Postdetection optimal diversity combiner for DPSK differentialdetection

Postdetection diversity reception weights and combines all the detector outputs before symbol decision to combat the effects of multipath fading. A theoretical analysis of a postdetection optimal diversity combiner that can minimize the symbol error probability for differential phase shift keying (DPSK) differential detection in the presence of multiplicative Rayleigh fading, and co-channel interference (CCI) is presented. The effect of unequal average powers among diversity branches is taken into account. It is shown that the postdetection maximal-ratio combiner (MRC) described previously by the author is not optimal unless all branches have the same average power. It is also found that the combiner optimized for the effect of CCI (fading induced random FM noise) should weight each branch detector output in inverse proportion to the average CCI power (desired signal power). Assuming two-branch diversity, calculated BER (bit-error-rate) performance of π/4-shift QDPSK due to AWGN, CCI, and random FM is presented. In addition, the BER due to multipath channel delay spread (which is not treated in the theoretical analysis) is also computed to find the optimal combiner     

Error rate performance of digital FM mobile radio withpostdetection diversity

An analysis of bit error rate (BER) in a binary digital FM system with postdetection diversity is presented. Expressions for the average BER due to additive white Gaussian noise (AWGN), random FM noise and delay-spread in the multipath channel are derived for reception using differential demodulation (DD), and frequency demodulation (FD) assuming independent fading signals. Calculated results for MSK show that the BER performance is strongly dependent on the RMS-delay/bit-duration ratio and that the delay-spectrum shape is of no importance when the receiver predetection filter product is optimized for the effect of AWGN. The effect of fading correlation on the diversity improvement is also analyzed for a two-branch case with multiplicative Rayleigh fading signals. Expressions for the average BER due to AWGN and random FM noise are derived. Calculated results are shown for the average BER due to random FM noise assuming a horizontally spaced antenna system at a mobile station. It is shown that the use of small antenna spacings leads to a diversity improvement greater than that obtainable for the case of independent AWGN     

Effects of postdetection selection diversity reception in QDPSK land mobile radio

Postdetection selection diversity reception for Nyquist pulse shaped quadrature differential PSK (QDPSK) signal transmissions is addressed. Average bit error rate (BER) performance with differential and coherent demodulation is analysed for multiple-branch diversity reception under slow multipath Rayleigh fading. Diversity effects in real fading environments are verified by 8 and 16 kbit/s transmissions at 1.45 GHz carrier frequency.<>     

Experimental evaluation of combined postdetection diversity andconcatenated channel coding

The combined effects of postdetection diversity reception and concatenated channel coding are experimentally evaluated for π/4-shift QDPSK signal transmission over a Rayleigh fading channel. Two-branch postdetection diversity reception using maximal ratio combining (MRC) and selection combining (SC) are considered. The concatenated channel coding uses the Reed-Solomon (15,k) code of GP(2 ⁴) as the outer code and the BCH (7,4) code as the inner code (k=9,11,13). Measured bit error rate (BER) performance results are presented under cochannel interference (CCI) and multipath channel delay spread, as well as additive white Gaussian noise (AWGN)     

Postdetection MRC diversity for pi /4-shift QDPSK mobile radio

Diversity reception using a postdetection maximal-ratio combiner (MRC) was experimentally investigated for pi /4-shift QDPSK signal transmission in Rayleigh fading environments. Two-branch postdetection MRC diversity reception provides a diversity gain, for a required E/sub b//N/sub 0/, of about 1.5 dB over selection diversity. It is also effective in reducing the impact of multipath channel delay spread. The average BER due to delay spread can be further reduced by a factor of about 1.5 times from selection diversity.<>     

Postdetection selection diversity effects on digital FM land mobile radio

The postdetection selection diversity effects on a binary digital FM system are theoretically analyzed in the fast Rayleigh fading signal environment encountered in the typical UHF or microwave land mobile radio channels. Both differential and discriminator detections are considered for demodulation of digital FM signal. The average error rate is presented by a simple closed form including both effects of Rayleigh envelope fading and random FM noise. A few examples of numerical results for minimum shift keying (MSK) are graphically presented.     

