EE6604 Personal & Mobile Communications. Week 13. Multi-antenna Techniques
|
|
- Audrey Murphy
- 6 years ago
- Views:
Transcription
1 EE6604 Personal & Mobile Communications Week 13 Multi-antenna Techniques 1
2 Diversity Methods Diversity combats fading by providing the receiver with multiple uncorrelated replicas of the same information bearing signal. There are several types of receiver diversity methods: spatial, angle, polarization, frequency, time, and multipath diversity There are different methods to combine the diversity branches. maximal ratio, equal gain, switched, and selective combining. If the signal s m (t) is transmitted, the received complex envelopes on the different diversity branches are r k (t) = g k s m (t)+ñ k (t), k = 1,..., L L is the number of diversity branches. g k = α k e jφ k is the fading gain associated with the k th branch. The AWGN processes ñ k (t) are independent from branch to branch. With Rayleigh fading, the instantaneous received modulated symbol energy-to-noise ratio on the kth diversity branch has the exponential pdf p γk (x) = 1 γ k e x/ γ k, where γ k is the average received branch symbol energy-to-noise ratio for the kth diversity branch. For balanced diversity branches γ k = γ c, k = 1,...L. 2
3 r 1 ( t ) detector ~ r 1 r ( t ) detector ~ r 2 2 diversity combiner ~ r r ( t ) L detector ~ r L Diversity Combining. 3
4 Selective Combining (SC) With ideal SC, the branch with the largest symbol energy-to-noise ratio is always selected such that r = max r k. g k The instantaneous symbol energy-to-noise ratio at the output of the selective combiner is where L is the number of branches. γ s s = max{γ 1, γ 2,, γ L }, If the branches are independently faded, then order statistics gives the cumulative distribution function (cdf) F γ s s (x) = Pr[γ 1 x,γ 2 x,,γ L x] = [ 1 e x/ γ c] L, x 0. Differentiating the above expression gives the pdf of the instantaneous output symbol energyto-noise ratio as p γ s s (x) = L γ c [ 1 e x/ γ c ] L 1 e x/ γ c, x 0. The above pdf can be used to evaluate the performance of various digital modulation schemes. 4
5 L = 1 L = 2 L = 3 L = 4 F(γ b s ) γ s b - γ (db) c Cdf of γ s b for selective combining; γ c is the average branch symbol energy-to-noise ratio. 5
6 Error Probability with Selective Combining (SC) The bit error probability with slow flat fading can be obtained by averaging the bit error probability,asafunctionofthesymbolenergy-to-noiseratio,overthepdfofγ s s. Forexample, the bit error probability for binary DPSK with differential detection on an AWGN channel is P b (γ s s) = 1 2 e γs s, where γ s s can be interpreted as the instantaneous bit energy-to-noise ratio since binary modulation is being used. Hence, with SC P b = 0 = 0 = L 2 γ c = L 2 P b (x)p γ s (x)dx L e (1+1/ γ ( c)x 1 e x/ γ ) L 1 c dx 2 γ c L 1 L 1 ( 1) n e (1+(n+1)/ γ c)x dx n=0 n 0 ( L 1 ) n ( 1) n, 1+n+ γ c L 1 n=0 where we have used the binomial expansion (1 x) L 1 = L 1 n=0 L 1 ( 1) n x n. n 6
7 L = 1 L = 2 L = 3 L = 4 P b γ (db) c Bit error probability for binary DPSK with differential detection and L-branch selective diversity combining. 7
8 Error Probability with Selective Combining (SC) The bit error probability for BPSK on an AWGN channel is P b (γ s s) = Q ( 2γ s b), whereγ s b istheinstantaneousbitenergy-to-noiseratioattheoutputoftheselectivecombiner. Hence, with selective combining P b = 0 = 0 = 1 2 P b (x)p γ s b (x)dx Q ( 2x ) L [ 1 e x/ γ ] L 1 c e x/ γ c dx γ c ( 1) k L 1+ k γ 1/2 k c L k=0 where γ c is the average branch bit energy-to-noise ratio. 8
