• State Resolved
  • Locked Locked
  • Replies 1 reply
  • Subscribers 99 subscribers
  • Views 453 views
  • Users 0 members are here
Support feedback
Options
Options
Related

This thread has been locked.

If you have a related question, please click the "Ask a related question" button in the top right corner. The newly created question will be automatically linked to this question.

The question about the SNR definition

Jacki Hsu
Intellectual 330 points

 

Hi

 

 

According to the training video "Cascaded Radar And Body & Chassis Automotive Applications", the TX Beamforming can improve a factor of 2 compared to MIMO (20log10(NTX) vs. 10log10(NTX) in MIMO).

Is there any reference to understand and deriviation of the relationship?

 

 

Thanks

  • 0
    TI__Mastermind 18500 points

    Hi Jacki, 

    The difference is where the increase in gain is being documented.

    TX-BF utilizes N simultaneous TX elements to transmit up to N times as much power. Our example TDMA-MIMO utilizes a single TX element and N RX elements. In the TX-BF case we are documenting the increase in output power due to the number of simultaneous TX. In the TDMA-MIMO case, we are documenting the increase in received voltage waveforms across the cumulative RX array.

    For the TX-BF case: 

    Assuming a simple bore-sight, 0-phase, scenario, you can multiply the output power of each element together. This yields a gain  in dB of 20 * log (N). 20 * log is used since the basic unit being computed for the gain calculation is a unit of power derived from a squared magnitude. For example, the individual E-field power radiated by each TX element is approximately the E-field-magnitude ^ 2, converting to dB -> 10 * log (|E-field|^2), then simplifying -> 20 * log (|E_field|) for a single element.

    Then comparing 1 element to N elements, you have  20 * log (N * |E_field|) / 20 * log (|E_field|)  -> approximately 20 * log (N) increase in output power, and subsequently in RX power or SNR for an N-element TX-BF array. 

    For the TDMA-MIMO case: 

    Assuming we are talking about just a single TX antenna per TDMA phase and N RX antenna, the system receives N ADC IQ sample waveforms (complex voltages), one from each receiver chain. Again we can convert to dB for a single RX virtual antenna path -> approximately 10 * log (V), then comparing to N RX, this becomes 10 * log(N * V). Comparing the single RX to the N RX you have 10 * log (N * V) / 10 * log(V) -> approximately 10 * log(N) increase in RX voltage gain. 

    Please let me know if that helps answer your question on this topic. 

    Thanks,

    -Randy