9

There are very few m-sequences of any given length with good cross-correlation properties. Their autocorrelation properties are excellent, but the cross-correlation properties are variable. For example, there are 18 m-sequences of period 127 but to have good cross-correlation properties, one must choose a set of no more than $\require{cancel}\cancel{\text{...


5

disclaimer Because of the lack of document about LoRa CSS in Internet, the analysis below may be wrong with respect to LoRa system, not to the (linear) CSS principle. Any comment or update are appriciated. Thanks. LoRa CSS modulation LoRa CSS uses linear chirp spread spectrum. To transmit $\log_2 M$ bits, LoRa CSS modulation divides bandwidth $[-\frac{B}{...


4

Let's start by fixing a symbol rate $R_s$ symbols per second. To modulate $R_s$ symbols per second without ISI, Nyquist says that we need a bandwidth at least $BW_0=1/R_s$ Hz. With spread spectrum, we use more bandwidth, say $M$ times, than what Nyquist advised. The used bandwidth is $BW=M\times BW_0=M/R_s$. In LoRa specifications, $BW=125, 250, 500 \...


4

Yes, it is possible to hide data inside audio files using FSSS technique. Have a look at this publication and this one. Since HAS (Human Auditory System) is more sensitive than HVS (Human Visual System), you are usually limited with audio steganography comparing to image steganography. There are not many detalied publications with "Audio Steganography" tag....


3

If I'm only using bandwidth B1, doesn't that mean I can filter some of the noise out? And if so, would I be able to get S/N down? Wouldn't that be an alternative to occupying the full channel bandwidth? Capacity increases linearly with bandwidth, but only logarithmically with SNR. So, increasing SNR by decreasing bandwidth is a bad idea if your noise isn't ...


3

You are mixing up two different notions that have little to do with each other. The use of spread-spectrum signaling is not in an effort to achieve (or even approach) the capacity of the (wideband) channel. Indeed, the spread signal uses only a small fraction of the capacity of the wideband channel, and the rest of the capacity is available for use by ...


3

In brief, we consider the channel as frequency-selective channel if the frequency of the signal is larger than then frequency of channel No offense, but that ought to win the prize for the least-accurate definition of frequency-selectivity I heard ;-) What you mean is channel is frequency-selective if the bandwidth of the signal is larger than the ...


3

Just despread the same way with two different integrate and dump times for your two symbol types with appropriate blanking on each between longer and shorter code sequence periods. I would be tempted to do all the acquisition and tracking on the longer symbol and then simply despread the shorter symbols using the synchronization from the longer one— with ...


3

Spreading refers to the process of multiplying your data sequence with a higher rate PRN sequence often but not necessary such that one complete duration of a repeating sequence occupies the time duration of one data symbol. For example one such modulation using BPSK to send a “1” you send the entire sequence before it repeats and to send a “0” you send the ...


3

In order to work well, a jamming signal must be well-correlated with the signal it is trying to jam. In the case of sine-wave modulated signals, it's easy to detect the signal one wishes to jam, to infer that it's narrowband (and, hence, riding on a real or suppressed sine-wave carrier), to infer its bandwidth, and from there to choose a suitable jamming ...


2

! The answer by @cbos is correct in spirit but wrong in its details. In an answer on crypto.SE, I wrote "The Berlekamp-Massey algorithm is an iterative algorithm that solves the following problem. Given a sequence $s_0, s_1, s_2, \ldots$ of elements of a field, find the shortest linear feedback shift register (LFSR) that generates ...


2

There are many ways to do this. A simple method is to take the current value of the register (not just its output) as the carrier frequency selector. For instance, a (6,1) LFSR with 63 states can select between 63 different channels. Other methods are based on cubic and quadratic congruence codes. I don't know much about them myself, but look up the papers ...


2

If your wireless channel has bandwidth $B$ but your signal has bandwidth $B_1 < B$, there are a few things you can do: If your data rate is satisfactory, don't use a channel of bandwidth $B$, use one of bandwidth $B_1$! Assuming you're paying for your bandwidth, you'll save money. Note that Shannon's theorem also applies when you use $B_1$ instead of $B$....


2

Assuming one antenna transmits one symbol per time unit, then 16 symbols require 4 time units to be out. Then it is simply that r_1 = H_1 * x_1(1:4) r_2 = H_2 * x_1(5:8) r_3 = H_3 * x_1(9:12) r_4 = H_4 * x_1(13:16) If channel H is fixed during these 4 time units, [r_1 r_2 r_3 r_4] = H * [x_1(1:4) x_1(5:8) x_1(9:12) x_1(13:16)]; or r = reshape(H*reshape(...


2

This can be accomplished by changing the carrier frequency using a Numerically Controlled Oscillator (NCO) which maintains an accurate and continuous phase versus time trajectory via the phase accumulator. This is markedly different than changing the frequency with a classical PLL where we would typically break and reacquire lock to change frequency ...