9 Bit error probability for BPSK and 1 and 2-branch selective diversity combining. 9
10 The vector Maximal Ratio Combining (MRC) r = vec( r 1, r 2,, r L ) has the multivariate complex Gaussian distribution p( r g, s m ) = 1 (2πN o ) exp 1 LN 2N o where g = (g 1,g 2,...,g L ) is the channel vector. L r k g k s m 2 The maximum likelihood receiver chooses the message vector s m to maximize the likelihood functionp( r g, s m )orthelog-likelihoodfunctionlogp( r g, s m ). Thisisequivalenttochoosing s m to maximize the decision variable µ( s m ) = L = L r k g k s m 2 ( rk 2 2Re{ r k g k s m}+ g k 2 s m 2) Alternatively, we can just choose s m to maximize the decision variable µ 2 ( s m ) = L L = Re Re{g k r k s m} E m L g k r k s m E m L g k 2 g k 2 10
11 r ~ Re Re ( r ~ ~ s ), 1 ( r ~ ~ s ), β β µ ( ~ ) 1 s 1 µ ( ~ ) 2 s 2 select largest s^ m Re µ ( s ~ M ) r ~ + (, ~ s M ) + - β M β m = E m g* k k Σ L =1 2 Metric computer for maximal ratio combining. 11
12 MRC Performance The MRC receiver combines the diversity branches according to r = L and chooses s m to maximize the decision variable g k r k µ( s m ) = Re( r, s m ) E m L To evaluate the performance gain with MRC, we note that r = L = g k(g k s m +ñ k ) L αk 2 s m + L where α 2 M = L α 2 k, ñ M = L g kñk and α 2 k = g k 2. g k 2 gkñk α 2 M s m+ñ M, (1) The first term in (1) is the signal component with average energy 1 2E[α 4 M s m 2 ] = α 4 ME av, where E av is the average symbol energy in the signal constellation. 12
13 MRC Performance The second term is the noise component with variance (per dimension) σ 2 ñ M = 1 2N E[ ñ M 2 ] = N o L The ratio of the two gives the symbol energy-to-noise ratio γ mr s = 1 2E[α 4 M s m 2 ] σ 2 ñ M = α2 ME av N o = L α 2 k = N o α 2 M. α 2 ke av N o = L γ k where γ k = α 2 ke av /N o. Note that γ mr s is the sum of the symbol energy-to-noise ratios of the L diversity branches. If the branches are balanced (which is a reasonable assumption with antenna diversity) and uncorrelated, then γ mr b has a central chi-square distribution with 2L degrees of freedom where p γ mr(x) = b 1 (L 1)!( γ c ) LxL 1 e x/ γ c, x 0 γ c = E[γ k ] k = 1,..., L The cdf of γ mr s is F γ mr (x) = 1 e x/ γ L 1 c s k=0 1 k! x γ c k, x 0. 13
14 L = 1 L = 2 L = 3 L = 4 F(γ b mr ) γ mr b - γ (db) c Cdf of γ mr s for maximal ratio combining; γ c is the average branch symbol energy-to-noise ratio. 14
15 Performance of BPSK with MRC When computing the probability of bit error, we must limit our attention to coherent signaling techniques since MRC is a coherent detection technique. The bit error probability with BPSK with L-branch diversity and MRC is where P b = 0 = 0 = P b (x)p γ mr(x)dx b Q ( 2x ) 1 e x/ γ (L 1)!( γ c ) LxL 1 c 1 µ 2 L L 1 k=0 µ = The last step follows after considerable algebra. L 1+k k γ c 1+ γ c 1+µ 2 k 15
16 L = 1 L = 2 L = 3 L = 4 P b γ (db) c Bit error probability for BPSK with maximal ratio combining against the average branch bit energy-to-noise ratio. 16