Random FM noise with selection combining

Random FM noise using two-branch selection combining with correlated Rayleigh fading signals is analyzed for land mobile radio systems. General expressions are derived for the cumulative distribution function and mean square value of the random FM noise; they can be applied to any type of diversity such as space, polarization, etc. Calculated results show that, if two horizontally spaced antennas parallel with the direction of vehicle motion are used at a mobile station, random FM noise can be significantly reduced for small antenna spacings     

Postdetection selection diversity reception with correlated,unequal average power Rayleigh fading signals for π/4-shift QDPSKmobile radio

The diversity gain degradations due to fading correlation and unequal average power are investigated for practical, two-branch postdetection selection diversity reception. The average bit error rate (BER) of π/4-shift QDPSK is theoretically analyzed taking into account additive white Gaussian noise (AWGN), cochannel interference, and multipath channel delay spread; exact diversity gain degradations are calculated. Simple and useful approximate expressions for the gain degradations are also presented     

Postdetection phase combining diversity

We propose a postdetection phase combining (PC) scheme for the two branch diversity reception of differential phase shift keying (DPSK) over multipath fading channels. The receiver has a differential phase detector (DPD) in each diversity branch, and the combiner weights each detector output in proportion to the vth power of the signal envelope at the detector's input. For π/4-shift QDPSK over frequency-flat Rayleigh fading channels, we find via computer simulation that the optimum weight factor is v=2, and that our simple, practical combining scheme performs almost as well as postdetection maximal ratio combining (MRC). We demonstrate similar relative performances for frequency-selective fading channels and for channels with co-channel interference (CCI)     

On the crossing statistics of phase processes and random FM noise in Nakagami-q mobile fading channels

The crossing statistics of phase processes and random frequency modulation (FM) noise are studied for Nakagami-q fading channels. Closed-form expressions are first derived for the probability density function (PDF) and the cumulative distribution function (CDF) of random FM noise. The crossing rate of the phase process is then obtained for any crossing level of the phase. Moreover, the conditional PDF of random FM noise and envelope processes-conditioned on the crossings of an arbitrary level of the phase-are investigated. Since the Rayleigh fading channel is a special case of the Nakagami-q fading channel, the derived expressions are verified by comparison with results known for Rayleigh fading channels. In addition, it is shown that the derived analytical results are in excellent agreement with those obtained by computer simulations. The presented results are useful, for example, for studying the statistics of noise spikes occurring in limiter-discriminator FM receivers and for investigating the cycle slipping phenomenon in phase-locked-loop schemes when considering the transmission over Nakagami-q mobile fading channels.     

BPSK system with sounder to combat Rayleigh fading in mobile radio communication

A simple method is proposed to remove random FM from a fast Rayleigh faded binary phase shift keying (BPSK) signal and the great improved performance of reducing the irreducible error is presented. In the mobile radio environment, there happens inevitably a fast Rayleigh fading which causes random FM. The phase error of the reference signal due to random FM will degrade the bit error rate (BER) performance, even if the signal-to-noise ratio is sufficiently high. In the realization of reliable mobile communication, removal of this random FM is an unavoidable theme. Proposed strategy is to transmit a sounding continuous wave (CW) together with a BPSK signal, each phase being kept orthogonal and each power being kept the same. This CW wave is also used as the reference signal in coherent reception. The BER performance of this system is worse by 3 dB than that of the coherent BPSK in a slow Rayleigh fading environment.     

Further results on the bit error probabilities of MDPSK over thenonselective Rayleigh fading channel with diversity reception

This paper presents a fundamental approach for deriving the bit error probability of BDPSK and QDPSK over the nonselective Rayleigh fading channel for a receiver with an arbitrary IF filter, and for a fading process with an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. The results generalize those published earlier which were restricted to matched filter reception and to a fading process with a small Doppler bandwidth compared to the symbol rate. This allows the error probability to be studied in the presence of varying degrees of ISI due to the bandlimitation of the received signal by the IF filter, and in the presence of fading fluctuations of various rates. The analytical approach presented is simple, and yet powerful in that it can handle the case of diversity reception. This is a great advantage over the alternative approach of using the distribution of the differential phase of the received signal over a symbol interval. The bit error probability results apply to both conventional BDPSK and QDPSK, as well as π/2-2DPSK and π/4-4DPSK, and allow the irreducible bit error probability as well as the SNR at which this irreducible value sets in to be studied as a function of the Doppler bandwidth and IF filter bandwidth. The computed results are applicable to the design of digital cellular mobile communication systems     

