Similar signal-to-noise ratio and its application in design

introduction

In digital communications systems, the received signal-to-noise power spectral density ratio (Pr/N0), the received bit energy to noise power spectral density ratio (Eb/N0), and other similar signal-to-noise ratios (SNRs) are often defined inaccurately at the input point of the receiver circuit. This inaccuracy comes from some common uncertainties, including where these SNRs should be defined and measured, and where the appropriate and accurate reference point for Eb/N0 in the receiver system should be located. This uncertainty inevitably leads to errors, which is compounded by the incorrect assumption that local SNR measurements correspond to a system SNR model (which is not always the case). In addition, the receiver circuit designer often chooses a physical location for the SNR (and system temperature) model inside the receiver circuit that is different from the location that the system designer usually uses as a reference. To reduce potential errors, designers need to clearly distinguish between measurements and models, and must fully understand how the simulation of these receiver circuit SNR parameters evolves. In addition, by recognizing the differences in the communication system (where the SNR and system temperature should be measured), mistakes can be avoided in system analysis.

Circuit Component Models

A digital communication receiving circuit system (Figure 1) includes a receiving antenna, a loss line, a receiving circuit mainly composed of an amplifier, a correlator or a matched filter and a sampler, and a detector functional block that performs discrete decisions. For simplicity, the functions such as down-conversion and equalization in the receiving circuit functional block are not shown, and the entire receiving circuit functional block will be treated as a single circuit element. It is assumed that the thermal noise that corrupts the received signal has a flat power spectral density and its amplitude is N0 = kT (W/Hz), where k is the Boltzmann constant and T is the temperature value in Kelvin units.

Figure 1 Receiving circuit system

Figure 2 Noise temperature input source

The concept of effective noise temperature is a simple model that allows the design engineer to represent the internal noise of a circuit element as a noise temperature input source for an ideal circuit. Figure 2a shows this concept applied to an amplifier and attenuator and summarizes the two relationships:

TR=(F-1)290 Kelvin (1)

TL=(L-1)290 Kelvin (2)

Where TR and TL are the effective temperatures of the amplifier (receiving circuit) and attenuator (lossy line), respectively, and F and L represent the noise spectrum and loss factor, respectively. Figure 2b is a model applied to a pair of cascaded circuit elements (a lossy line plus an amplifier), where the gain of the lossy line can be expressed as 1/L.

Therefore, the composite noise temperature Tcomp can be expressed as:

Tcomp=TL + LTR (3)

Multi-point measurement mode

[page] When measuring SNR at a location in the receiver circuit, T represents the local noise temperature (Tlocal) at that location. As shown in Figure 3, Tlocal (whose effect can be measured at a chosen observation point or reference point) represents the source noise power. The effect of the load is negligible because it will be canceled when calculating the SNR.

Figure 3 Multipoint receiving system

FIG3 shows three measurements of Tlocal and Pr/N0 at locations A, B, and C in the receiving system. The superscripts A, B, and C in the parameters indicate that the measurements were performed at these different locations.

SNR measurement usually uses the following steps:

An information signal is applied to the communication system and the power of the received waveform is measured at the output of the receiving antenna. The power of the received waveform is proportional to the power of the sum of the signal and the noise.

Filter out the signal and measure only the received noise power. The final step is to subtract the noise power from the first measurement to calculate the signal power to noise power ratio, or SNR.

The demodulation/detection function of the receive circuit can be broken down into two steps.

In the first step, during each symbol duration, the correlator or matched filter recovers a baseband pulse representing the digital symbol and then samples it. The output of the sampler (point C), the pre-detection point, generates a test statistic that contains two components: the received symbol and the noise. The voltage value of the test statistic is proportional to the energy in the symbol and the noise, and thus contains the basic measurement information of the SNR.

[page] The second step is to make a decision (detection) on the discrete meaning of the symbol, the result of which is an information bit (digital bit for binary modulation). The accuracy of the detection is a function of the pre-detection SNR. In digital receiving systems, the pre-detection point is an important position for all error performance analysis. The bit error probability PB is a function of Eb/N0. It is an important function of the detector block to derive this function. The more energy the signal in the sample (relative to N0), the better the error performance.

So the simple answer to where Eb/N0 is is to define it at the pre-detection point. The problem is that the answer is too simple because it does not reflect the model that is typically used when specifying these SNRs. It should also be noted that Eb/N0 is defined at a point where there are no information bits. The information bits appear after the detection process is complete. Perhaps a more appropriate name for Eb/N0 would be the energy per effective bit relative to N0.

Conclusion

In the early days of digital communications, Pr/N0 was measured directly at point C in Figure 3, or at point A at the output of the receiving antenna, and then converted to the pre-detection point to account for the SNR degradation caused by lossy lines and receiving circuits. R is the data transmission rate in bits per second.

Once the received pre-detection SNR was used to describe the communication system, it was quickly realized that the available system model for Pr/N0 would also allow the same pre-detection SNR to be stated at the receive antenna output (or any reference point in the receive system) in addition to point C. In textbooks, Pr/N0 and Eb/N0 are often stated at the receive antenna output point. This can be confusing because one would think that a simple measurement at the receive antenna output point can be used directly as the system SNR in preparation for link budget analysis, which is incorrect. The system SNR or Pr/N0 can only be directly measured at this location, the pre-detection point, but can be simulated at other locations in the receive circuit. Eb/N0 is defined at point C, the pre-detection point in Figure 3. So where should the Eb/N0 in the receive system be located as the reference point in a simulation environment? The same Eb/N0 value can be obtained from the system SNR stated at any point in the receive system. The receive antenna output point is the most common location used as a reference point when a model is used to specify the SNR in the receive system.

Through the above analysis, we have summarized how to establish or specify the correct reference point for Eb/N0 and other similar SNR values ​​in a receiving system. Assuming that there is an accurate model, we believe that any position can be used as an allowable reference point. However, in the development of receiving circuit specifications, the output point of the receiving antenna is the most commonly used reference point in these SNR models.