Asymptotic performance of M-ary orthogonal modulation ingeneralized fading channels

The asymptotic (M→∞) probability of symbol error P_e,_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_b/N₀) and E_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_b/N₀. These channels exist for all m⩾1/2. The special case of m=1 corresponds to Rayleigh fading, an inverse linear channel     

Asymptotic performance of M-ary orthogonal signals inworst case partial-band interference and Rayleigh fading

It is shown that for worst-case partial-band jamming, the error probability performance (for fixed E_b/N_I) becomes worse with increasing M for (M>16). The asymptotic probability-of-error is not zero for any E_b/N _I(>ln 2), but decreases inverse linearly with respect to it. In the fading case, the error-probability performance (for fixed E_b/N₀) improves with M for noncoherent detection, but worsens with M for coherent detection. For large E_b/N₀ the performance of the Rayleigh fading channel asymptotically approaches the same limit as the worst case partial-band jammed channel. However, for values of M at least up to 4096, the partial-band jammed channel does better. While it is unlikely that an M-ary orthogonal signal set with M>1024 will be used in a practical situation, these results suggest an important theoretical problem; namely, what signal set achieves reliable communication     

Differential detection of π/4-shifted-DQPSK for digital cellularradio

The detection of π/4-shifted-DQPSK modulation using a tangent-type differential detector with an integrated symbol timing and carrier frequency offset correction algorithm is discussed. π/4-shifted-DQPSK modulation has been proposed for use in a high-capacity, TDMA-based digital cellular system being developed in the US; differential detection could potentially allow the production of low-complexity mobile units. Results obtained using the proposed IS-54 TDMA frame structure for base to mobile transmissions are presented. Theoretical and simulation bit-error-rate (BER) results are presented for static and Rayleigh fading channels. BER results are provided as a function of E_b/N₀ and C/I, where the interferer is a second π/4-shifted-DQPSK signal. Additional results are provided which show the BER sensitivity to Doppler frequency shifts, time delay spread, and carrier frequency offsets     

Performance limits of coded multilevel DPSK in cellular mobileradio

Performance limits of coded multilevel differential PSK (MDPSK) in multipath Rayleigh fading channels are described. The simple Gaussian metric is assumed for reasons for practicality even though it is not the maximum likelihood. The channel cutoff rate, R₀ of MDPSK is analyzed based on the metric. Account is taken of additive white Gaussian noise (AWGN), cochannel interference, and multipath channel delay spread. For the analysis of the spectrum efficiency of a cellular mobile radio system employing coded MDPSK, its service area is defined as the area in which, with a bit rate of R information bit/symbol (R⩽R₀), reliable communications are possible. Three optimal information bit rates are determined from the channel cutoff rate to minimize the required average signal energy per information bit-to-noise power spectral density ratio (E_b/N₀) to maximize the tolerable r.m.s. delay spread τ_r.m.s. and to maximize the spectrum efficiency     

Differential detection in quadrature-quadrature phase shift keying(Q2PSK) systems

A generalized quadrature-quadrature phase shift keying (Q² PSK) signaling format is considered for differential encoding and differential detection. Performance in the presence of additive white Gaussian noise (AWGN) is analyzed. Symbol error rate is found to be approximately twice the symbol error rate in a quaternary DPSK system operating at the same E_b/N₀. However, the bandwidth efficiency of differential Q²PSK is substantially higher than that of quaternary DPSK. In differential detection, it is quite reasonable to suspect that errors tend to occur in pairs. It is shown that when the error is due to AWGN, the ratio of double error rate to single error rate can be very high, and the ratio may approach zero at high signal-to-noise ratio. In an attempt to improve the error rate performance, differential detection through maximum-likelihood decoding based on multiple or N symbol observations is considered     

