: SNR=(Eg/N)*(f/ W) (4.1) where Eb is the energy required per bit of information (Joules), fb is the bit rate (Hz), No is the noise power density (Watts/Hz) and W is the bandwidth of the modulated carrier signal (Hz). Note that for our example, considering a DSSS system, it is the de-spread bandwidth that is considered in Eq. 4.1. Using a spread spectrum rather than a narrow band transmission results in an additional gain known as the processing gain. Processing Gain = 10 logio(C) dB (4.2) Chapter Four where C is the code length in chips (11 for the Barker code discussed above). This processing gain is effectively included in the calculation of channel SNR by using the de-spread bandwidth in Eq. 4.1. The bit rate per Hz of bandwidth, fb/, is a function of the modulation method employed, as discussed in the Section "Introduction, p. 95". BER is then given by: BER = 1/2 erfc (SNR) 1/2 (4.3) where erfc is the SO called complementary error function which can be looked up in mathematical tables. Figure 4-29 shows BER as a function of SNR for some of the common modulation methods. 16-PSK 8-PSK DQPSK DBPSK Eb/No (dB) Figure 4-29: Bit Error Rate (BER) for Some Common Modulation Methods The figure shows that for the example DQPSK modulated signal, with 1 bit per Hz of bandwidth, a signal-to-noise ratio of 10.4 dB is required to achieve a bit error rate of 1 in 105. Receiver Noise Floor The receiver noise floor has two components, the theoretical thermal noise floor (N) for an ideal receiver, and the receiver noise figure (NF) Radio Communication Basics which is a measure of the additional noise and losses in a particular receiver. The thermal noise is given as: N = kTW (4.4) where k is the Boltzmann constant (1.38 X 10-23 Joules/°K), T is the ambient temperature in °K and W is the bandwidth of the transmission (Hz)¹. Receivers for wireless networking will typically have noise figures in the range from 6 to 15 dB. The receiver noise floor (RNF) is then the sum of these two terms: RNF = kTW + NF (4.5) For the example 802.11