Receiving sensitivity index analysis

JasonYoo

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Receiver sensitivity index analysis
This article analyzes some problems encountered in receiver design and testing, such as the impact of noise coefficient on receiver sensitivity; the impact of local oscillator frequency error on receiver sensitivity; the relationship between the two expressions of receiver sensitivity, etc. Due to the limitations of my theoretical level, there must be many misunderstandings. Please discuss the inappropriateness. Receiver sensitivity is to test the
ability of base station receivers to receive weak signals. It is a decisive technical indicator that restricts the uplink range of base stations. It is also one of the technical indicators required to be tested in the air interface standard of the RCR STD-28 protocol. Reasonable determination of receive sensitivity directly determines the performance and feasibility of large base station RF transceivers. It is a quantitative measure of the overall performance of the receiving system of the CSL system. Receiver sensitivity refers to the minimum received power measured at the antenna port of the user terminal while ensuring that the bit error rate (BER) does not exceed a certain value. Here, BER is usually taken as 0.01. The receiver's receive sensitivity can be derived as follows:
According to the definition of noise coefficient, the input signal-to-noise ratio should be:
(S/N)i=NF(S/N)o,
where NF is the noise coefficient and the input noise power Ni=kTB. When (S/N)o satisfies the bit error rate less than 10-2, that is, the noise threshold, the power Si of the input signal is the receiving sensitivity:
Si=kTBNFSYS(S/N)o (1)
Where:
k: Boltzmann constant (1.38×10-23 J/K);
T: absolute temperature (K);
B: noise bandwidth (Hz);
NFSYS: receiver noise coefficient;
(S/N)o: noise threshold.
k and T are constants, so the receiver sensitivity is expressed in logarithmic form, and we have:
Si = -174dBm + 10lgB + NFSYS + (S/N)o (2)
For example, for a PHS system with a noise figure of 3dB, its bandwidth is 300KHz. If the system sensitivity is -107dBm, the noise threshold of the system is:
(S/N)o = 174-107-10lg(3×105)-3 = 9.2
From the above formula, it can be seen that in order to improve the receiver sensitivity, that is, to make Si smaller, we can start from two aspects: one is to reduce the system noise figure, and the other is to make the noise threshold as small as possible.
π/4DQPSK has three demodulation methods: baseband differential detection, intermediate frequency differential detection, and discriminator detection. It can be proved [1] that the three incoherent demodulation methods are equivalent. We take baseband differential detection as an example for analysis. In a steady-state Gaussian channel with ideal transmission characteristics, the bit error rate curve of baseband differential detection is shown as the solid line in Figure 1 [2]. It can be found from the figure that when the bit error rate BER is 0.01, the noise threshold (S/N)o is 6dB. For the above example, its noise threshold still has the potential to be further developed.

Figure 1 Bit error rate performance of π/4DQPSK and the impact of phase drift Δθ=2πΔfT
caused by frequency difference Δf on bit error rate
For baseband differential detection, the phase drift Δθ=2πΔfT caused by the frequency difference Δf between the transmitting and receiving ends. When Δθ>π/4, it will cause system error judgment. Therefore, the system design must ensure that Δθ<π/4. When Δθ takes different values, the bit error rate curve is shown in Figure 1. It can be seen from the figure that when Δf=0.0025/T, that is, when the frequency deviation is 2.5% of the symbol rate, a phase difference of 90 will be caused within one symbol. When the bit error rate is 10-4, the phase difference will cause a 1dB performance degradation.
Therefore, in order to obtain a higher receiver sensitivity, on the one hand, we can consider reducing the noise coefficient of the low noise amplifier, and on the other hand, improving the frequency accuracy of the local oscillator is also very important to improve the sensitivity of the system.
There are two ways to express receiver sensitivity. We usually use dBm, while in the protocol, the unit of receiver sensitivity is usually expressed in dBμv. What is the relationship between the two? dBm is the unit of power, and dBμv is the unit of potential. The relationship between the signal potential Es and the signal power Si is:
(3)
The impedance of the system we use is generally Rs=50Ω. When the signal power Si is expressed in dBm and the signal potential Es is expressed in dBμv, then
20lgEs=113+10lgSi (4)
For example, the sensitivity is -106dBm, which is 7dBμv.
Equations (2) and (4) are often used and should be remembered and converted proficiently.