Communications Toolbox

What the Example Does

The example creates a random digital signal consisting of integers between 0 and 8, and modulates it using two varieties of the 8-ary quadrature amplitude shift keying (QASK) technique. This technique associates each integer in the signal with some point in an eight-point signal constellation, and then uses the associations to create a modulated signal.

There are 8!, that is, factorial(8), ways to associate eight symbols with eight constellation points. One category of configurations implements what is called Gray coding. In a Gray coded constellation, the symbol associated with a given point and the symbol of any of the point's nearest neighbors differ in exactly one bit. Thus, the constellation point associated with the symbol 3 (= 011) can have as a nearest neighbor the point associated with the symbol 1 (= 001), 2 (= 010), or 7 (= 111), but not any other number.

In order to compare the behavior of different constellation configurations, the example modulates the message signal separately using two varieties of 8-QASK modulation. Both varieties use constellations with the same points, but one variety labels the constellation points so as to implement Gray code while the other variety does not implement Gray code. After modulating, the example adds noise to both modulated signals, demodulates both noisy signals, and compares the bit error rates in the two cases.

The example outputs the two bit error rates. The expectation is that although noise might cause demodulation errors in both cases, the errors in the Gray coding case should involve fewer bits. When you execute the example, check to see whether the bit error rate from the Gray coding case is smaller than the bit error rate from the non-Gray coding case.

A Detailed Example

Functions in the Example