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1

Clearly it doesn't make a difference if you use the real part or the imaginary part (as long as you know what you're doing), because $$\textrm{Im}\left\{a(t)e^{j2\pi f_ct}\right\}=\textrm{Re}\left\{b(t)e^{j2\pi f_ct}\right\}\tag{1}$$ with $$b(t)=-ja(t)=a_Q(t)-ja_I(t)\tag{2}$$ So you basically just exchange the in-phase and quadrature components (apart from a ...


3

It's whatever makes the most sense for the problem at hand. Which can get confusing, and the same signal may have multiple definitions of "bandwidth" -- sometimes even in the same document, when, for example, one is reading up on or designing a communications system. Useful Bandwidth A signal's user is interested in the practically useful ...


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Will we be able to recover the complex modulated symbol based on $s_2(t)$ too? Yes, no information is lost between the two. How can we prove that mathematically? One way to think about it is to write out each individually and see what you have. Let $a(t)=a_I(t)+ja_Q(t)$, expanding $s_1(t)$ and $s_2(t)$ we have: \begin{align} s_1(t) &= a_I(t)\text{cos}(...


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I don't fully understand what the OP means by DQPSK but suspect that he believes that the D in DQPSK stands for "differentially coherent demodulation of" QPSK, that is, DQPSK means differentially-coherent demodulation of a plain vanilla QPSK signal, and that in his terminology, differentially encoded DQPSK is differentially-coherent demodulation of ...


0

Channel Capacity and Bit/Symbol Error rate are two different key performance indicators (KPI) of a system. BER/SER, as it's obvious from its name, is number of errors per Bit/Symbol. and you can use channel coding to improve it so it's not a fixed KPI. while Channel Capacity is maximum rate that the system can achieve and it's a fixed KPI. so it make sense ...


1

The Noise Figure of a passive attenuator is indeed the attenuation value of the attenuator. This is because noise figure of a device is by definition the SNR of the output minus the SNR of the input with the input terminated with the characteristic impedance of the system (typically 50 ohms). Similarly, using the same relationship to SNR, the noise figure ...


1

RF direct sampling architecture? Will there be DC offset? No, since the center of your signal doesn't end up on DC, so there's no DC offset. If not, then is it okay not to insert a DC null? yes. However, you might want to use quadrature mixers for the other end, so you might not want to do that. Also note that instead of direct sampling, superhet / low-IF ...


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Both indicators are used. It depends what you mean in speaking of your indicators. One of common usages is to compare systems where we use indicators of the same type. For example, to compare 5G NR and LTE RANs, we usually use max throughput which is defined as the multiplication of number of antennas, number of subcarriers and QAM order per subframe. There ...


1

A polyphase channelizer is not a special kind of filter. It is a structure that works well when using filters in multi rate settings. Polyphase is a sampling rate conversion method that leads to efficient implementations that are useful for building filter banks. The efficiency comes from only having to design one filter. The downside is that the extracted ...


0

Analog AGC is mainly used to increase the signal level to match the ADC sensitivity? Is Analog AGC also used to attenuate the signal?. For "Analog AGC" we use analog control components (typically voltage variable amplifiers and voltage variable attenuators) to adjust the receiver gain, and we use an analog power detector to measure the total band ...


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Loosely speaking: Capacity is the supremum of data rate that one can send data with arbitrarily small error probability over a given channel; ergodic capacity is also the supremum of rate with arbitrarily small error probability, but for fading channels, in assuming the fading process is ergodic, as the term "ergodic" suggests; spectral efficiency ...


2

The idea of solving the integral in the frequency domain is good, but you made a mistake rewriting the integral. Note that $$\int_{-\infty}^{\infty}\phi_n(t)\phi_k(t)dt\tag{1}$$ equals the Fourier transform of $\phi_n(t)\phi_k(t)$ evaluated at $f=0$. As you know, that Fourier transform is given by the convolution of the two individual Fourier transforms of $\...


0

No problem at all if $B_s \ll B_c$. However, $B_s = 10\text{Hz}$ is considerably small that makes synchronization very difficult especially for low-cost receivers. For example, Sigfox Ultra Narrow Band uses $10\text{Hz}$ bandwidth (are you studying the standard?) that requires precise but expensive oscillators like TCXO. Even with that, there must be random ...


