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Enhancement Of Diversity Gain In Mimo System


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Enhancement Of Diversity Gain In Mimo System

  1. 1. ENHANCEMENT OF DIVERSITY GAIN IN MIMO SYSTEM SUNJEEV KUMAR GUPTA Telecommunication Department of Nepal Telecom (NTC), URL:, Kathmandu, Nepal E-mail: /, Tel: +977-9855068555 Abstract- In wireless Environment the signal is Antenna separation: With wider separations betweenpropagating from transmitter to receiver along number of transmit antennas and between receive antennas, there is adifferent paths collectively called multipath causing three greater time difference among the various signal receiver caneffects: path loses, microscopic and macroscopic fading which more easily distinguish between those paths and recover thecan be mitigated by different diversity techniques. Multiple-Input-Multiple-Output (MIMO) on the front exploits spatial data with fewer errors than with closed spaced antennas.diversity by having several transmit and receive antenna, each Signal path knowledge: To coordinate the decoding ofreceive antenna sees different versions of transmitted signal and transmitted signals, and to adjust the transmitted signal forwhen this versions are combined in a proper manner, the impairment in the signal path, additional information must beoutcome has better quality (lower bit-error-rate, BER) or higherdate rate than a single version of signal. Specifically, if the communicated between transmitter and receiver. For this,number of multi path components exceeds certain value, the transmitter sends a “training signal” in addition to the normalincrement of channel capacity can be proportional to the data content, to enable synchronization of the receiver withnumber of transmit and receive antennas and no additional all transmitted channels. But these signals can consume apower or bandwidth is required. In this paper, I strongly focus significant portion of total data stream when operation is in aon spatial receiving antenna diversity concept accomplishing difficult propagation environment with deep, rapidDiversity processing technique called Maximum Ratio propagation changes.combining (MRC), in which output signals from diversityantennas are weighted by their respective SNR, Co-phased and Equipment complexity: The enhance performance ofadded to optimize the received signal power or Signal-to Noise MIMO comes at the cost of complexity. Each channelRatio (SNR) which is one of the key features that constitute the requires most of a transmitter’s and receiver’s circuitry-performance improvement of MIMO system. modulator through power amplifier in a transmitter, LNA through demodulator in a receiver. 1. INTRODUCTION MIMO is the single frequency system uses space –time 2. RECEIVING ANTENNA DIVERSITYdiversity, transmitting different portions of data via separate CONCEPTantennas. These multiple signals are summed at the receiver The multiple propagation paths of the mobile signal to theto recover the entire data stream. Because transmitted data is radio base station antenna results in short term or fast fadingdivided among two or more channels, the net data rate can be of the signal. This multiple path propagation channel oftenhigher than a single channel, single antenna system. The referred to as a Rayleigh fading channels experiences largedifficulty is that the channels use same frequency-the drops in received signal strength. So one technique toseparation is accomplished by the different time delays as the mitigate these short-term fades is receiving antenna diversitysignal travels between transmit antenna and each receive in which the signals received over different antenna/channelsantenna [1]. are combined properly to increase the probability that the There is some functional similarity to Orthogonal received signal is of adequate strength. The basic principle ofFrequency Domain Multiplexing (OFDM) which also divides antenna diversity is that multiple antenna outputs experiencethe data into multiple channels. However, in OFDM, different signals due to the different channel conditions andchannels are separated in frequency and phase but are these signals are only partially correlated. Thus, it is highlytransmitted by a single transmitter and antenna. The biggest likely that if one antenna is of deep fade then the other one isdifferences are that OFDM requires more bandwidth for its not and provides sufficient signal, because in multipathtotal signal, while MIMO requires more antennas, with a propagation conditions, as encountered with a blocked orseparate transmitter and receiver for each antenna. The key shadowed direct line-of-sight(LOS) path, each receivefactors that influence a MIMO system are: antenna experiences different fading environments. Diversity antennas provide three major benefits [2] as: Reliability is improved in multipath channels where interference from
