the bandwidth of the composite signal is expanded. The converse process applied in the receiver will take the composite 'wideband' signal and collapse the signal back to its original (data) bandwidth. This is the principle of spreading gain used in CDMA systems and is in many ways analogous to the bandwidth gain achieved in a wideband FM radio system. 3.3.2 An Example - The Barker Code Used in Legacy 802.11b WiFi Systems Basic 802.11 b WiFi systems provide an example. The original 802.11 b standard supports data rates of 1Mbit/ and 2 Mbits/s using either BPSK modulation (1 Mbit/s) or QPSK (2 Mbit/s). The data bits are multiplied with an 11-bit Barker sequence at a 1-MHz data rate that expands the data bandwidth of 2 MHz to an occupied channel bandwidth of 22 MHz, giving just over 10 dB of coding gain. Barker sequences are named after RH Barker. The concept was introduced, in his 1953 paper on 'Group Synchronisation of Binary Digital Systems' read at the IEE in London. They were/are widely used in radar systems to help in distance estimation and were first used in low-cost commercial two-way radio systems in the first generation of digital cordless phones developed for the 902-908 MHz US ISM band. Note that when demodulated the codes can be sum error checked by converting to binary numbers as shown in Table 3.4. The 11-bit Barker code used in 802.11 b is as follows shown in Table 3.5. Table 3.4 Counting in binary Counting in binary Table 3.5 Barker sequence 11-bit Barker sequence +1 -1 +1+1-1+1+1+1-1-1 - 1 Making Telecoms Work Table 3.6 Spreading/despreading codes Input data bit Spreading code Composite code Despreading code Output data bit If we take this spreading sequence and multiply it with an input data bit -1 and apply the rule that if the signs are different, the result is a - 1, if the signs are the same the result is a +1 then we get the outputs shown in Table 3.6. As you can see, the despreading code is the same as the spreading code. Effectively we have answered the question 'is at a -1 or +1?' eleven 