Error rate performance of noncoherent detection of duobinary coded MSK and TFM in mobile radio communication systems

Two continuous phase constant envelope modulation schemes are considered for use in digital mobile radio communication systems. These two schemes, duobinary coded minimum shift keying (MSK) and tamed frequency modulation (TFM), use partial response signaling to achieve efficient power spectrum. Therefore, they are suitable candidates for the application of digital data transmission via mobile radio where spectrum efficiency is an important consideration. The mobile communication channel is characterized by fast Rayleigh fading and cochannel interference resulting from the reuse of the channels. The error rate performance of duobinary coded MSK and TFM has been studied under these environments with noncoherent detection. A closed form expression for the probability of error of duobinary coded MSK with discriminator detection has been derived and evaluated for different cases of fast and slow fading and cochannel interference. The probability of error of duobinary coded MSK and TFM with differential detection has been calculated by numerical integrations for different cases of slow and fast fading and cochannel interference.     

Optimum Time Diversity and BCH Codes for DS SS-CDMA Cellular Mobile Channels

This paper presents the results of optimum diversity and coding of a cellular radio system using spread-spectrum code division multiple-access (SS-CDMA) and binary phase-shift-keying modulation (BPSK). The base-to-mobile link is considered with the mobile at the boundary between cells. Hence, the received signal is subject to Rayleigh or log-normal fading, as well as to interference from neighbouring cells.First, the probability of error for the fading-interference channel is approximated as a simple, closed-form expression, with one-parameter which signifies the degree of channel fading and interference. It is shown that the approximation is quite satisfactory for a wide range of channel fading and interference. Beside avoiding numerical integration, the use of such simplification offers more insight into the nature of the channel.The use of error-correcting codes to enable increasing the system capacity is then investigated. Since employment of either SS or forward-error correction (FEC) techniques results in bandwidth expansion for a communication system using a fixed alphabet size, there exists a trade-off between how much processing gain and how much coding gain the system should employ such that the bit-error rate is minimum. Two types of coding are analysed, viz. repetitive coding and binary BCH codes. For the repetitive code, Chernoff upper-bound is used to approximate the bit-error rate (BER) and the optimum diversity is then found by a simple minimisation.To find the optimum trade-off between code rate k/n and correction capability t of BCH (n,k,t) codes, the first term of the series representing the BER is used as an estimate of the probability of error. Such approximation is shown to yield a nearly exact estimate of the optimum coding parameters, which minimise the BER. Although exact analysis can be used, the present approach yields a general solution, and optimum design parameters can be related to channel conditions.The essence of the results is as follows: (i) fading and interference channel is approximated as a one parameter family; (ii) optimum diversity increases and processing gain decreases, almost linearly, with the increase of interference and fading severity; (iii) optimum BCH code rate is 0.3 over a wide range of fading and interference conditions, and (iv) optimising coding gain and processing gain can provide substantial increase in system capacity.     

BPSK Bit Error Outage over Nakagami-m Fading Channels in Lognormal Shadowing Environments

In this letter, we address the problem of finding a tractable expression for the bit-error outage (BEO) defined as the probability to observe a given average bit error rate (BER) over a fading channel in a shadowing environment. Our contribution is two-fold: (1) a simple yet tight approximation of the bit error probability (BEP) for binary phase shift keying (BPSK) over a frequency-flat Nakagami-m fading channel is derived, which (2) facilitates the derivation of a tight lower bound of the BEO in presence of lognormal shadowing in closed form. Theoretical results are corroborated by means of simulation results, confirming the tightness of the bounds.     