  2. 2. reflected signals causes fading of the received signal. The 4. MAXIMUM RATIO COMBININGfade level experienced on average for a given outage (MRC)probability is decreased through diversity. The overall Maximum ratio combining is a method of diversityreceived signal power is increased and it allows us to use combining in which the signals from each channel are addedlower transmit power for a given level or reliability. This together, the gain if each channel is made proportional to thedecreases interference, increase battery life and reduces the rms level and inversely proportionally to mean square noiseprobability that a hostile party will intercept the signals.The level in that channel and the different proportionalitydiversity technique in this case I prefer is spatial diversity constants are used for each channel, so as to call it as ratio-where main goal is to obtain uncorrelated signals. squared combining and predetection combining as a optimum combiner for independent Additive White Gaussian Noise 3. MATHEMATICAL DERIVATION (AWGN) channels [3].OF RECEIVING DIVERSITY I assumed x(1) and x(2) are the received signal voltages r1from a two antennas diversity scheme and these signal at the a1receiver are passed to a combining or processing system toreduce channel distortion such as fading and co-channelinterference creating a signal x(t). The amount of reduction in r2 a2signal fading or diversity gain on x(t) depends on twoproperties: the cross correlation and the relative signalstrength levels between the received signals x1(t) and x2(t).The average received signal strength at each of the antenna Receiverbranches can be expressed as: Adder Detector P1 = E {[x1(t)] ^2} and P2 = E {[X2 (t)] ^2} Where E is the expectation and I can also define thecomplex cross correction between the signals as follow: rL aL It is also further related to envelope cross correlation Phase Attenuatorsbetween the signals with the complex cross correlation: Shifters Fig. 1 L- Branch antenna diversity receiver (L=5). With MRC, the attenuation/amplification factor is proportional to the signal amplitude ai=ri for each channel i.By assuming that the received signals have a Rayleigh- It obtains the weight that maximizes the output SNR that isdistributed envelope and randomly distributed phase. Under it is optimal in terms of SNR. Writing the received signal atthose definitions, typically good diversity gain is said to be the arra9ty elements as a vector x (t) and the output signal aspossible when the received signals satisfied the following two r (t):conditions, power imbalance and low correlation: X (t) = h (t) u (t) + n (t) h = [h0, h1………..h N-1] T n = [n0, n1……….n N-1] T As further, we can also obtain a close form expression for r (t) = WHX = WHhu(t) + WHn.the envelope correlation as the function of power correlation Since the signal u (t) has unit average power, thefor the correlated Rayleigh channel: instantaneous power SNR is: Where E () is the complete elliptical integral of secondkind.
  3. 3. The noise power in the demodulator is given by: Rayleigh channel, the real and imaginary part of hi are H 2 H H 2 H 2 2 Gaussian distributed having mean µhi = 0 and variance σ2hi = Pn = E {|W n| } = W E{nn } W = σ W INW = σ ||W|| 1/2. The channel experienced by each receive antenna is Where IN represents an N*N identity matrix. Since independent from the channel experienced by the otherconstant do not matter, one should always scale W such that receive antennas. On each receive antenna, the noise n has||W|| = 1. The SNR is therefore given by: the Gaussian probability density function with By the Cauchy-Schwarz inequality, this has a maximumwhen W is linearly proportional to h i.e. W = h The noise on each receive antenna is independent from the noise on the other receive antennas. In the presence of channel hi, the instantaneous bit energy to noise ratio at ith receive antenna is |hi|2 Eb / N0 that is: γi = |hi|2 Eb / N0 6. A MRC EQUATION PATTERN WITH AWGN On the ith receive antenna, the received signal is, The output SNR is therefore the sum of the SNR of yi = hi x + nieach element. The best a diversity combiner can do is to Where yi is the received symbol on the ith receive antenna,choose the weights to be the fading to each element. Sincematched filter is effectively used, from above equations, the hi is the channel on the ith receive antenna, x is theexpected value of output SNR is therefore N times the transmitted symbol and ni is the noise on ith receive antenna.average SNR at each element, i.e. Expressing it in matrix form, the received signal is, E {γ} = N γ y = hx +n where Which indicates that on average, the SNR improves by a T y= [y1, y2……..yN] is the received symbol from all thefactor of N, this is significantly remarkable improvement at receive antenna, h= [h1, h2……..hN] T is the channel on all thetotal SNR at the receiver side having N multiple antennas [4]. receive antenna, x is the transmitted symbol and n = [n1, n2…….nN] T is the noise on all the received antenna [5]. 5. ASSUMPTION MADE FOR MRCCALCULATION The equalized symbol is: Channel is a flat fading Rayleigh Multipath channel, themodulation is BPSK and noise added is purely AdditiveWhite Gaussian Noise (AWGN). In Rayleigh fading model,the phase of each path can change by 2π radian when thedelay τn (t) changes by 1/fc. If is fc is large, relative small It is intuitive to note that the term,motions in the medium can cause changes of 2π radians.Since the distance between the devices are much larger thanthe wavelength of the carrier frequency, it is reasonable toassume that the phase is uniformly distributed between 0 and2π radians and the phases of each path are independent. HereI assumed large number of paths, applying central limit This is the sum of the channels powers across all thetheorem, each path can be modeled as circularly symmetric received antennas.complex Gaussian random variable with time as variablewhich is inferred as Rayleigh fading channel model. 6. B EFFECTIVE Eb/No WITH MRC Some constraints assumed as: In the presence of channel hi, the instantaneous bit energy to noise ratio at ith receive antenna is: I have assumed N received antennas, channel is flatfading, the channel experienced by each receive antenna is γi = |hi|2 Eb / N0randomly varying in time. For ith receive antenna, each Given that I am equalizing the channel with hH with the Ntransmitted symbol gets multiplied by a randomly varying receive antenna case, the effective bit energy to noise ratio is:complex number hi. As channel under consideration is a