An adaptive coding scheme with code combining for mobile radiosystems

The authors propose and study an adaptive error-control coding scheme for binary digital FM (BFM) mobile radio transmission. The scheme employs code combining through packet retransmissions. The number of transmissions of a packet is in proportion to the channel fading/noise levels, which is in contrast to time diversity techniques where a fixed number of repetitions of a data packet is performed even in the absence of channel errors. Furthermore, the receiver uses received signal envelopes as channel state information, which significantly improves the throughput and bit error rate (BER) performance. Performance of the proposed scheme is analyzed for frequency-flat Rayleigh fading channels with additive white Gaussian noise (AWGN), co-channel interference and random FM noise     

瑞利衰落信道MDPSK相位比较解调性能

本文提出一种适合于瑞利衰落信道多进制差分相移键控系统相位比较解调的性能分析方法，推导出符号错误率解析表示式，考虑了瑞利衰落、时间选择性衰落和高斯白噪声对体制性能的影响，并针对衰落功率谱为高斯型和矩形分别对二进制、四进制和八进制情形进行了数值计算。     

Differential phase noise distribution of Rayleigh faded DPSK signal with selection diversity

Closed-form expressions for the distribution of differential phase noise due to additive white Gaussian noise (AWGN) are derived for predetection selection diversity with independent, equal power very slow Rayleigh fading signals. Also investigated are the effects of fading correlation and unequal powers between diversity antennas on practical two-branch diversity reception. The derived phase distribution is used to calculate the average symbol error rate of 8 DPSK as an example.<>     

采用两条支路分集接收的相关瑞利衰落信道容量

本文研究采用两条支路最大比合并(MRC)或选择合并(SC)分集接收的相关瑞利衰落信道理论容量推导恒定发射功率自适应M进制正交幅度调制(M-QAM)的频谱效率,并将它们与独立同分布瑞利信道理论容量进行比较,其结果对收发信机之间无视距分量路径、接收机上分集天线之间的距离小于半个波长的无线通信系统设计具有指导作用.     

A formula for an FM signal under Rayleigh fading [mobile radio]

A simple formula for the baseband signal-to-noise ratio of an FM signal under Rayleigh fading is derived. The formula automatically includes the noise component due to modulation. Calculated values of the average signal-to-noise ratio for FM and AM signals under Rayleigh fading are given. The results show that the FM signal with a modulation index of one or greater, outperforms an AM signal under identical fading conditions     

Postdetection phase combining diversity for reception of faded DPSK signals

A new postdetection diversity scheme for the differential phase detection of faded DPSK signals is proposed. It combines the detector outputs in proportion to the squared value of each branch signal envelope. The average BER of pi /4-shift quaternary differential phase shift keying (QDPSK) with two-branch diversity is obtained through computer simulations assuming Rayleigh fading. It is found that the proposed diversity is superior to selection diversity by approximately 1.5 dB.<>     

Analysis of DPSK error rate due to multipath delay spread

The intersymbol interference (ISI) produced by multipath channel delay spread can be approximated as Gaussian noise. The equivalent average signal-to-noise power ratio (SNR) is defined. Very simple expressions for average bit error rate (BER) due to delay spread are derived for linear quaternary DPSK (QDPSK) transmission with differential detection over mobile radio Rayleigh fading channels.<>     

Error probability performance of L-branch diversity reception ofMQAM in Rayleigh fading

New exact expressions involving hypergeometric functions are derived for the symbol-error rate (SER) of M-ary quadrature amplitude modulation (MQAM) for L branch diversity reception in Rayleigh fading and additive white Gaussian noise (AWGN). The diversity combining techniques considered are maximum ratio combining (MRC) and selection combining (SC). MRC with identical channels and dissimilar channels are analyzed