Performance of a TDM/TDMA portable radio link for interference,noise, and delay spread impairments

Presents the measured/simulated performance of a time division multiplexing/time division multiple access (TDM/TDMA) portable radio link for noise, interference and delay spread impairments. The radio link transmits short TDMA bursts of 82 symbols at 450 kbits/sec using 4QAM. This modulation is also referred to 4PSK, but phase shift modulation is constant envelope. Nyquist filtering of quadrature signal components yields quadrature amplitude modulation which, of course, also contains π/2 phase variations at the sampling instants. Demodulation is performed by a low-overhead digital coherent demodulator with 2-branch selection diversity. The port or base has two receivers for diversity but the portable or handset uses only a single receiver to perform selection diversity. Signal-to-noise ratio and signal-to-interference ratio performance of the link was measured for a stationary channel and for a channel with different fading rates. In a Rayleigh fading environment, increasing the fading rate causes only a small performance degradation. The results also show that selection diversity is effective against interference in a slow Rayleigh fading environment. A separate set of experiments were performed to measure the effects of delay-spread on the link. Selection diversity is effective in reducing the word-error ratio floor caused by frequency-selective fading. As a result, relatively high data rates can be supported by a multipath fading channel without using adaptive equalization. Thus, a portable radio communications system using low complexity hardware design incorporating selection diversity can achieve good performance     

The Effects of Time Delay Spread on Portable Radio Communications Channels with Digital Modulation

Frequency-selective fading caused by multipath time delay spread degrades digital communication channels by causing intersymbol interference, thus resulting in an irreducible BER and imposing a upper limit on the data symbol rate. In this paper, a frequencyselective, slowly fading channel is studied by computer simulation. The unfiltered BPSK, QPSK, OQPSK, and MSK modulations are considered first to illustrate the physical insights and the error mechanisms. Two classes of modulation with spectral-shaping filtering are studied next to assess the tradeoff between spectral occupancy and the performance under the influence of time delay spread. The simulation is very flexible so that different channel parameters can be studied and optimized either individually or collectively. The irreducible BER averaged over fading samples with a given delay profile is used to compare different modulation/detection methods, while the cumulative distribution of short-term BER is employed to show allowable data symbol rates for given values of delay spread. It is found that both GMSK and QPSK with a raised-cosine Nyquist pulse are suitable for a TDM/TDMA digital portable communications channel.     

A New Method for the Computation of the Error Probability of Differentially Detected Modulation Formats in Mobile Radio Channels – The Case of Minimum Shift Keying

We show a new approach to analytically compute the error probability BER in mobile radio channels. The method is applicable to a variety of differentially detected modulation formats; here we use minimum shift keying (MSK) as an example. We include the following effects: (i) fading and (ii) time dispersion of the mobile radio channel (iii) noise, and (iv) filtering both of the data sequence and the received signal. Sampling is at a fixed but arbitrary instant. We develop a new mathematical formalism, which we call the two-path equivalent-matrix (TPEM) method. In this method, we reduce the general channel (including noise) exactly to a two-path fading channel without noise, whose BER can be easily computed. With this method, we can find analytically the BER for both filtered and unfiltered (G)MSK if the BER is small; for large BER a single well-behaved integral must be solved numerically. Asymptotic equations for unfiltered MSK and small BERs are also given. To a first approximation, the BER is 0.5· [(S/T)²+1/SNR] for pure MSK, where S/T is the delay spread normalized to the bit duration and SNR is the signal-to-noise ratio. The BER is increased by less than 50% for Gaussian filtering of the data sequence and receiver filtering with a time-bandwidth product larger than 0.3.     

Performance analysis of mobile radio systems over composite fading/shadowing channels with co-located interference

This paper presents an analytical framework for performance evaluation of mobile radio systems operating in composite fading/shadowing channels in the presence of colocated co-channel interference. The desired user and the interferers are subject to Nakagami fading superimposed on gamma shadowing. The paper starts by presenting generic closed-form expressions for the signal-to-interference ratio (SIR) probability density function (pdf). From this pdf, closed-form expressions for the outage probability, the average bit error rate and the channel capacity are obtained in both cases of statistically identical interferers and multiple interferers with different parameters. The newly derived closed-form expressions of the aforementioned metrics allow us to easily assess the effects of the different channel and interference parameters. It turns out that the system performance metrics are predominantly affected by the fading parameters of the desired user, rather than by the fading parameters of the interferers.     

