New technique of near maximum likelihood detection processes Текст научной статьи по специальности «Медицинские технологии»

Visiiyk NTIJU KP1 Seriia Radiolekhnika tiadioaparatobuduuannia, "2016, Iss. 67, pp. 84—88

УДК 681.3.09

New Technique of Near Maximum Likelihood

Detection Processes

AL-Rawi Muhanned1, AL-Rawi MuaayecP

1 University of Ibb, Yemen 2AL-Mustansiryia University, Iraq

E-mail: muhrawi&yahoo. com

This paper introduces new detector named newly adapt.ively designed near maximum likelihood detector (NADD). This detector combines adapt.ively three types of near maximum likelihood detectors, pseudobinary, pseudoquat.ernary, and pseudooct.onary. The performances of NADD. pseudobinary, pseudoquat.ernary, and pseudooct.onary detectors are measured using data transmission at. 9.6 kb/s over telephone channel. Simulation results show that, the performance of NADD is better than the performances of pseudobinary. and pseudoquat.ernary detectors, but. little bit. worse than the performance of pseudooct.onary detector.

Key words: Int.ersymbol interference: Near maximum likelihood detector: Adaptive detection

Introduction

The Maximum Likelihood Sequence Detector(MLSD) is a procedure for estimating a sequence of bits from a sequence of channel output observables. given a model of the communication system. In the presence of Intcrsyriibol Interference(ISI). the Viterbi algorithm(VA) provides an efficient way of computing the MLSD [1,2]. However, the VA still becomes impractical when the time spread of the ISI is large because of the exponential relation between ISI time spread and VA complexity.

One way of reducing the complexity of Viterbi detector is by giving the VA an approximate channel model with a shorter time spread than that of the original channel. Considerable researches have nsed this way to achieve the performance of the VA at reduced complexity [3 18].

Another way which is considered in this paper is to nse detectors called Near Maximum Likelihood Detectors [19 26]. These detectors operate similarly to Viterbi algorithm, but using different selection process for the stored sequences of possible data symbol values, and only a very few of these sequences are stored with the corresponding costs.

1 Data transmission system

Fig. 1 shows the model of data transmission system. The first part in this model is random data generator which generates binary data, and each 4-bit is mapped into one of 16-point QAM constellation. Tims, the output of random data generator is data symbols jsj}, and the possible values of Sj are given % all combination of ±1,

±3, & ±ji, ±j3 where j = %/—I. Then, the data symbols jsj} enter the Quadrature Amplitude Modulation(QAM) transmitter which consists of transmitter filter and QAM modulator. The transmitter filter is a low-pass filter performs the function of limiting the signal spectrum before modulation process.

Fig. 1. Model of data transmission system

The resulting output of the QAM transmitter is QAM signal with carrier frequency of 1800 Hz and symbol rate of 2400 band giving an information rate

of 2400 x 4 bits = 9600 b/s. The output of the QAM transmitter passes through telephone channel, and Additive White Gaussian Noise (AWGN) added to the signal before entering the QAM receiver. The QAM receiver consists of QAM demodulator and receiver filter. The receiver filter is a low-pass filter used in combination with the transmitter filter to produce realistic levels of intersymbol interference. The output of QAM receiver is data symbols {r.} used by the Least Mean Square (LMS) estimator to estimate the sampled impulse response (SIR) of baseband telephone channel. Finally, the data symbols {ri} and SIR are used by the detector to obtain the detected symbols {si}.

2 Detector model

2.1 Pseudo-binary, -quaternary, -octonary detector

The pseudobinary detector (BD), psondoqnatorriary detector (QD) [20]. and pseudooctonary detector (OD) [24] are described as follows.

Just prior to the receipt of the signal sample ri at time t = iT, the detector holds in store k (n-component) vectors Qi-1 given below (k = 2 for pseudobinary, k = 4 for pseudoquaternary and k = 8 for pseudooctonary),

Qi—1 [Xi—n

Xi-l]

i-1

Ui—1 = E

3=0

i — 2 E

3=0

- E X(3 — h)vh

h=0

g

: - EX(3—h)Vh

h=0

Pi [Xi—n ^i — n+1

Xi]

on any one of the four different values of its 16 possible values. In pseudobinary. the number of expanded vectors is 8 (see Fig. 2). in pseudoquaternary is 16 (see Fig. 3). while, in pseudooctonary is 32 (see Fig. 4). Then the detector evaluates for each expanded vector Pi its cost given by

Ui

Ui-1 +

r'i - E X(i — h)Vh

h=0

Ui—2 + Wi—1 + Wi (4)

The detector then selects the vector Pi with the smallest cost and takes its first component xi-n as the detected value s'i-n of the data symbol si-n.