Refinements to the theory of error rates for narrow-band digital FM

The bit-error-rate performance of narrowband digital FM with limiter-discriminator detection is considered for the cases of integrate and dump postdetection filtering with partial-bit integration, and sample-and-hold bit detection at the discriminator output. Error rate curves are presented for Gaussian, six-element Butterworth, and two-stage synchronously tuned IF filters. The calculations illustrate just how much more E_b/N₀ is required as the partial-bit integration time goes from 100% down to the limiting case of sample and hold. The results show that it is important to have a well-designed IF filter especially if the entire bit time is not available for detection     

Error probability of M-ary FSK with differential phasedetection in satellite mobile channel

Formulas are derived for the error probability of M-ary frequency shift keying (FSK) with differential phase detection in a satellite mobile channel. The received signal in this channel is composed of a specular signal, a diffuse signal, and white Gaussian noise; hence, the composite signal is fading and has a Rician envelope. The error probability is shown to depend on the following system parameters: (1) the signal-to-noise ratio; (2) the ratio of powers in the specular and diffuse signal components; (3) the normalized frequency deviation; (4) the normalized Doppler frequency; (5) the maximum normalized Doppler frequency; (6) the correlation function of the diffuse component, which depends on the normalized Doppler frequency and the type of the antenna; (7) the number of symbols; and (8) the normalized time delay between the specular and diffuse component (t _d/T) where 1/T is the symbol rate. Except for T_d/T, all normalized parameters are the ratios of the parameter value and symbol rate. The Doppler frequency depends on the velocity of the vehicle and the carrier frequency. The error probability is computed as a function of the various parameters. The bit error probability is plotted as a function of signal-to-noise ratio per bit and other system parameters     

The cutoff rate for on-off keying

It is well known that on-off keying (OOK), i.e. the transmission of a pulse for a data one (mark) and transmission of no signal for a data zero (space), exhibits a 3 dB inferiority to antipodal signalling, in terms of the signal-to-noise ratio required to achieve a specified bit error probability. When the channel is characterized by the cutoff rate R₀, this 3 dB inferiority persists, in the sense that the required E_b/N₀ to operate at a given value of R₀ is 3 dB greater for the OOK channel than for the antipodal channel. However, it is shown that, if the definition of cutoff rate is generalized in an appropriate way to reflect the fact that signal energy is expended only in the transmission of marks, part of this penalty is recovered. In fact, it is shown that, in the limit of low R₀, there is no penalty in signal-to-noise ratio. Even at rates of realistic interest, the penalty is significantly less than the expected 3 dB     

Quantization loss in convolutional decoding

The loss in quantizing coded symbols in the additive white Gaussian noise (AWGN) channel with binary phase-shift keying (BPSK) or quadrature phase-shift keying (QPSK) modulation is discussed. A quantization scheme and branch metric calculation method are presented. For the uniformly quantized AWGN channel, cutoff rate is used to determine the step size and the smallest number of quantization bits needed for a given bit-signal-to-noise ratio (E_b/N₀) loss. A nine-level quantizer is presented, along with 3-b branch metrics for a rate-1/2 code, which causes an E_b/N₀ loss of only 0.14 dB. These results also apply to soft-decision decoding of block codes. A tight upper bound is derived for the range of path metrics in a Viterbi decoder. The calculations are verified by simulations of several convolutional codes, including the memory-14, rate-1/4 or -1/6 codes used by the big Viterbi decoders at JPL     

Multi-H phase-coded modulations with asymmetric modulationindexes

Multi-H phase-coded modulation (MHPM) is a bandwidth-efficient modulation scheme which offers substantial coding gain over conventional digital modulation schemes. MHPM with asymmetric modulation indices corresponding to the bipolar data +1 and -1 is considered, and numerical results for the minimum Euclidean distances are provided. It is shown that performance improvements on the error probability over conventional MHPM are gained with essentially the same bandwidth and a very slight modification in implementation. The upper bounds on the error probabilities as functions of observation intervals and received E_b/N₀ are also investigated in detail. It is concluded that the concept of asymmetric modulation indices for MHPM is attractive for bandwidth and power-efficient modulation     

Optimal probability-of-error thresholds and performance for twoversions of the sign detector