17 Optimum Combining Maximum ratio combining (MRC) maximizes the output signal-to-noise ratio (SNR) and is the optimal combining method in a maximum likelihood sense for channels where the additive impairment is additive white Gaussian noise. When the additive channel impairment is dominated by co-channel interference, it is better to use optimum combining (OC) which is designed to maximize the output signal-tointerference-plus-noise ratio (SINR). OC uses the spatial diversity not only to combat fading of the desired signal, as is the case with MRC, but also to reduce the relative power of the interfering signals at the receiver, such that the instantaneous SINR is maximized. This is achieved by exploiting the correlation of the interference across the multiple receiver antenna elements. By combining the signals that are received by multiple antennas, OC can suppress the interference and improve the output signal-to-interference-plus-noise ratio by several decibels in interference dominant environments. 17
18 Received Signal, Interference and Noise Consider a situation where a desired signal is received in the presence of K co-channel interferers. The signal space dimensionality is assumed to be unity, i.e., N = 1, so that the signal vectors are complex-valued scalars chosen from an appropriate constellation such as M-QAM. The received signal scalars at the L receiver antennas are equal to r k = g k,0 s 0 + K i=1 g k,i s i +ñ k, k = 1,..., L, where s 0, s i andñ k arethedesiredsignalvector,i th interferingsignalvector,andnoisevector, respectively, and K is the number of interferers. The L received signal scalars can be stacked in a column to yield the L 1 received vector where r t = g 0 s 0 + K i=1 g i s i +ñ, r t = ( r 1, r 2,..., r L ) T g i = (g i,1,g i,2,...,g i,l ) T ñ = (ñ 1,ñ 2,...,ñ L ) T. 18
19 Signal Correlations The L L received desired-signal-plus-interference-plus noise correlation matrix is given by Φ rt r t = 1 2 E s 0, s i,ñ g 0 s 0 + K i=1 where ( ) H denotes complex conjugate transpose. g i s i +ñ g 0 s 0 + K i=1 H g i s i +ñ, Likewise, the received interference-plus-noise correlation matrix is given by Φ ri r i = 1 2 E s i,ñ K i=1 K g i s i +ñ i=1 H g i s i +ñ. Note that the expectations are taken over a period that is much less than the channel coherence time, i.e., several modulated symbol durations. If the desired signal, interfering signal, and noise vectors are mutually uncorrelated, and Φ rt r t = g 0 g H 0E av + K Φ ri r i = K i=1 i=1 g i g H i E i av +N o I, (2) g i g H i E i av +N o I, respectively, where I is the L L identity matrix and Eav i is the average energy in the ith interfering signal. It is important to note that the matrices Φ rt r t and Φ ri r i will vary at the channel fading rate. 19
20 Optimum Combining and MMSE Solution The received signals scalars r k,k = 1,2,...,L are multiplied by controllable weights w k and summed together, i.e., the combiner output is r = L w k r k = w T r t, where w = (w 1,w 2,...,w L ) T is the weight vector. Several approaches can be taken to find the optimal weight vector w. One approach is to minimize the mean square error where Φ rt r t is defined in (2) and J = E [ r s 0 2] = E [ w T r t s 0 2] = 2w T Φ rt r t w 2Re{Φ s0 r t w } 2E av, Φ s0 r t = E [ s 0 r H t ] = 2Eav g H 0. The weight vector that minimizes the mean square error can be obtained by setting the gradient w J to zero. This gives the minimum mean square error (MMSE) solution w J = J J,, = 2w T Φ rt r w 1 w t 2Φ s0 r t = 0. L The solution is w opt = Φ r 1 t r t Φ T s 0 r t = 2E av Φ r 1 t r t g0, where the fact that Φ T s 0 r t = 2g0E av was used. 20
