Flow cytometric sorting can be used to separate sperm based on sex chromosome content. Differential fluorescence emitted by stained X- vs. Y-chromosome-bearing sperm enables sorting and collection of samples enriched in either X- or Y-bearing sperm for use to influence the likelihood that the offspring will be a particular sex. Herein we report the effectiveness of flow cytometric sorting of human sperm and its use in human ART procedures.
Methods of Gender Selection
Can sperm sorting improve our chances of having a baby girl? • Sensible Surrogacy
Sex selection by means of infanticide is condemned as outrageously immoral by the Western world. But what about sex selection by means of "sperm sorting"? Is this an acceptable option? It does not involve killing as do sex selection and infanticide by means of pre-implantation diagnosis and selective abortion. While this aspect of the technology is commendable, its morality depends on the purpose for which it is employed. What is involved, rather, is the separation of male sperm from female sperm.
Spinning semen provides a measurement of fertility
There are various reasons for which couples or a single parent desire gender selection. Often the couple has one or two offspring of the same gender and would like to have a child of the opposite gender. Other times the couple or single parent has no children but have a desire to have a specific gender. There are also rare situations in which a parent desires a specific gender to avoid a specific genetic mutation that can be transmitted only to a male or a female offspring.
The idea was to use only XY sperm to fertilize the embryos, and you would get more male embryos. For reasons that remains a mystery, the FDA ruled against gender selection via sperm sorting. But as you pointed out, PGS is flawed because it can only test embryos and the gender is already determined at that point. So your odds of having a boy or a girl are not really helped by the test.