Expressions are obtained for specifying the optimal error probability (minimum P_e) thresholds λ₀₁ and λ₀₂ for the traditional and modified sign detectors, respectively. These thresholds are shown to depend on the parameters p, P₁, and M where: M is the number of observations z_i used in the test statistic; P₁=P(H₁ ) is the prior probability for hypothesis H₁ that signal s₁ is present and 1-P₁ =P(H₀) corresponds to the hypothesis H₀ that signal s₀ is present; and p=Pr{z_i⩾0|H₁} with s₀=0 for the traditional sign detector and p=Pr{z_i⩾λ|H₁ }=Pr{z_i<λ|H₀} with λ =(s₀+s₁)/2 for the modified sign detector. The expressions for λ₀₁ and λ₀₂, are given explicitly, and shown to be independent of P₁ for sufficiently large M. Optimal P_e versus M performance curves, corresponding to both versions of the sign detector, are obtained for a representative range of values for p and P₁     

Rayleigh fading compensation for QAM in land mobile radiocommunications

A pilot symbol-aided Rayleigh fading compensation is investigated for M-ary quadrature amplitude modulation (QAM) to achieve highly spectrally efficient land mobile communication systems. The optimum parameters for fading compensation, bit error rate (BER) performance against E_b/N₀ (energy per bit to the noise power spectrum density), adjacent channel interference, and cochannel interference for 16-QAM, 64-QAM, and 256-QAM, and the spectral efficiencies for these modulation schemes in Rayleigh fading environments are investigated by computer simulation. To further verify the effect of pilot symbol-aided fading compensation from a a practical point of view, a 16-QAM modem is implemented, laboratory experiments are executed, and the impact of the dynamic range limitation due to the resolution of the analog-to-digital (A/D) converters is evaluated, along with the imperfection of the analog circuits. It is demonstrated by computer simulation and laboratory experiments that the pilot symbol-aided fading compensation can sufficiently compensate for fast varying Rayleigh fading, and 16-QAM gives the highest spectral efficiency in the case of cellular systems     

Multiuser signal detection using sequential decoding

The application of sequential decoding to the detection of data transmitted over the additive white Gaussian noise channel by K asynchronous transmitters using direct-sequence spread-spectrum multiple access (DS/SSMA) is considered. A modification of R.M. Fano's (1963) sequential-decoding metric, allowing the messages from a given user to be safely decoded if its E_b/N₀ exceeds -1.6 dB, is presented. Computer simulation is used to evaluate the performance of a sequential decoder that uses this metric in conjunction with the stack algorithm. In many circumstances, the sequential decoder achieves results comparable to those obtained using the much more complicated optimal receiver     

Burst error statistics of simulated Viterbi decoded BPSK on fadingand scintillating channels

The author presents and analyzes burst error statistics of a soft-decision Viterbi decoder when the transmitted signal is encoded with the 313 (3, 1/2) or 31123 (5, 1/2) convolutional codes, modulated via coherent binary phase-shift keying (BPSK) for the additive white Gaussian noise (AWGN) channel, and subjected to slow and nonselective scintillation/fading modeled by the Nakagami-m distribution. These statistics were generated by Monte-Carlo simulations, and presented in terms of burst error length average and quantile (90 and 99%) statistics versus SNR (E_b/N₀) parameterized by the fading intensity parameter m. The results indicate how Viterbi decoder burst error statistics vary with the fading/scintillation intensity m for Nakagami-m channels, and, consequently, provide information important to the design of interleaved or noninterleaved concatenated coding schemes for such channel environments     

Truncation length for Viterbi decoding

A bound is derived and analyzed for the bit error rate (BER) of a Viterbi decoder with survivor truncation. Estimates of the SNR (signal-to-noise ratio) loss on the AWGN (additive white Gaussian noise) channel due to truncation are obtained for convolutional codes. Larger truncation lengths are required than the smallest value that does not effectively decrease the code's free distance, especially at low E _b/N₀     

The bandwidth performance of a two-element adaptive array withtapped delay-line processing