All vectors {Pi} for which s'_n = discarded,

and the first components of all remaining vectors are omitted to give the corresponding n-component vectors {Qi} where

Qi = [a

-n+1

-n+2

]

(5)

(1)

The detector then selects from the resulting vectors {Q'} the k vectors with the lowest costs {U'}.The k vectors {Q'} together with their costs are stored in preparation for the next detection cycle.

where x. is possible value of s..

Each stored vector is associated with a cost Ui-1 given by

+ Wi—1 =

= Ui—2 + Wi—1 (2)

where {vh} is the sampled impulse response of baseband telephone channel (estimated by LMS estimator) having length of (g + 1) (where g < n), and wi-1 is the corresponding estimate of the noise component in the received sample ri-1.

On the receipt of the signal sample r., the detector expands every vector Qi-1 into four (n + 1) components vectors {P'}, given below, having smallest cost. The selection of P.' is achieved through the use of simple threshold-level comparison and does not involve the computation of any costs.

t=(i-1)T

Vector having 1st minimum cost

Vector having 2nd minimum cost

t=iT

t=(i+1)T

Vector having 1st minimum cost

Vector having 2n minimum cost

t Vector having 1s minimum cost

yVector having 2n minimum cost

(3)

The first n-components of P.' 9T6 clS shown in the original vector Qi-1 and the last component x. takes

Fig. 2. Configuration of pseudobinary detector

After each detection process, and to prevent overflow duo to the increase in costs over any transmission, the smallest cost is subtracted from the cost of each vector, so that the value of the smallest cost is always reduced to zero.

The starting up procedure for the detector begins with k stored vectors {Qi-1} that are all the same and correct. A zero cost is allocated to one of the k vectors and a very high cost to each of the remaining vectors. After a few received samples, the detector holds k vectors which are all different and are all derived from the original vector with zero cost.

2

X

X

2

r

2

t=(i-1)T

Vector having 1s minimum cost

Vector having 2nd minimum cost

Vector having 3r minimum cost

Vector having 4 minimum cost

t=iT

t=(i+1)T

Vector having 1st minimum cost

Vector having 2nd minimum cost

Vector having 3rd minimum cost

Vector having 4th minimum cost

Vector having 1s minimum cost

Vector having 2n minimum cost

Vector having 3r minimum cost

Vector having 4t minimum cost

Fig. 3. Configuration of pseudoquaternary detector

t=(i-1)T

Vector having 1st minimum cost

Vector having 2n minimum cost

Vector having 3r minimum cost

Vector having 4 minimum cost

Vector having 5 minimum cost

Vector having 6 minimum cost

Vector having 7 minimum cost

Vector having 8 minimum cost

t=iT

t=(i+1)T

Vector having 1st minimum cost

Vector having 2n minimum cost

Vector having 3r minimum cost

Vector having 4 minimum cost

Vector having 5 minimum cost

Vector having 6 minimum cost

Vector having 7 minimum cost

Vector having 8 minimum cost

Vector having 1s minimum cost

»Vector having 2nd minimum cost

Vector having 3r minimum cost

Vector having 4t minimum cost

Vector having 5t minimum cost

, Vector having 6 h minimum cost

Vector having 7t minimum cost

Vector having 8t minimum cost

changos between 2. 4, and 8 which is assi gnod every time a signal sample r is received (see Fig. ). One criteria of assigning the value of k is given below,

2 if (Wi)min ^ 2

4

if (Wi)

and <

Wi )min > 2

(wí-3)mín + (wí-2)mín + (wí-1)^

3

(wí-3)mín + (wí-2)mín + (wí-1)^

(Wi-3)min + (Wi-2)„

3

8 if (Wi)r

>

3

(Wj-3 )mjn + (Wj-2 )mjn + (Wj- 1 )„

3

(6)

The above criterion assigns the value of k depending on comparison between the current minimum value of w and the average or half of the average of previous three minimum values of w. When the value of (Wi)min increases, more vectors are needed to be evaluated, so k increases too. and vice versa.

