2.5 Receiver dimensions

2.5 Receiver dimensions

The receiver noise figure derives largely from the system requirement for sensitivity. The logical starting point for the calculation is the estimation of the signal-to-noise ratio(SNR)needed at the demo dulator/equaliser of apseudo-ideal receiver. According to basic system simulations, the E_b/N₀ required for an 8 per cent BER with a TU50 propagation channel is 5.2 dB. When a correction factor of 1.32 dB is applied to take account of the ratio of the bit rate to the channel bandwidth (i.e. 270.833/200), the SNR estimate becomes 6.5 dB. Hence if the desired sensitivity, P_sen,is −108 dBm, the total noise power at the input to the receiver under these conditions, P_n, must be given by:

If this is compared with the thermal noise level (−173.83 dBm) raised by 53 dB to account for the 200 kHz channel bandwidth, the overall receiver noise figure, F_dB, must then be:

The frontend alone needs a noise figure slightly less than this to allow for the quantisation noise contribution of the ADC. By assigning the frontend a noise figure of 6.0 dB, the degradation in receiver noise figure caused by the ADC must be approximately 0.5 dB, which corresponds to a referred ADC noise power, P_adc, of:

In further references to this parameter the value will be rounded down to −125 dBm. A graphical illustration of the preceding calculations is given in Figure 2.5. One final step is required if proper account is to be taken of the signal losses in the RF frontend. With an estimated 2.5 dB losses in the passive RF parts including the band selection filters and antenna feed arrangement, the noise figure of the main active part of the receiver must be further reduced to a value of 3.5 dB.

Figure 2.5: Calculating noise figure from reference sensitivity

The adjacent-channel and alternate-channel rejection requirements of the receiver are illustrated by the curves plotted in Figure 2.6. These represent the spectral envelopes of a wanted signal, a cochannel, an adjacent-channel and an alternate-channel interferer at the relative frequencies and levels stipulated in the GSM specification. For the tests in question, the wanted signal is at a relatively high level of −82 dBm, at which point the receiver noise can be ignored. Given that the receiver can achieve an 8 per cent BER in a TU50 propagation channel with an SNR of 6.5 dB, there is generally no difficulty in meeting the cochannel rejection requirement of −9 dB. Then, on the basis that an adjacent-channel interferer at a level +9 dB above the wanted signal must be attenuated to the level of a cochannel interferer, the adjacent-channel rejection requirement must be at least 18 dB. Similarly, the alternate-channel rejection requirement must be in the order of 50 dB.

Figure 2.6: Illustrating channel filter rejection requirements

Of the different blocking signals referenced in the 3GPP specification, it is the signal at a 3 MHz offset with a level of −23 dBm (P_int) that is generally regarded as the most demanding. Under the relevant test conditions the wanted signal is at a level of −99 dBm and if the required SNR of 6.5 dB is to be achieved, the residual power of the blocking signal after filtering must be no higher than −(99+6.5) =−105.5 dBm. At the level of −114.5 dBm, the receiver noise power can largely be ignored and the rejection requirement for the blocking interferer, A_blk, is then simply:

The dynamic range requirement of the ADC in the receiver is determined by the level of this same blocking interferer and by the permitted level of the ADC quantisation noise, P_adc. Hence, the difference between the −23 dBm level of the blocking signal and the −125 dBm level of the noise gives a dynamic range requirement of 102 dB. Although substantial, this is known to be within the capability of the ΣΔ modulator type of ADC to be described. The design problem is also not quite so severe if the SINAD (SIgnal-to-Noise-And-Distortion) requirement of the ADC is taken into consideration which, for the purposes of passing the blocking-interferer test, is a lower value of 85.5 dB. This is derived in much the same way as the filtering requirement for the blocking signal, i.e.

the extra 3 dB being inserted to allow both the ADC noise and the residue of the blocking signal to contribute equally towards the maximum permitted noise residue mentioned above of −105.5 dBm.

The AM interferer test can be translated into an IP2 requirement using a mixture of simple reasoning and system simulation. If the wanted signal is at a level of −99 dBm and the SNR requirement for a 2 per cent BER under static fading conditions is 6.5 dB, it follows that the maximum tolerable power level of the second-order intermodulation products (referred back to the receiver input) is −105.5 dBm. With an interferer power level of −31 dBm, some simple linear extrapolation yields an initial estimate for the IP2 requirement of a zero-IF receiver of +43.5 dBm. It remains then to estimate how much this is reduced for a low-IF receiver by virtue of the filtering effects of the AC coupling and channel filter. The most reliable way to estimate this reduction is to perform a system simulation for a receiver whose IF can be changed and whose second-order non-linearity can be adjusted. For the sake of brevity, the details of the simulation will not be described here but the results are summarised in Figure 2.7. The IP2 value obtained for the zero-IF receiver was 42.5 dBm, which is close to the original, crude estimate of 43.5 dBm. This corresponds to a maximum tolerable level of second-order intermodulation distortion of −104.5 dBm, suggesting that the receiver is just meeting specification at an SNR of 5.5 dB. More interestingly, the simulation suggests that the low-IF receiver can meet the AM interferer test with an IP2 of only +28.5 dBm, which is a very worthwhile improvement of 14 dB on the zero-IF receiver. This could be used to reduce power consumption or give the receiver much greater immunity to the AM interference.

Figure 2.7: IP2 requirements for zero and low-IF options