  4. 4. The above expression shows effective bit energy to noiseratio in a N receive antenna case is N times the bit energy tonoise ratio for single antenna case. 7. A SIMULATIONS RESULTS FORSNR IMPROVEMENT WITH MRC Computing SNR improvement considering followingparameters as input to the Mat lab script [6]: Fig. 2 Parameters Symbol (n) = 10^4 Modulaiton: BPSK Receiving antennas (N) = 10 Channel: Rayleigh fading channel Noise: AWGN Diversity combining: MRC Fig. 3 Parameters Fig. 2 Effective SNR improvement with MRC using N =10 in Rayleigh fading channel. Symbol (n) = 10^4 Modulaiton: BPSK Receiving antennas (N) = 30 Channel: Rayleigh fading channel Noise: AWGN Diversity combining: MRC 7. B SIMULATION INTERPRETATION As seen to the simulations figures, it is concluded thatfor the BPSK modulation along with increasing number ofreceiving antenna, the performance of optimized signals (orSNR) is enhanced. Considering other parameters constraints,as increasing the receiving antennas, the signal to noise ratio(SNR) is drastically increased, as shown in Figure 2. But theratio of increasing SNR when receiving antennas areincreasing from 10 to 30 is not same proportional to theinitial increments N = 10 as shown in figure 2 and 3. In figure3. The increments when N increases from 10 to 20 resultsonly 3dB increment of SNR, Like wise 3dB more when Nincreases from 20 to 30 as shown in figure 3. This stronglysignifying that large increase of receiving antennas do notresults same proportional increment of SNR because ofcircuit complexity. Fig. 3 Effective SNR improvement with MRC using N =30 in Rayleigh fading channel.
  5. 5. 8. A EFFECTIVE BIT ENERGY TONOISE RATION WITH MRC From above 6. A, I have calculated effective bit energyto noise ratio in a N receive antenna case is N times the bitenergy to noise ratio for single antenna case:Computing Eb / N0 improvement considering followingparameters as input to the Mat lab script: Fig. 4 Parameters Symbol (n) = 10^6 Modulaiton: BPSK Receiving antennas (N) = 1 Channel: Rayleigh fading channel Noise: AWGN Diversity combining: MRC Fig. 4 Eb / N0 measurement with MRC using N =1 in Rayleigh fading channel. Fig. 5 Parameters Symbol (n) = 10^6 Modulaiton: BPSK Receiving antennas (N) = 3 Channel: Rayleigh fading channel Noise: AWGN Diversity combining: MRC 8. B SIMULATION INTERPRETAITON As seen in the simulations results, it is concluded thatfor BPSK modulation with MRC in Rayleigh fading channel,effective bit energy to noise ratio is enormously increasedapproximately to the N times to the increasing number ofreceiving antennas without significant increasing Bit ErrorRate. As shown if figure 3. It is found that for receivingantenna N = 1, effective bit energy to noise ratio is 16 dBwith Bit Error Rate 10^ -1.2 but when number of receivingantennas is increased upto N = 3, effective bit energy to noiseratio is enormously increased upto the level 34 dB. Thus, thisvalue of bit energy to noise ratio is (N-0.87) times the bitenergy to noise ratio for single antenna case which isapproximately supporting theoretical calculation of bit energyto noise ratio as calculated above. On other side, The BitError Rate is 0.2 which shows its significance on increasingreceiving antennas is tolerable and can be comprised inMIMO system when Diversity Gain is prime factor to Fig. 5 Eb / N0 improvement with MRC using N =3 in Rayleigh fadingincrease. channel.
  6. 6. 9. CONCLUSIONS In this paper, I have proposed Maximum Ratio combining(MRC) as a spatial diversity which is one of the promise techniquesof Diversity Gain that constitute the performance improvement ofMIMO system. Considering both theoretical and practical researchdata, it is concluded that outcome of signal at receiving side hasbetter quality, tolerable Bit Error Rate or higher data rate than asingle receiving antenna that signify that increment of channelcapacity is proportional to the number of receiving antennas withoutadditional power or bandwidth requirement. From the simulationresults, it is said that both signal to noise ratio and effective bitenergy to noise ratio are enormously increased with the increment ofnumber of receiving antennas under BPSK modulation, Rayleighfading channel, Additive White Gaussian Noise (AWGN)considered to be constraints parameters for simulationcomputation. 10. REFERENCES[1] Technical Report on MIMO and Related Diversity techniques improves wireless range and reliability, from June 2007 high frequency electronics, LLC.[2] Alfred Grau Besoli, “Influence of Reconfigurable antenna Parameters on the Diversity gain in fading MIMO parameters on the Diversity gain in fading MIMO environments”, university of California, Iravine, 2005.[3] Analog and Digital Transmission, Diversity, from Wireless Communication.NL URL.[4] R. Janaswamy, Radiowave Propagation and Smart Antennas for Wireless Communications, Kluwer Academic Publishers, 2000.[5] Google Search on .[6] Use of Language of Technical Computation “MATLAB” for simulation results.