Bit Error Ratio or Channel Capacity: Which metric should I use? [Frequently Asked Questions]

[@Wireless-AI]

I find all three points very insightful. In my opinion, low-level physical layer signal processing tasks such as MIMO detection focus on BER. On the other hand, higher-level physical layer optimization tasks such as power allocation and beamforming design, are focused on channel capacity because their optimization objectives are related to SNR.

[@WirelessFuture]

Yes, bit errors are particularly important in decoding algorithms. However, you need all bits to be received without error eventually, so if a codeword is decoded incorrectly, you need to retransmit. If you then measure the bit rate for the correctly decoded bits (compensated for the retransmissions), it will approach the channel capacity if you use a good channel code and long codewords.

[@Julia-hu4xe]

In the transmission MISO channel we have the equation y=h^T*x+n.......the letters h and x are bold faced - but we have just one value for x, is that right? X is a vector and not a scalar in the equation - so in the x vector hase everywhere the same entry, right? Thanks.

[@WirelessFuture]

The bold face indicates that h and x are vectors, with a length equal to the number of antennas. A more precise way to write the model is y[i]=h^t x[i] + n[i], where i is a time index. So during the transmission, we have many x-vectors, on at each discrete symbol time i. The channel vector is constant for many time indices. We typically pick the x vector as a fixed precoding vector (selected based on h) multiplied by a time-varying scalar data symbol. See Chapter 3.2-3.3 in “Introduction to Multiple Antenna communications and Reconfigurable Surfaces” to learn more.

[@PhilMiller-ef4vp]

Thanks for all of your work. With respect to the exercises from your new book, the solutions are in github in a PDF file. Are there any additional files which give a more extenive explanation to the solutions (e.g. video)? Perhaps I missed something. (At some points I struggle to get to the solutions.)

[@WirelessFuture]

Hi! We provide detailed answers in the PDF that you refer to, but not the complete solutions. If we would make that public, the exercises can no longer be used as teaching exercises. If you have questions related to specific exercises, we can try to provide hints here on KZbin.

[@antonyjudice4417]

Hello Dr. Your videos are thought provoking !!!Are signal-to-noise ratio (SNR) and bit error rate (BER) always inversely proportional? could you provide some insights on enhancing channel capacity beyond employing MIMO or multiplexing or advanced modulation techniques?

[@WirelessFuture]

The BER is a decreasing function of the SNR (for any well designed system), but it is generally not inversely proportional. The capacity is the highest possible data rate for a given channel, so the only way to enhance it by “changing the channel”. This can either be done by adding antennas or deploying infrastructure such as relays and RIS in between transmitters and receivers. In multi-user scenarios, to coexistence of the users can possible be modified to strike a better balance between the capacities of the individual users.

[@antonyjudice4417]

@@WirelessFuture Thank you very much sir

[@aimenal-odaini3212]

Thank you for the informative content you keep sharing on this channel. Can you please recommend any research paper that can help me to formulate an expression for the data rate of a specific user connected to an antenna array

[@WirelessFuture]

I would recommend downloading our new book: www.nowpublishers.com/article/BookDetails/9781638283140 You can first read Section 2.4 and then move to Chapter 3, where we step-by-step explain how to obtain the data rate expressions with multiple antennas.

[@Amine1z]

Why are SNR values negative? Does this mean that the signal is significantly smaller than the noise? Additionally, what is the utility of such communications? Thank you for your informative video.

[@bumsupark3074]

Might be the SNR in decibell (dB) scale

[@WirelessFuture]

@bumsupark3074 is correct. The SNR value is often reported on a decibel scale because it can vary greatly, particularly in wireless communications where the propagation distance can be anything from 10 m to 10 km. Negative decibel values represent that the noise power is stronger than the received signal power, but one can still communicate using small-sized modulation schemes and strong channel codes.

[@HarinduJayarathne]

Could you explain how coded modulation capacity I(X;Y) for a fixed constellation fits in with the explanation? I have seen that it is strictly below Shannon capacity but can get very close to Shannon capacity at low SNR.

[@WirelessFuture]

If you want a precise mathematical formulation, then you can read the following book: www-sigproc.eng.cam.ac.uk/foswiki/pub/Main/AG495/bicm_fnt.pdf A simple approximation is the following: Suppose you transmit a block of M-QAM symbols using a block length L and coding rate R. This will result in a block error probability P_L(SNR), which is a decreasing function of the SNR. Then I(X;Y) ≈ log2(M)*R*(1-P_L(SNR)).

[@HarinduJayarathne]

@@WirelessFuture Thank you.

[@divyar8462]

Sir please give basic explanation ideas on ISAC, sensing, localization and tracking

[@ahmeddeiaa3943]

Many thanks for that tutorial It's really beneficial. Would you please make another tutorial for how to calculate the BER?. As its equation varies significantly based on the used system ( single carrier, OFDM, and so...)

[@WirelessFuture]

There are some analytical BER expressions, but mainly for uncoded transmission with BPSK and QPSK. There are barely any analytical expressions for coded transmission, which is what matters in practice. One can compute approximations and bounds, but this is most interesting to understand scaling behaviors. Hence, the simplest and most accurate solution is to run a Monte Carlo simulation where you measure the BER by sending a lot of data using the exact modulation and coding scheme and decoding algorithms as your practical system. We cover Monte Carlo methods in this video: kzbin.info/www/bejne/m2HEYZWcrJaEe9Usi=JANsS8ZOkwiqUzS5

[@ahmeddeiaa3943]

@@WirelessFuture well, thank you. I will give it a try

[@ahmednor5806]

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