Several energy normalization problems in communication system simulation

(Note: Part of this article is transferred from the Internet)
1. How is the constellation mapping normalization factor obtained?
A: All energy averaged after the root obtained is the waveform amplitude value, the inverse is the normalization factor. For example, such as 16QAM, the value is, the energy of 2 has 4 constellation points, 10 has 8 points (+-1+-3i), 18 has 4 points, a total energy 72+80+8=160, and then the 16 points of the equal probability distribution is 16 1, so to 160 divided by 16=10, which is the average energy, Its average after the waveform amplitude of sqrt (10), and QPSK a total of 4 Energy 2 constellation, the probability of One-fourth, so 8 divided by 4=2, the result is sqrt (2), and other analogy.

2. What is the use of energy (power) normalization? A: The power normalization factor is added to allow the same average power to be achieved for different modulation modes (or for all mappings). In fact, normalization is to facilitate the comparison of system performance, so it is necessary to distinguish between the module is what. For example, the gain problem of channel coding, whether there is no channel encoding, the bit energy is the same, so the comparison should be based on eb/no, rather than to enter the channel before the symbolic energy es/no as a benchmark. For example, in the comparison between the space-time code system and a single antenna system, or to enter the space-time code before the signal energy as a benchmark, then the total energy transmission is consistent, that is, the space-time code system of each antenna transmit power sum should be the same as the transmission power of the single antenna system. Generally, normalization is handled at the transmitter.

3. When simulating the ifft transformation of OFDM, why multiply the sqrt (number of FFT points) for normalization? A: in MATLAB after the ifft to multiply sqrt (FFT points), so as to ensure that the same power in the time domain and frequency domain, otherwise in the calculation of power error, if not multiply you just know is also possible. As for the signal power normalization, it is for more convenient calculation of Snr, is to compare the performance under the same standards.

Several energy normalization problems in communication system simulation