FER and Outage capacity analysis of Space-Time Trellis Coding using Modulation Techniques

FER and Outage capacity analysis of Space-Time Trellis Coding using Modulation Techniques

Ishita Aggarwal, India, iaggarwal1988@gmail.com

Abstract : In this paper, we analyze the performance of space-time codes.Here we derive FER and outage capacity for space- time trellis coded modulations over Rayleigh fading channels. This thesis is concerned with the FER and Outage Capacity Analysis of Space-Time Trellis Coding (STTC) using Modulation Techniques. The analysis of channel codes for improving the data rate and the reliability of communications over fading channels using multiple transmit antennas has been considered. Data is encoded by a convolutional encoder and the en- coded data is split into streams that are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals with noise. Performance criteria for designing such codes, under the assumption that the fading is slow and frequency nonselective, is also analysed.

I.INTRODUCTION

High rate of data transmission is limited in wireless communication due to factors like limited bandwidth, propagation loss,noise.

Radio waves propagate from a transmitting antenna, and travel through free space un- dergoing absorption, reflection, refraction, diffraction, and scattering. They are greatly affected by the ground terrain, the atmosphere, and the objects in their path,

like buildings, bridges, hills, trees, etc. These multiple physical phenomena are responsible for most of the characteristic features of the received signal. In most of the mobile or cellular systems, the height of the mobile antenna may be smaller than the surrounding structures. Thus, the existence of a direct or line-of-sight path between the transmitter and the receiver is highly unlikely.

At the receiver, these multipath waves with randomly distributed amplitudes and phases combine (constructively and destructively) to give a resultant signal that fluctuates in time and space. Therefore, a receiver at one location may have a signal that is much different from the signal at another location, only a short distance away, because of the change in the phase relationship among the incoming radio waves. This causes significant fluctuations in the signal amplitude. This phenomenon of random fluctuations in the received signal level is termed as fading. Space time (ST) codes have recently attracted significant attention since they provide an effective way to fully exploit both transmit diversity and receive

diversity to overcome the impairments of wireless fading channels.

1. Space Time Coding

   A spacetime code (STC) is a method employed to improve the reliability of data transmission in wireless communication systems using multiple transmit antennas. STCs rely on transmitting multiple, redundant copies of a data stream to the receiver in the hope that at least some of them may survive the physical path between transmission and reception in a good enough state to allow reliable decoding.

   Space time codes may be split into two main types:

   convolutional) code distributed over time and a number of antennas ('space').

   Space-time trellis codes encode the input symbol stream into an output vector symbol stream. Unlike space-time block codes, space-time trellis codes map one input symbol at a time to an Mt × 1 vector output. Since the encoder has memory, these vector codewords are correlated in time. Decoding is performed via maximum likelihood [5]-

   1. sequence estimation.

      • Spacetime trellis codes (STTCs) distribute a trellis code over multiple antennas and multiple time-slots and provide both coding gain and diversity gain.

      • Spacetime block codes (STBCs) act on a block of data at once (similarly to block codes) and provide only diversity gain, but are much less complex in implementation terms than STTCs.

   Space-time coding has been intro- duced as an effective means to achieve high data rates in such wireless communication environment. This technique inte- grates channel coding, modulation, and multiple transmit an- tennas at the base station, with optional receive diversity incor- porated at the mobile station.

2. Spacetime trellis codes

   STTCs are a type of spacetime code used in multiple-antenna wireless communications. This scheme transmits multiple, redundant copies of a trellis (or

   The input data bits coming at the rate of m bits/symbol are encoded by a channel (convolutional) encoder, to produce m + r bits which are mapped with the help of a constellation mapper to give on of the possible states of the encoder. This is then further modulated using techniques like PSK, FSK, QAM etc. and transmitted through Nt transmit antennas to the channel, where the signal gets corrupted by noise. At the receiving end, Nr receive antennas are used to receive the transmitted signal which is then demodulated and the resultant noise affected signal is feed to a Viterbi Decoder. It is a maximum likelihood (ML) decoder that gets back the original signal by construction a trellis structure. The decoder is designed such as to minimize the error due to noise or any other factors.

   A convolution code is generated by passing by passing the information sequence to be transmitted through a linear finite-state shift register. In general, the shift reg-

   ister consists of K (k -bit) stages and n linear algebraic function generators as shown

   below.

   A convolution code is generated by passing by passing the information sequence to be transmitted through a linear finite-state shift register. In general, the shift reg- ister consists of K (k -bit) stages and n linear algebraic function generators as shown

   below.

   Code Rate: It is defined as the ratio of the input bits to the encoder to the output bits produced per unit time.

