refer example 5-38 in [DIG-COMM-BARRY-LEE-MESSERSCHMITT])

Figure: 16-PSK constellation plot

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Frequency offset estimation using 802.11a short preamble

From the previous post on OFDM (here), we have understood that an OFDM waveform is made of sum of multiple sinusoidals (also called subcarriers) each modulated independently. In this post, let us try to understand the estimation of frequency offset in a typical OFDM receiver (using the short preamble specified per IEEE 802.11a specification as a reference).

Understanding frequency offset

In a typical wireless communication system, the signal to be transmitted is upconverted to a carrier frequency prior to transmission. The receiver is expected to tune to the same carrier frequency for downconverting the signal to baseband, prior to demodulation.

Figure: Up/down conversion

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