Coding for a Multiple-Access Frequency-Hopping System

A multiuser system employing on-off FSK modulation in conjunction with frequency hopping is examined for digital transmission. The receiver consists of a bank of bandpass noncoherent detectors followed by a message decoder. An analysis is presented for a transmission channel characterized by Rayleigh fading and additive Gaussian noise. The main source of impairment is interference between users. An upper limit on the number of simultaneous system users for acceptable transmission quality is derived. An example of a system with (one-way) bandwidth of 20 MHz and transmission rate of 32 kbits/s per user shows a maximum of 169 users at an average SNR on the channel of 25 dB and a bit error probability not exceeding 10^-3. The effect of applying error correcting codes to the system is evaluated. It is shown how Reed-Solomon codes can be used to generate both user identification and message coding. Such coding increases the number of users the system can accommodate in the example above to 212. Convolutional codes are shown to be even more effective. Such a code of constraint length 2 results in 285 simultaneous users in the example, which is an increase of 70 percent over an uncoded system. The drawback of coding is an increased complexity of the receiver. The amount of computation needed for the decoding of block and convolutional codes is estimated.