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The answer is yes it is possible and any amount of frequency offset can be corrected to the extent your sampling rate is sufficiently high enough for unambiguous frequency resolution over ±10 KHz. A very simple frequency discriminator that can be used in a carrier tracking loop is further described at this post:Carrier frequency offset estimation for QPSK ...


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The power of a deterministic signal $s(t)$ is given by $$P_s=\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^Ts^2(t)dt\tag{1}$$ A unit power signal is obtained by normalizing $s(t)$ by the root of its power: $$\hat{s}(t)=\frac{s(t)}{\sqrt{P_s}}\tag{2}$$ In the case of $s(t)=A\cos(2\pi f_0t)$ you obtain from $(1)$ $$P_s=\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^TA^2\cos^...


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There doesn't seem to be much discussion of CRC in this forum but on the sister site math.SE, there are several postings. See, for example, CRC Computation or What is the theory behind seeding a CRC.


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In general terms, it is usually advantageous to down-sample to the lowest sampling rate wherever possible- all things being equal it would be better to reduce to a lower sampling rate earlier in the receiver processing - for purposes of reducing resources required, power dissipation, etc. The OP is using both a CIC and timing recovery block where the ...


1

I would suggest you to use the GnuRadio API usualy used for Software Defined Radio (SDR) projects. As Marcus Müller said in the comments, it is easier to develop this kind of project and test it with a software implementation. I am also pretty sure that you will find a lot of existing examples to help you with your project. Guided Tutorials API documentation ...


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That is the whole point of decoding: to get the original sequence back, if possible. So, this is doing exactly what you'd want. In many decoders (such as the Viterbi), the transmitted code bit sequence is never explicitly recovered anywhere. As Dilip's answer shows: You can, however, determine the original transmit sequence by re-encoding the decoded bits. ...


3

Yes, it is possible to determine the path that the Viterbi algorithm found through the trellis. Just apply the encoding algorithm to what you are calling Y_dec and you will get the corresponding codeword of length $2048$. You can then compare it to Y, the transmitted codeword, to see where the channel made errors. Additional notes: If the data to be ...


1

What you did by saying a $0$ bit is mapped to a voltage of zero Volts, and a $1$ bit is mapped to $5$ Volts is exactly what it means to map bits to symbols. Your symbols are 'zero Volts' and '$5$ Volts'. A bit is just a unit of information, and you have to decide which type of analog signal you choose to transmit the source information. You always have to ...


1

As provided pics show, there is no difference between the DC value of input and output signal of the filter i.e. they are both zero. but there is a problem in your filter design and that is, you set the 'FilterOrder' key to 1. I think its better to remove 'FilterOrder' key and its value and let the algorithm choose the smallest filter order for you. As for ...


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According to my reading, LDPC is almost the best channel coding we can use for channel coding, but I have a question regarding that kind of coding. Mentally, something being "the best" should always instantly raise a mental flag for you, saying "under which conditions, according to which measure". It is right that iterative LDPC decoders ...


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Stop thinking about the maths and just think about the reality. You have 1 receiver. That means there is a signal coming from the receiver into the processor. There is only one signal. You can't measure it twice and get two different signals. You may be thinking of the channel matrix, which has dimension 1x4 (not 4x1, sorry). That's because the channel ...


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Multi-input single-output (MISO) is describing the inputs and outputs of the system. In communication, this is the channel, so if you have a single-output it means that the received vector is $1 \times 1$. The general model for a MISO system is: \begin{split} y &= \mathbf{h^Tx}+\text{noise} \\ &= (h_1x_1+h_2x_2+...+h_Nx_N)+\text{noise} \end{split} ...


2

Note that for the complex noise envelope $z(t)=x(t)+jy(t)$, the autocorrelation $R_z(\tau)$ is defined by (cf. Eq. $(4.1.47)$ in Proakis) $$R_z(\tau)=\frac12E\big\{z^*(t)z(t+\tau))\big\}=\frac12\big[R_x(\tau)+R_y(\tau)\big]+j\frac12\big[R_{xy}(\tau)-R_{yx}(\tau)\big]\tag{1}$$ As shown in the chapter you refer to, for the real-valued bandpass noise $n(t)$ to ...


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welcome. As MMSE estimators are unbiased, try reducing Cramér–Rao bound and maybe your MMSE equalizer can achieve a better performance. Note that in general the MMSE estimator is known to be asymptotically efficient. Note also that you must specify criteria before say something is "optimal". Even so, it is usually not easy to prove the optimality.


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