   Constraint Length: It is the number of shifts over which a single message bit can influence the encoder output. In an encoder with M -stage shift register, the memory of the encoder equals M message bits, and K = M + 1 shifts are required to enter the shift register and finally come out. Hence the constraint length of the encoder is K.

   Generator Polynomial: Each path connecting the output to the input of a convolutional encoder may be characterized in terms of its impulse response, defined as the response of that path to a symbol 1 applied to its input, with each flip-flop in the encoder set initially in the zero state. Equivalently each path can be characterized in terms of a generator polynomial, defined as the unit-delay transform of the impulse- response. To be specific, let the generator sequence (g0i), g1i), g2i), · · · · · · , gMi)) denote the impulse-response of the ith path, where the coefficients g0i), g1i), g2i), · · · · ·

   • , gMi) equal 0 or 1. Correspondingly, the

   generator polynomial of the ith path is defined by

   g(i)(D) = g0i) + g1i)D + g2i)D2 + · · · · · · + gMi)DM

3. System Model: STTC

   Consider a mobile communication system

   where the base-station is equipped with antennas and the mobile is equipped with antennas. Data is encoded by the channel encoder, the encoded data goes through a serial-to-parallel converter, and is divided into n streams of data. Each stream of data is used as the input to a pulse shaper. The output of each shaper is then modulated. At each time slot t, the output of modulator i is a signal ct that is transmitted using transmit antenna (Tx antenna) i for 1 i n.

   We emphasize that the n sinals are transmitted simultaneously each from a different transmit antenna and that all these signals have the same transmission period T . The signal at each receive antenna is a noisy superposition of the n transmitted signals corrupted by Rayleigh fading. It is assumed that the elements of the signal constellation are contracted by a factor ofEs chosen so that the average energy of the constellation is 1.

   Important parameters:

   • Frame error rate

     In this case Ei,j = 0 and Ki,j for all i and j. Then the inequality obtained above can be written as

     Let r denote the rank of matrix A, then the kernel of A has dimension n r and exactly nr eigen values of A are zero. Say the

     nonzero eigen values of A are 1,2,···,r, then it follows from inequality above that

     This is the expression for the Frame Error Rate (FER).

   • Outage Capacity

     It is defined in terms of mutual information between input and output, I(input, output).

     When the output is composed of independent additive noise, and multiple of the transmitted signals, then I(input, output)

     = (output) (noise). Here () represents entropy. Since (output) and (noise) are each expressed as the sum of NT conditional entropies.

4. RESULTS

   The plot of outage capacity and frame error rate (FER) is drawn for different number of transmit and receive antenna.

   Case 1:

   N =2 ,M =1 ,Frame length = 100 Frames = 20 ,Initial SNR = 1 dB

   Fig1.FER v/s SNR for 4-PSK using N=2 transmit and M=1 receive antennas

   Fig 2.Outage capacity v/s FER for 4- PSK usingN=2 transmit and M=1 receive antennas

   Case 2:

   N =2 ,M =2 ,Frame length = 100 Frames = 20 Initial SNR = 1 dB

   Fig 3: FER v/s SNR for 4-PSK using N=2 transmit and M=2 receive antennas

   Fig 4. Outage capacity v/s FER for 4- PSK using N=2 transmit and M=2 receive antennas

   Case 3: 8-PSK N=2 transmit and M=1 receive antennas

   N =2,M =1

   Frame length = 99 Frames = 20 Initial SN R = 1 dB

   Fig 5 : FER v/s SNR for 8-PSK using N=2 transmit and M=1

   receive antennas

   Fig 6: Outage capacity v/s FER for 8- PSK using N=2 transmit and M=1 receive antennas

5. CONCLUSION

This paper defined the analysis and evaluation of Space-Time Trellis Coding (STTC) using PSK modulation in digital communication. We provided examples of

spacetime trellis codes for transmission using multiple transmit antennas. we compare the performance of STTC in terms of frame error rate keeping the transmit power, spectral efficiency and number of trellis states fixed. We discover that a simple concatenation of space time block codes with traditional AWGN (additive white Gaussian noise) trellis codes outperforms some of the best known space-time trellis codes at SNRs of interest. Our result holds for a small number of trellis states with one or two receive antennas, and is useful for the design and implementation of multiple- antenna wireless systems. But for higher number of receiver space time trellis code are used. In this simulations have been conducted to study the Frame Error Rate (FER) performance and outage capacity in wireless communication for different number of transmit (N=2) and receive antennas (M=1,2,5) with 4-PSK and 8-PSK modulation Scheme.

ACKNOWLEDGMENT

I would like to thank Prof. Javed Ashraf,

A.F.S.E.T for his support for the success of this work.The present work is a part of M.Tech.(ECE) carried out at AL-Falah School of Engineering and Technology

(AFSET), Dhauj, Haryana affiliated to Maharshi Dayanand University, Rohtak.

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