t=(i-1)T

k=8, Initial state

Vector having 1st minimum cost

Vector having 2n minimum cost

Vector having 3r minimum cost

Vector having 4 minimum cost

Vector having 5 minimum cost

Vector having 6 minimum cost

Vector having 7 minimum cost

Vector having 8 minimum cost

t=iT

k=2, assuming the condition for k=2 in eq.6 is satisfied

Vector having 1 minimum cost

Vector having 2ni minimum cost

t=(i+1)T

k=4, assuming the condition for k=4 in eq.6 is satisfied

Vector having 1s minimum cost

Vector having 2n minimum cost

Vector having 3r minimum cost

Vector having 4 minimum cost

Fig. 4. Configuration of psendooctonary detector

2.2 Newly adaptively designed detector

This newly adaptively designed detector (NADD) combines adaptively BD, QD, and OD. The value of k

Fig. 5. Newly adaptively designed detector

The detector needs to store (wi-3)min, (wi-2)min, and (wi-1)min before subtracting the cost of any vector from the smallest cost.

The starting up procedure begins with k = 8 vectors that are all the same and correct. A zero cost is allocated to one of the eight vectors and a very high cost to each

k

of the remaining seven. The initial values of (wi-3)min, (wi-2) min, and (w'-1)min are zero.

3 Simulation results

A series of computer simulation tests have been carried out on the system in Fig. 1 with four types of detectors. BD. QD, OD, and NADD to determine their relative tolerance to AWGN when operating over telephone channel.

The performance of the whole system is measured by-drawing symbol error rate (SER) versus signal-to-noise ratio (SNR). The SER is given by

SER = NEDS/ NTS

where NEDS is the number of erroneous detected samples & NTS is the number of total transmitted samples.

Fig. 6 shows comparison among the four detectors. It seems that at error rate of 10-5 ,the performance of NADD is better than the performance of BD by approximately O.C dB, and better than the performance of QD by approximately 0.2 dB , but worse than the performance of OD by approximately 0.1 dB.

0 1-------

16 18 20 22 24 26 28 30 S/N.dB

Fig. 6. Error rate perfomance

Conclusion

A new detector was developed to mitigate the ISI introduced by the communication channel. This detector which is named NADD combines adaptivoly tliroo detectors BD. QD. and OD. So. the three detectors can be replaced by one detector which leads to reduce the complexity of whole detector model. Simulation results show that the performance of NADD is better than that for BD and QD but little bit worse than that for OD.

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Новий шдхщ до реал!защ1 декодера ква-з1максимально*1 правдопод1бност1

Муханнед Аль-Равг, Муаайед Аль-Равг

В робот! представлений повий адаптивпий детектор кваз!максималыюго правдопод1бпост1 (НАДКП). Цей детектор представляв собою адаптивпе иоедпаппя в соб! трьох тишв детектор!в максимально! правдопод1бпост1: псевдобшарпого, псевдочетвертпого 1 псевдов!с!мкового. Продуктившсть НАДКП, псевдобшарпого, псевдочетве-р1чпого 1 псевдовосьмер!чпого детектор!в вим!ряпа за допомогою передач! дапих по телефонному каналу па швпдкост! 9.6 кб/с. Результати моделюваппя показали, що продуктившсть НАДКП краща, шж у псевдобшарпого ! псевдочетвертпого детектор!в, але трохи г!рша шж продуктившсть псевдов!с!мкового детектора.

Клюновг слова: м!жсимвольпа !птерферепц!я: детектор кваз!максималыю1 правдопод!бпост!: адаптивпе виявлеп-

Новый подход к реализации декодера квазимаксимального правдоподобия

Муханнед Аль-Рави, Муаайед Аль-Рави

В работе представлен новый адаптивный детектор квазимаксималыюго правдоподобия (НАДКП). Этот детектор представляет собой адаптивное сочетание в себе трех типов детекторов максимального правдоподобия: псевдобипарпого, псевдочетверичпого и псевдово-сьмеричпого Производительность НАДКП, псевдобипарпого, псевдочетверичпого и псевдовосьмеричпого детекторов измеряла с помощью передачи даппых по телефонному каналу па скорости 9.6 кб/с. Результаты моделирования показали, что производительность НАДКП лучше, чем у псевдобипарпого и псевдочетверичпого детекторов, по немного хуже чем производительность псевдовосьмеричпого детектора.

Ключевые слова: межеимвольпая интерференция: детектор квазимаксималыюго правдоподобия: адаптивное обнаружение