The performance of asynchronous fast frequency hopping-multiple access (AFFH-MA) systems with multiple hops per bit is investigated with a linear-combining receiver in Rayleigh fading. We present an accurate approximation method for evaluating the error probability by using the characteristic function, Taylor series, and Gauss-Chebyshev quadrature rule. We will show that the proposed method provides an accurate approximation, compared with a simple Gaussian approximation. The validity of proposed analytic works is verified through Monte Carlo simulations.

The bit error rate (BER) degradations of fast frequency hopping multiple access (FFH-MA) systems due to the frequency and timing offsets are investigated over a Rician fading channel. It is shown that as the received average SNR increases, the BER is affected much larger by frequency and timing offsets. When the frequency offset or the timing offset exists alone, the BER of the FFH-MA system is degraded much more due to the timing offset than due to the frequency offset. The BER degradation due to both the frequency offset and the timing offset is larger than the sum of the degradations due to each offset.

In order to investigate the sensitivity of fast frequency hopping-multiple access (FFH-MA) systems due to the frequency offset under Rician fading, we evaluate the bit error rate (BER) performance of the FFH-MA system using noncoherent M-ary frequency shift keying (FSK) with the hard decision decoding and the majority logic decision. Numerical results show that for satisfying the BER performance of 10-5 at a given normalized frequency offset of 0.2, the additional signal to noise ratio (SNR) of about 4 dB is required with the 8-ary FSK signaling compared to the case of the perfect frequency synchronization. While the frequency offset increases at a given SNR, the BER is more severely degraded, and subsequently, the BER performance is saturated at the normalized frequency offset of 0.5 regardless of fading environments. For the SNRs of more than 15 dB, the threshold level of the receiver suffering from normalized frequency offsets of less than 0.4 should be larger than that of the perfectly frequency synchronized receiver.

This paper proposes Coherent-HYBrid Direct-Sequence Fast-Frequency-Hopping (CHYB-DS-FFH) CDMA with Adaptive Interference Cancelling (AIC) for cellular mobile communications. The features of CHYB-DS-FFH are symbol-by-symbol frequency diversity and low chip-rate DS multiplexing both of which are based on a coherent FFH modulation and demodulation scheme. The combination of coherent FFH, space diversity, and AIC is very effective for reducing the performance degradation due to interference. Computer simulations demonstrate BER performance of a 2 hop 500-kHz-interval frequency hopping system using () a linear canceller or () a nonlinear canceller. Both systems employ the two branch space diversity reception of 10kb/s QPSK with FFH over a 1MHz system bandwidth. In quasi-static channels, the average BER performance is 10-2 with average Eb/N0 less than 8dB. In dynamic fading channels under full interference conditions, CHYB-DS-FFH with the linear adaptive interference canceller realizes a BER of 10-2 at the average Eb/N0 of 15dB with maximum Doppler frequency fD of 5Hz, whereas CHYB-DS-FFH with the non-linear adaptive interference canceller achieves the same BER at the average Eb/N0 of 15dB with fD, equal to 30Hz.