21 Optimum Combining and MMSE Solution Since Φ rt r t = g 0 g H 0E av +Φ ri r i, it follows that w opt = 2E av ( Φ ri r i +g 0 g H 0 E av) 1 g 0 = 2E av ( Φ ri r i +g 0g T 0E av ) 1 g 0. (3) Next, a variation of the matrix inversion lemma is applied to (3) resulting in (A+uv H ) 1 = A 1 A 1 uv H A 1 1+v H A 1 u w opt = 2E av = 2E av Φ 1 where C = 2E av /(1+E av g0 TΦ 1 r i r i g0 ) is a scalar. r i r i g0 gt 0 Φ 1 r i r i g r i r i g0 0 r i r i E avφ 1 1+E av g0φ T E av g0φ T 1 Φ 1 r i r i g 0 r i r i g 0 = C Φ 1 r i r i g 0, (4) 21
22 Optimum Combining and Maximum SINR Solution Another criterion for optimizing the weight vector is to maximize the instantaneous signalto-interference-plus-noise ratio (SINR) at the output of the combiner Solving for the optimum weight vector gives ω = wt g 0 g0 HE avw w T Φ r 1. i r i w w opt = B Φ 1 r i r i g 0, where B is an arbitrary constant. Hence, the maximum instantaneous output SINR is ω = E av g H 0Φ 1 r i r i g 0. Note that the maximum instantaneous output SINR does not depend on the choice of the scalar B. Therefore, the MMSE weight vector in(4) also maximizes the instantaneous output SINR. When no interference is present, Φ ri r i = N o I and the optimal weight vector becomes w opt = g 0, N o so that the combiner output is r = L g0,k k. N o r OC reduces to MRC when no interference is present. 22
23 Performance of Optimum Combining To evaluate the performance of OC, several definitions are required as follows: average received desired signal power per antenna Ω = average received noise plus interference power per antenna average received desired signal power per antenna γ c = = E[ g 0,k 2 ]E av average received noise power per antenna N o γ i = average received ith interferer power per antenna = E[ g i,k 2 ]Eav i average received noise power per antenna N o instantaneous desired signal power at the array output ω R = average noise plus interference power at the array output instantaneous desired signal power at the array output ω = instantaneous noise plus interference power at the array output In the above definitions, average refers to the average over the Rayleigh fading, while instantaneous refers to an average over a period that is much less than the channel coherence time, i.e., several modulated symbol durations so that the channel is essentially static. Note that Ω = γ c 1+ K γ i. 23
24 Fading of the Desired Signal Only ω R is equal to where, with a single interferer, ω R = E av g H 0 Φ 1 r i r i g 0, Φ ri r i = E 1 ave[g 1 g H 1]+N o I. Note that the above expectation in is over the Rayleigh fading. The pdf of ω R is and the cdf of ω R is p ωr (x) = e x/ γ c (x/ γ c ) L 1 (1+L γ 1 ) γ c (L 2)! F ωr (x) = x/ γ c 0 which are valid for L 2. e y y L 1 (1+L γ 1 ) (L 2)! e ((x/ γ c)l γ 1 )t (1 t) L 2 dt (5) 0 e (yl γ 1)t (1 t) L 2 dtdy. (6) Note that ω R in (5) and (6) is normalized by γ c. Since γ c = (1+ γ 1 )Ω for the case of a single interferer, it is apparent that ω R can be normalized by Ω as well, i.e., replace x/ γ c in the above pdf and cdf with x/(1+ γ 1 )Ω. The normalization by Ω allows for a straight forward comparison of OC and MRC. 24
