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Python - QAM
Introduction
In order to structure the utility relating to constellation modulation, I wrote a class Quadrature_Amplitude_Modulation in Python.
TR38.901
3GPP TR38.901 offers the guidance and methodology of channel modelling, including both system-level simulation (SLS) and link-level simulation (LLS).
[Read More]Kalman Filter
Without loss of generality, the probability density function (pdf) of Gaussian distribution can be denoted by function \[\begin{aligned} N(x, \mu, \sigma) = \frac{1}{\sqrt{2\pi}\sigma} e^{-\frac{(x-\mu)^2}{2\sigma^2}}, \end{aligned}\] where \(\mu\) and \(\sigma\) are the mean and standard deviation repectively. Then, we have \[\begin{aligned} N(x, \mu_1, \sigma_1) N(x, \mu_2, \sigma_2) = \frac{e^{-\cfrac{(\mu_1-\mu_2)^2}{2(\sigma_1^2+\sigma_2^2)}}}{\sqrt{2\pi(\sigma_1^2+\sigma_2^2)}} N\left(x, \frac{\mu_1\sigma_2^2 + \mu_2\sigma_1^2}{\sigma_1^2 + \sigma_2^2}, \frac{\sigma_1^2\sigma_2^2}{\sigma_1^2+\sigma_2^2}\right) \end{aligned}\]
Python - Matplotlib
Background
Matplotlib is a popular python package for figure plot and data visualization.
C++ - Basic
本文是阅读 Professional C++, third edition 中文版1的读书笔记.
[Read More]NR - Cell Search
Synchronization signals
In NR, synchronization signals consist of primary synchronization signal (PSS) and secondary synchronization signal (SSS). Together with physical broadcast channel (PBCH), PSS and SSS are jointly termed synchronization signal block (SSB1).
A SSB spans 4 OFDM symbols in the time domain and 240 subcarriers in the frequency domain. Within a SSB, the PSS and SSS lie in the 1st and 3rd symbol, respectively. The PBCH situates in the 2nd and 4th symbols, as well as the 48 subcarriers on the each side of the SSS (in the 3rd symbol), as shown in the figure below. Therefore, within a SSB, there are totally \(240 + 48 \times 2 + 240 = 576\) RE's for PBCH transmission2.
It should be noted that 60kHz numerology cannot be used for SSB transmission.
The SSB is periodically transmitted and the periodicity can be 5/10/20/40/80/160ms. But a UE always assumes that a SSB is repeated at least once every 20ms no matter whether it is the truth.
PSS
Similar to LTE, there are 3 PSS sequences, including a basic m-sequence of length 127, and its two cyclically shifted versions3. The initial values of the basic sequence are {0, 1, 1, 0, 1, 1, 1}. The subsequent values can be derived according to \[\begin{aligned} x_0(n) = x_0(n - 7) \oplus x_0(n - 3). \end{aligned}\] Then, the cyclically shifted sequences can be obtained by \[\begin{aligned} x_1(n) = x_0(n + 43 \mod 127), \\ x_2(n) = x_0(n + 86 \mod 127). \end{aligned}\]
SSS
There are 336 SSS sequences which are the sums of two m-sequences with different shifts, i.e., \[\begin{aligned} x_{m_1, m_2}(n) = x(n + m_1) + y(n + m_2), \end{aligned}\] where the two m-sequences can be obtained according to \[\begin{aligned} x(n) = x(n - 7) \oplus x(n - 3), \\ y(n) = y(n - 7) \oplus y(n - 6). \end{aligned}\]
NR - Demodulation Reference Signal (DMRS)
Conceptions
Just as its name indicates, demodulation reference signal (DMRS) is the reference signal dedicated for demodulation. Different from LTE system, the DMRS in NR system is comprised of a frontloaded DMRS and a few optional additional DMRS.
Frontloaded DMRS
Frontloaded DMRS aims to reduce the duration of demodulation and decoding. There are a couple of mapping schemes.
- Mapping type A: it lies the symbol second to the PDCCH region, e.g., in normal-slot-based transmission.
- Mapping type B: it begins with the first data symbol scheduled, e.g., in mini-slot-based transmission.
Additional DMRS
Additional DMRS is proposed to support high speed mobility, e.g., 500km/h. Each additional DMRS is a simple repetition of the corresponding frontloaded DMRS, e.g., identical subcarriers and equal OFDM symbol number.
- For single-symbol frontloaded DMRS, up to 3 additional DMRS can be supported.
- For double-symbol frontloaded DMRS, at most 1 additional DMRS is supported.
NR - Channel State Information Reference Signal (CSI-RS)
Introduction
In NR system, channel state information reference signal (CSI-RS) plays a variety of roles, including
- CSI measurement
- Beam management
- Tracking
- Mobility management
- Rate match
Generally, there are two types of CSI-RS, termed non-zero-power (NZP) CSI-RS and zero-power (ZP) CSI-RS, respectively. The former is configured by .
NR - Downlink Codebook
In NR release 15, there are roughly two types of codebooks for spatial-domain CSI acquisition, termed type I and type II, respectively. The former is comprised of a finite set of vectors or matrices, as the same as the codebook in LTE systems. While for the type II codebook, each precoding vector is represented as a linear weighted sum of an incomplete orthogonal basis vectors. Further, frequency-domain compression is introduced in NR release 16 for enhancement, which is expected to remarkably reduce the feedback overhead. Note that this section aims to reveal the rationale behind the codebook design, in lieu of covering everything detail related in the specifications.
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