Degradation in FH-MFSK mobile radio system capacity due to Rayleighfading and log-normal shadowing

A frequency-hopped multilevel frequency-shift-keying (FH-MFSK) system has been proposed for digital mobile radio communications. The performance of the system is evaluated by studying average probability of error caused by transmission impairments. The degradation in performance due to Rayleigh fading and log-normal shadowing environments is determined. With perfect transmission, where the degradation in the system performance is due to mutual interference between users only, the system can accommodate up to 209 simultaneous users at an average bit error rate of 10^-3. The system capacity decreases to 110 users as a result of additive white Gaussian noise (AWGN), mutual interference, frequency-selective Rayleigh fading, and log-normal shadowing with normalized area mean of 20 dB and standard deviation of 6 dB     

Measurements and models of a land mobile satellite channel and their applications to MSK signals

The fading and shadowing effects observed on land mobile satellite signals are characterized in statistical terms. Models are developed in terms of probability distribution of the signal's envelope and phase as well as its rate of change with time. The multipath fading and shadowing effects modelled are typical of those encountered in a mobile-satellite link in rural and suburban areas. A comparison of the models with experimental data at 870 MHz and 1542 MHz is given. Applications of the models to predict performance of a minimum shift keying (MSK) signal at 2400 bits/s show that large margins are required to compensate for the effects of fading and shadowing. In addition, the results show that conventional coherent demodulation of a MSK signal may not be feasible due to phase variation caused by fading and shadowing. On the other hand, the results show that random FM has negligible effect on the probability of error of the MSK signal at 2400 bits/s when frequency demodulation is used.     

Interference Modelling in DS/CDMA Cellular Systems Operating in a General Fading Environment

Multiple access interference and the mobile radio environment are the primary limitations on the performance of DS/CDMA cellular systems. This paper presents the analysis of a DS/CDMA cellular system operating in a general fading environment. In particular the issues of signal fading, multiple access interference, and power control are addressed. A computationally efficient statistical method is used in the estimation of system performance. It is assumed that the variability of each received signal can be represented by fast Nakagami_m fading plus slower log-normal shadowing. Average bit-error-rate (BER) and outage probability are estimated as system performance indicators. The analysis shows, that as the variability of the fast fading of the received signal reduces, the performance of the system improves. However, when the signal undergoes both fast fading and shadowing, it is largely the shadowing that determines system performance. Use of forward link power control (that compensates for the variability due to shadowing) results in minimal performance improvement. However, in the reverse link significant improvement in performance can be achieved using a similar power control scheme.     

Micro- and macrodiversity MDPSK on shadowed frequency-selectivechannels

The performance of M-ary differential phase shift keying (MDPSK) on frequency-selective slow Rayleigh fading, lognormal shadowed channels with diversity combining is analyzed for mobile and portable applications. The use of L-branch equal gain postdetection microdiversity combining to mitigate the effects of fading and P-port macrodiversity to alleviate the effects of shadowing are investigated. Four performance criteria are considered for a frequency-selective multipath fading, intersymbol interference channel. These are, the short term bit error rate (BER), the irreducible BER, the complementary distribution over the lognormal shadowing of the average BER, and the probability that the instantaneous BER exceeds a threshold value, averaged over a spatial environment. Closed-form expressions for the four performance criteria are obtained. The BER and outage performance results show that diversity combining is an effective method for improving the system performance (and hence system reliability), when the normalized delay spread is not large. It is also seen that, in most cases, 4DPSK gives the best performance followed by 8DPSK and 2DPSK, respectively, for a given information throughput     

Performance analysis of digital cellular radio systems in Nakagamifading and correlated shadowing environment

The bit error rate (BER) performance of digital cellular radio systems was investigated in a Nakagami (1960) fading, correlated lognormal shadowing and additive white Gaussian noise (AWGN) environment for noncoherent differential phase shift keying (DPSK) modulation. Two models were used to determine the BER; the first one is based on the cumulative power levels of cochannel interferers while the second one is based on instantaneous cochannel interference power. The relative advantages of the two models were presented for various design parameters. The effects of bit energy to noise ratio, frequency reuse distance, cluster size, correlation coefficient, shadow spread, and fading parameter were studied. The BER was observed to be lower in a correlated shadowing environment compared with the uncorrelated case. The near-far effect was studied by assuming that both the desired and interfering mobiles are randomly located in their corresponding cells     