25 10 0 γ 1 =0 γ 1 =1 (0 db) 10 1 γ 1 =2 (3 db) F ωr (x) 10 2 L=2 L= x/ω (db) Cdf of ω R for optimal combining; γ c is the average branch symbol energy-to-noise ratio. 25
26 BER Performance The probability of bit error for coherently detected BPSK is given by P b = 0 Q ( 2x ) p ωr (x)dx Bogachev and Kieslev derived the bit error probability (for L 2) as where P b = ( 1)L 1 (1+L γ 1 ) 2(L γ 1 ) L γ 1 + L 1 1+L γ 1 L 2 ( L γ 1 ) k 1 γ c 1+ γ c 1+ k γ c 1 1+ γ c 1+L γ 1 (2i 1)!! i!(2+2 γ c ) i i=1 (2i 1)!! = (2i 1). γ c 1+L γ 1 + γ c Simon and Alouini have derived the following expression which is valid for L 1: P b = γ c 1+ γ c γ c 1+L γ 1 + γ c L 2 k=0 2k k 1 L γ 1 1 [4(1+ γ c )] k L L γ 1 L 1 k 26
27 γ 1 =0 γ 1 =1 (0 db) γ 1 =2 (3 db) 10 2 P b 10 3 L= L= L= Ω (db) Bit error probability for coherent BPSK and optimal combining for various values of γ 1 and various number of receiver antenna elements, L. 27
28 Fading of the Desired and Interfering Signals The maximum instantaneous output SINR is equal to where, with a single interferer, ω = E av g H 0Φ 1 r i r i g 0, Φ ri r i = E 1 av g 1g H 1 +N oi. In this case, the matrix Φ ri r i varies at the fading rate. Using eigenvalue decomposition, the probability of bit error with coherent BPSK is P b = P b γ1 (x)p γ1 (x)dx = γ c γ c +1 L 2 1 2Γ(L)( γ 1 ) L 1 γ c γ c +1 L 2 k=0 k=0 (2k)! k! 2k k 1 4( γ c +1) k π γ c exp γ c+1 erfc γ 1 γ 1 γ 1 4( γ c +1) k. γ c +1 γ 1 28
29 γ 1 =0 γ 1 =1 (0 db) γ 1 =2 (3 db) 10 2 P b 10 3 L=4 L= Ω (db) Bit error probability for coherent BPSK and optimal combining for various values of γ 1 and various number of receiver antenna elements, L. 29
30 faded interferer o non faded interferer γ 1 =0 γ 1 =1 (0 db) γ 1 =2 (3 db) 10 2 P b 10 3 L= L= Ω (db) Comparison of the bit error probability for coherent BPSK and optimal combining for a non-faded interferer and a faded interferer; the performance is almost identical. 30
Received Signal, Interference and Noise
Optimum Combining Maximum ratio combining (MRC) maximizes the output signal-to-noise ratio (SNR) and is the optimal combining method in a maximum likelihood sense for channels where the additive impairment
More informationEE 5407 Part II: Spatial Based Wireless Communications
EE 5407 Part II: Spatial Based Wireless Communications Instructor: Prof. Rui Zhang E-mail: rzhang@i2r.a-star.edu.sg Website: http://www.ece.nus.edu.sg/stfpage/elezhang/ Lecture II: Receive Beamforming
More informationDigital Band-pass Modulation PROF. MICHAEL TSAI 2011/11/10
Digital Band-pass Modulation PROF. MICHAEL TSAI 211/11/1 Band-pass Signal Representation a t g t General form: 2πf c t + φ t g t = a t cos 2πf c t + φ t Envelope Phase Envelope is always non-negative,
More informationOutline - Part III: Co-Channel Interference
General Outline Part 0: Background, Motivation, and Goals. Part I: Some Basics. Part II: Diversity Systems. Part III: Co-Channel Interference. Part IV: Multi-Hop Communication Systems. Outline - Part III:
More informationEE6604 Personal & Mobile Communications. Week 15. OFDM on AWGN and ISI Channels
EE6604 Personal & Mobile Communications Week 15 OFDM on AWGN and ISI Channels 1 { x k } x 0 x 1 x x x N- 2 N- 1 IDFT X X X X 0 1 N- 2 N- 1 { X n } insert guard { g X n } g X I n { } D/A ~ si ( t) X g X
More informationCHAPTER 14. Based on the info about the scattering function we know that the multipath spread is T m =1ms, and the Doppler spread is B d =0.2 Hz.