The bandwidth performance of a two-element adaptive array with a tapped delay line behind each element is examined. It is shown how the number of taps and the delay between taps affect the bandwidth performance of the array. An array with two weights and one delay behind each element is found to yield optimal performance (equal to that obtained with continuous-wave interference) for any value of intertap delay between zero and T₉₀/B, where T ₉₀ is a quarter-wavelength delay time and B is the fractional signal bandwidth. Delays less that T₉₀ yield optimal performance but result in large array weights. Delays larger than T₉₀/B yield suboptimal signal-to-interference-plus-noise ratio when each element has only two weights. For delays between T₉₀/B and 4T₉₀/B , the performance is suboptimal with only two taps but approaches the optimal if more taps are added to each element. Delays larger than T₉₀/B result in suboptimal performance regardless of the number of taps used     

Repeated convolutional codes for high-error-rate channels

An error-correction scheme for an M-ary symmetric channel (MSC) characterized by a large error probability p_e is considered. The value of p_e can be near, but smaller than, 1-1/M, for which the channel capacity is zero, such as may occur in a jamming environment. The coding scheme consists of an outer convolutional code and an inner repetition code of length m that is used for each convolutional code symbol. At the receiving end, the m inner code symbols are used to form a soft-decision metric, which is passed to a soft-decision decoder for the convolutional code. The effect of finite quantization and methods to generate binary metrics for M>2 are investigated. Monte Carlo simulation results are presented. For the binary symmetric channel (BSC), it is shown that the overall code rate is larger than 0.6R₀, where R₀ is the cutoff rate of the channel. New union bounds on the bit error probability for systems with a binary convolutional code on 4-ary and 8-ary orthogonal channels are presented. For a BSC and a large m, a method is presented for BER approximation based on the central limit theorem     

Performance of π/4 SQAM in a hard-limited channel in thepresence of AWGN

A strategy that reduces the spectral spreading when an ideal hard-limiter is used as a first approximation to a fully saturated power amplifier is presented. This strategy combines superposed quadrature amplitude modulation (SQAM) filtering with the π/4-shift quadrature phase-shift keying (QPSK) digital transmission format adopted for the first generation of US digital cellular systems. Simulation results showed that this π/4 SQAM filtering strategy increased capacity by 35% in comparison to hard-limited π/4 QPSK. Using computer-aided design, a receive filter that would limit the degradation of E _b/N₀ to less than 1.4 dB at a bit error rate of P_e=10^-4 was selected     

Effect of conduction-band discontinuity on lasing characteristicsof 1.5 μm InGaAs/In(Ga)AlAs MQW-FP lasers

The characteristic temperature (T₀), relaxation frequency (f_r), differential gain (dg /dn) and nonlinear gain coefficient (ϵ) of 1.5-μm InGaAs/In(Ga)AlAs multiple-quantum-well (MQW) Fabry-Perot (FP) lasers grown by gas source molecular beam epitaxy (GSMBE) are reported. It is found that T₀ is little affected by the difference in the conduction band discontinuity. A maximum T₀ value of 86 K is obtained. The dg/dn and ϵ∈ were calculated from the slope of the f_r versus √ power plot and the damping K-factor. It is demonstrated that dg/dn and ϵ of InGaAs/In(Ga)AlAs MQW lasers increase with an increase in the conduction band discontinuity     

Maximum heat-sink temperature for CW operation of adouble-heterostructure semiconductor injection laser

Assuming that the temperature dependence of the threshold current for pulsed operation is known, an analytical expression for the maximum heat-sink temperature, T_hm, for CW operation of the laser can be derived. The maximum heat-sink temperature is expressed in terms of the characteristic temperature T₀, the room-temperature threshold current for pulsed operation I₀ , the equivalent effective thermal resistance &thetas;, and the equivalent effective series electrical resistance r of the device. It is shown that the values of T_hm can be enhanced by increasing the value of T₀ or by decreasing the values of I₀, &thetas;, and r