Channel coding for satellite mobile channels

The deployment of channel coding and interleaving to enhance the bit-error performance of a satellite mobile radio channel is addressed for speech and data transmissions. Different convolutional codes (CC) using Viterbi decoding with soft decision are examined with inter-block interleaving. Reed-Solomon (RS) codes with Berlekamp-Massey hard decision decoding or soft decision trellis decoding combined with block interleaving are also investigated. A concatenated arrangement employing RS and CC coding as the outer and inner coders, respectively, is used for transmissions via minimum shift keying (MSK) over Gaussian and Rayleigh fading channels. For an interblock interleaving period of 2880 bits, a concatenated arrangement of an RS(48,36). over the Galois field GF(256) and punctured PCC(3,1,7) yielding an overall coding rate of 1/2, provides a coding gain of 42dB for a BER of 10^?6, and an uncorrectable error detection probability of 1–10^?9.     

Frequency-hopping versus interference cancellation for TD-CDMA

This work considers asynchronous time division code division multiple access (TD-CDMA) systems with RAKE receivers and one stage of parallel interference cancellation (PIC) or serial interference cancellation (SIC). A general method based on the concept of spherically symmetric signals is presented for the evaluation of the average probability of error of uncoded TD-CDMA systems. Slow frequency-hopping (SFH) with frequency overlap (FO) between adjacent carriers and interference cancellation are also included in the analysis, which considers the multipath Rayleigh fading channel (which models indoor and outdoor vehicular radio propagation). We analyze quadrature phase shift keying (QPSK) modulation with coherent demodulation and multipath (frequency) diversity with maximal ratio combining (MRC). Power control, adaptive SFH, and interference cancellation are employed for improving the bit-error rate (BER) performance. It is found that the scheme with SFH, in spite of the FO, always improves the performance substantially, and interference cancellation, in general, provides the highest BER improvement     

Theory of the performance of a DECT receiver in a multipath channel

The performance of a digital enhanced cordless telecommunications (DECT) receiver in a multipath channel is studied. The following issues were investigated: irreducible bit-error rate (BER) performance of the differentially coherent detector in Rayleigh and Rician channels; BER performance in the presence of both the noise in the receiver and a multipath interference. The theoretical estimates of the irreducible error rate developed in the paper showed reasonable agreement with the data obtained from computer-based simulation of the DECT link through a Rayleigh multipath channel. The combined effect from receiver noise and multipath interference has been studied, and asymptotic formulas for the total error probability have been developed. The results of calculating the error probabilities using these asymptotics demonstrate good agreement with measured data     

Error floors of digital FM in simulcast and Rayleigh fading

A digital FM system in the presence of simulcast interference and/or Rayleigh fading exhibits performance floors, where increased signal strength does not reduce the error rate. Results obtained both in the lab, using a radio channel simulator, and in the field show this performance. Observation of signal waveforms indicates that the bit-error rate (BER) floor is a result of FM clicks during deep fades. We present a mathematical model that can be used to calculate the BER floors. The model is based on the calculation of the click shape as a function of amplitude imbalance, frequency offset, and postdetection filter impulse response. The Rayleigh fading is approximated with a two-signal simulcast by substituting the RMS Doppler spread for the simulcast frequency offset. A good match between calculated and measured results is obtained. It is found that the symbol errors caused by simulcast and Rayleigh fading can be treated as independent, and their effect is cumulative     

Error floor of unequalized wireless personal communications systemswith MSK modulation and training-sequence-based adaptive sampling