2

The disadvantage is that the signal V21 = V1 + V2 = [2, 0, 2, 0] disappears every other chip interval which makes maintaining carrier and phase synchronization more difficult. Also, while the total energy in V21 is equals to the sum of the energies of V1 and V2, V21 uses 4 times the instantaneous power needed by either V1 or V2 and so the transmitter needs ...


2

There is no requirement that Direct Sequence Spread Spectrum (DSSS) have an integer number of chips per symbol, nor for the repetition rate of the code to be synchronous with the data (although this is often done). So in this case you have a spreading sequence with a code of some particular length that is running at 6.138Mcps that is multiplied by your data ...


2

This is the common case for receiving spread spectrum signals since we do not know carrier frequency and phase offset but can determine that from the complex output of our correlators. Each correlator (Early, Prompt and Late) would be complex; the complex Prompt correlator output is used for Carrier Recovery (measure rate of rotation or change in phase from ...


2

A Pseudo-random noise (PRN) sequence ia a closer approximation to white random noise in that its energy is spread equally over the occupied frequency band (The energy is spread as a Sinc function if reconstructed with pulses just because of the pulse shape but the underlying code as a stream of impulses has a more uniform distribution), and its auto-...


2

Yes, that is the whole point of Gold sequences. If $x$ and $y$ are a pair of preferred m-sequences of period $N$, then their periodic cross-correlation function is bounded. It also happens to be take on only three distinct values. The $N+2$ Gold sequences are $$x,~~ y,~~ x\oplus y, ~~x\oplus Ty, ~~x\oplus T^2y,~~ \cdots, ~~x \oplus T^{N-1}y$$ (where operator ...


1

OK, let me explain that for you. First, if you want to understand anything in engineering, it's recommended to write it in mathematical form, then try to solve it theoretically and build its code accordingly. Second, regarding your question, is it possible to use MRC for MIMO - CDMA, Yes, that's possible, why not? Now, The code you provided is not right. ...


1

Your query is mixing up ideas and formulas from very different systems to arrive at very questionable answers. The expression $\frac 12 \log_2(1+\text{SNR})$ is the capacity (measured in bits per use) of a discrete-time Gaussian channel. The model for this channel is that the $i$-th use of the channel consists of the transmission of a single real number ...


1

That's right, you can do spread using the kroon function, but be careful what you spread is not the data, it's the whole possibilities of data which is mod.The data is one of them, which is either, 0.7+0.7i or 0.7-0.7i ...etc. then you should know how you can do despread in the receiver side too. Good luck


1

Walsh-Hadamard matrix is usually used for DS CDMA. In this case, $\mathbf{x}$ contains symbols from different users. Since your matrix $\mathbf{H}$ is $4\times 4$, then the vector $\mathbf{x}$ must be of length of $4\times 1$. This means that you can support $4$ users at any given time. So, the answer to your question is no, you cannot spread a signal of ...


1

Yes you can, because you do spreading for each bit of data. So, regardless the length of your data, you are going to spread every bit on your code. In case if you have $x = 10$ you will have data after spreading with length 8, and if $x=101101$ you will have data to send with length 4 x 6 = 24. Just try to understand the process of spreading (I think it's ...


1

I totally agree with the above comments, but I'd like just to add a small note: CDMA is a special case of spread sequence, I mean using spread sequence doesn't mean that you are using CDMA. Spread sequence is using the sequence to spread your signal. for example if your signal is 1, then you can use the sequence 0101001 in order to spread the signal 1 ...


1

When you multiply the real and imaginary parts by $\mathbf{W}_1$ and $\mathbf{W}_2$, respectively, the resulting signal is no longer $S$. It will be a matrix. Regarding your questions: 1- Yes, the signal after spreading has the same duration. 2- One of the disadvantages of Walsh-Hadamard codes is that they don't have clear auto-correlation peak, which ...


1

$$A\cos(2\pi f+\theta_1)+B\cos(2\pi f+\theta_2)=C\cos(2\pi f+\theta_3)$$ where $$C=|u|\quad\textrm{and}\quad \theta_3=\arg\{u\}$$ with $$u=Ae^{j\theta_1}+Be^{j\theta_2}$$ The constant $C$ can be written as $$C=\sqrt{A^2+2AB\cos(\theta_1-\theta_2)+B^2}$$


1

As the answer by @MBaz points out, one can use the contents of a $n$-bit maximal-length binary LFSR to select from $2^n-1$ different frequencies to hop to, thus creating a frequency-hopping sequence of period $2^n-1$. The difficulty is in creating more than one frequency-hopping sequence for use in a multiple-access scheme: the FH/CDMA scheme that the OP ...


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