Paul J. Crepeau

Uncoded and coded performance of MFSK and DPSK in Nakagami fading channels

The author presents uncoded and coded performance results for noncoherent M-ary frequency-shift keying (MFSK) and differentially coherent binary phase-shift keying (DPSK) in a slow nonselective Nakagami-m (1960) fading channel. He gives simple expressions for the asymptotic slopes of probability of bit error for large signal-to-noise ratio and shows that the effective order of diversity compared to an uncoded Rayleigh channel is the product of two parameters, one for the channel and one for the code. He also compares the uncoded Nakagami-m results to those of the Rician channel in order to show performance differences between these two generalized fading channel models. >

Asymptotic performance of M-ary orthogonal modulation in generalized fading channels

The asymptotic (M to infinity ) probability of symbol error P/sub e/,/sub m/ for M-ary orthogonal modulation in a Nakagami-m fading channel is given by the incomplete gamma function P(m, mx) where x=In 2/(E/sub b//N/sub 0/) and E/sub b/ is the average energy per bit. For large signal-to-noise ratio this leads to a channel where the probability of symbol error varies as the inverse mth power of E/sub b//N/sub 0/. These channels exist for all m>or=1/2. The special case of m=1 corresponds to Rayleigh fading, an inverse linear channel. >

Performance of FH/BFSK with generalized fading in worst case partial-band Gaussian interference

For frequency-hopped (noncoherent) binary frequency shift keying (FH/BFSK) on a worst-case partial-band Gaussian interference channel, the bit error probability results are well known for the extreme cases where the signal is either nonfading or Rayleigh fading. In this work, the region between these extremes is filled in by considering the general Nakagami-m fading model. The worst-case partial-band Gaussian interference results are given by a one-parameter family which for m to infinity gives the Viterbi-Jacobs nonfading result, and for m=1 gives the Rayleigh fading result. In the latter case, a broadband interference strategy is optimal. Thus, the Nakagami-m results provide a smooth one-parameter bridge between the Viterbi-Jacobs channel and the Rayleigh fading channel. The results show that the worst-case interference fraction rho increases as the fading variance increases, up to Rayleigh fading. Any fading less severe than Rayleigh, however slight the departure from Rayleigh, requires a partial-band strategy for sufficiently large E/sub b//N/sub I/. >

Coding performance on generalized fading channels

The author presents the uncoded and coded performance results of MFSK (M-ary frequency-shift keying) and DPSK (differentially coherent binary phase-shift keying) on a generalized fading-channel model, the slow nonselective Nakagami-m fading channel. Simple expressions are given for asymptotic slopes of probability of bit error for a large signal-to-noise ratio, and it is shown that the effective diversity of the system is in the product of two parameters, one for the code and one for the channel. It is concluded that the results obtained are potentially useful in the performance assessment of several current MFSK and DPSK systems that are required to operate on channels with a wide variety of fading or scintillation conditions.<<ETX>>

Anomalous Union Bound Behavior for MFSK Signaling on Inverse Linear Channels

Application of the union bound to MFSK signaling on certain channels where probability of bit error varies in an inverse linear fashion with E_{b}/N_{0} can lead to the erroneous conclusion that performance degrades with increasing alphabet size. The anomaly is shown for the worst-case partial band Gaussian interference channel and the Rayleigh fading channel.

A connection between Rayleigh fading and worst-case partial band interference

For FH/BFSK (frequency hopping/binary frequency-shift keying) on a worst-case partial-band Gaussian interference channel, the bit error probability results are well known for the extreme cases in which the signal is either nonfading or Rayleigh fading. In the present work the author fills in the region between these extremes by considering the general Nakagami-m fading model. Here the worst-case partial-band Gaussian interference results are given by a one-parameter family, which for m to infinity gives the Viterbi-Jacobs (1975) nonfading result and for m=1 gives the Rayleigh fading result. In the latter case a broadband interference strategy is optimal. Thus the Nakagami-m solutions provide a smooth one-parameter bridge between the Viterbi-Jacobs channel and the Rayleigh fading channel. The results show that the worst-case interference fraction rho increases as the fading variance increases, up to Rayleigh fading. Any fading less severe than Rayleigh, however slight the departure from Rayleigh, requires a partial-band strategy for sufficiently large E/sub b//N/sub I/.<<ETX>>

Performance of Coded FH/MFSK with a Quantizer-Limiter in a Worst-Case Partial Band Gaussian Interference Channel

The performance of coded FH/MFSK with a quantizerlimiter soft decision metric is presented for a worst-case two-level partial band Gaussian interference channel. This receiver structure is easy to implement and does not require side information concerning the on-off state of the interference. For a constraint length seven (K = 7), rate one-half (R = 1/2) convolutional code with Viterbi decoding, this receiver performs within 1.4 dB of the required Eb/No at Pb = 10-5 when compared to an ideal unquantized soft decision receiver assisted by perfect side information. The cutoff rate parameter Ro is plotted versus channel symbol signal-to-noise ratio for alphabet sizes M = 2, 4, 8, 16, and 32.

A new look at double error correcting BCH codes

We give a complete classification of the error locator polynomials that occur in the decoding of DEC BCH codes. We present a new construction showing that all quadratic error locator polynomials produced by received vectors falling in the interstitial region between decoding spheres are illegitimate and have no roots. Furthermore we show that a small subset of received vectors in the interstitial region produce cubic error locator polynomials that are illegitimate except for the correctable case of a triple error pattern with three equally spaced errors in the cyclic sense.

Reed-Solomon coding performance with errors and erasures decoding on a Rayleigh fading channel

Presents analytical results for a specific case of message transmission over a Rayleigh fading channel using NCMFSK signaling and RS coding with errors and erasures decoding. The authors show that errors and erasures decoding provides greater than 3 dB coding gain compared to errors-only (hard decision) decoding. Furthermore, it is shown that the ratio of erasures to errors must be very large to achieve minimum message error probability.<<ETX>>

Multiple Access Performance of FH/NCMFSK with List Decoding

Multiple Access (MA) performance of list metric decoding is evaluated for frequency hopped (FH), noncoherent M-ary frequency shift keying (NCMFSK). In a list decoding receiver, the demodulator constructs an energy-ordered list of the channel symbols, and the decoder then awards each symbol a score based on its ranking in this list. We considered two cases: in one, the decoder assigns the same set of scores on each use of the channel; in the other, the decoder is adaptive and assigns metrics which award one of M sets of scores depending on how many energy detector outputs were believed to have contained user signals. We show that in a fading environment a list decoding system can accommodate five times more users than the best hard decision system, and that an adaptive metric doubles the capacity of the static list metric.