We analyze the error floor of unequalized personal communications systems using minimum-shift keying (MSK) with training-sequence-based adaptive sampling in a two-delay fading channel. We include Gaussian filtering of the input, finite accuracy in determining the optimum sampling time, and filtering at the receiver. We prove that for pure MSK and low time dispersion, training-sequence-based adaptive sampling can completely avoid errors caused by intersymbol interference. The actual errors are caused by “secondary” effects (filtering and finite-resolution sampling) in conjunction with the channel time dispersion. Errors occur if the normalized phasor of the channel impulse response falls into certain error regions; the computation of these regions gives physical insights into the error mechanism and allows a highly efficient computation of the average bit-error rate (BER). The average BER varies as K·(S/T)², where S is the RMS delay spread and T is the bit length. The proportionality constant K depends on the Gaussian filtering in the transmitter, the receiver filtering, and the amount of oversampling. The BER can be orders of magnitude lower than for the (quasi-) fixed sampling case, in which timing is derived solely based on the channel delay power profile. For two-branch diversity reception, we show that the BER is proportional to (S/T)⁴     

On the performance of DQPSK communication systems impaired bytiming error, mixer imbalance, and frequency nonselective slow Rayleighfading

In this paper, the error performance of the differential detection scheme is assessed for differentially encoded quaternary-phase-shift-keying (DQPSK) and π/4-shifted-DQPSK signals, It is assumed that the receiver suffers from mixer imbalance and timing error impairments. Expressions for the system bit-error rate (BER) are obtained when the channel is free of fading and when the channel suffers from frequency nonselective (flat) slow Rayleigh fading in the face of additive white Gaussian noise. To arrive at the desired expressions, the probability density function (pdf) of the phase angle between a pair of Gaussian random vectors is used to obtain the probability of bit error conditioned on the channel fading and timing error. The resulting expressions are then averaged over the nonnegligible timing error and the channel fading to arrive at the desired expressions for the system BER. Finally, with the aid of numerical analysis and in the presence of the aforementioned impairments, a number of conclusions are drawn and the performance of differential receivers for DQPSK and π/4-shifted-DQPSK modulation schemes are compared. It is shown here that the performance of a DQPSK receiver in the absence of fading and timing error is substantially impaired by mixer imbalance for BERs less than 10^-4. In the presence of fading, the performance is noticeably degraded due to mixer imbalance when a nonzero timing error is present     

Improving link layer performance on satellite channels with shadowing via delayed two-copy selective repeat ARQ

This paper focuses on improving performance of land mobile satellite channels (LMSCs) at high band (Ka-band or EHF band), where shadowing is the primary impediment to reliable data transmission. Compared with multipath fading, shadowing exists on a longer time scale; hence, interleaving to combat shadowing introduces unacceptably large decoding delay. We use Lutz's model to investigate bit-error rate/packet-error rate (BER/PER) performance of interleaving with various forward error correction (FEC) coding as a function of different channel parameters to demonstrate its limited effectiveness for combatting burst errors whose mean duration significantly exceed a link layer (LL) packet. We propose a delayed two-copy selective repeat ARQ (DTC-SR-ARQ) scheme, whereby two copies of a packet are sent-the second with a delay relative to the first-in every transmission or retransmission. Closed-form expressions for mean transmission time, success probability, and residual loss probability are provided and simulations used to validate the analysis. Furthermore, the issue of optimum delay is addressed as well, and a simple yet effective strategy is suggested to support transmission control protocol (TCP) traffic over this data link layer. DTC-SR-ARQ is shown to achieve much shorter additional delay than interleaving and compared with normal SR-ARQ, reduces mean transmission time at expense of a small increase in residual packet loss probability. Furthermore, ns2 simulation results show that for TCP traffic, DTC-SR-ARQ acquires higher end-to-end throughput than normal SR-ARQ.     

Optimal channel reuse in cellular land mobile radio systems

Origination probability for cochannel interference is introduced to the study of the influence of all cochannel interferers surrounding the base station of interest. In addition, the probability of cochannel interference, which is of importance in determining system parameters in a cellular communication scheme, is evaluated for the mobile radio environment as expressed by Rayleigh fading and shadowing. As a consequence, the optimal number of radio channels to allocate to each cell is derived through the use of a simple mathematical model. The theoretical results obtained are useful not only as a step in the maturation of the cellular land mobile radio system, but also for the development of the portable radio telephone system.