CHAPTER 4 Problem 4. : Based on the info about the scattering function we know that the multipath spread is T m =ms, and the Doppler spread is B d =. Hz. (a) (i) T m = 3 sec (ii) B d =. Hz (iii) ( t) c
More informationImpact of channel-state information on coded transmission over fading channels with diversity reception
Impact of channel-state information on coded transmission over fading channels with diversity reception Giorgio Taricco Ezio Biglieri Giuseppe Caire September 4, 1998 Abstract We study the synergy between
More informationWeibull-Gamma composite distribution: An alternative multipath/shadowing fading model
Weibull-Gamma composite distribution: An alternative multipath/shadowing fading model Petros S. Bithas Institute for Space Applications and Remote Sensing, National Observatory of Athens, Metaxa & Vas.
More informationOn the Throughput of Proportional Fair Scheduling with Opportunistic Beamforming for Continuous Fading States
On the hroughput of Proportional Fair Scheduling with Opportunistic Beamforming for Continuous Fading States Andreas Senst, Peter Schulz-Rittich, Gerd Ascheid, and Heinrich Meyr Institute for Integrated
More informationDiversity Combining Techniques
Diversity Combining Techniques When the required signal is a combination of several plane waves (multipath), the total signal amplitude may experience deep fades (Rayleigh fading), over time or space.
More informationOptimal Receiver for MPSK Signaling with Imperfect Channel Estimation
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 27 proceedings. Optimal Receiver for PSK Signaling with Imperfect
More informationLECTURE 16 AND 17. Digital signaling on frequency selective fading channels. Notes Prepared by: Abhishek Sood
ECE559:WIRELESS COMMUNICATION TECHNOLOGIES LECTURE 16 AND 17 Digital signaling on frequency selective fading channels 1 OUTLINE Notes Prepared by: Abhishek Sood In section 2 we discuss the receiver design
More informationBER Performance Analysis of Cooperative DaF Relay Networks and a New Optimal DaF Strategy
144 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 1, NO. 4, APRIL 11 BER Performance Analysis of Cooperative DaF Relay Networks and a New Optimal DaF Strategy George A. Ropokis, Athanasios A. Rontogiannis,
More informationTitle. Author(s)Tsai, Shang-Ho. Issue Date Doc URL. Type. Note. File Information. Equal Gain Beamforming in Rayleigh Fading Channels
Title Equal Gain Beamforming in Rayleigh Fading Channels Author(s)Tsai, Shang-Ho Proceedings : APSIPA ASC 29 : Asia-Pacific Signal Citationand Conference: 688-691 Issue Date 29-1-4 Doc URL http://hdl.handle.net/2115/39789
More informationDirect-Sequence Spread-Spectrum
Chapter 3 Direct-Sequence Spread-Spectrum In this chapter we consider direct-sequence spread-spectrum systems. Unlike frequency-hopping, a direct-sequence signal occupies the entire bandwidth continuously.
More informationPerformance Analysis of Wireless Single Input Multiple Output Systems (SIMO) in Correlated Weibull Fading Channels
Performance Analysis of Wireless Single Input Multiple Output Systems (SIMO) in Correlated Weibull Fading Channels Zafeiro G. Papadimitriou National and Kapodistrian University of Athens Department of
More informations o (t) = S(f)H(f; t)e j2πft df,
Sample Problems for Midterm. The sample problems for the fourth and fifth quizzes as well as Example on Slide 8-37 and Example on Slides 8-39 4) will also be a key part of the second midterm.. For a causal)
More informationECE6604 PERSONAL & MOBILE COMMUNICATIONS. Week 3. Flat Fading Channels Envelope Distribution Autocorrelation of a Random Process
1 ECE6604 PERSONAL & MOBILE COMMUNICATIONS Week 3 Flat Fading Channels Envelope Distribution Autocorrelation of a Random Process 2 Multipath-Fading Mechanism local scatterers mobile subscriber base station
More informationDesign of MMSE Multiuser Detectors using Random Matrix Techniques
Design of MMSE Multiuser Detectors using Random Matrix Techniques Linbo Li and Antonia M Tulino and Sergio Verdú Department of Electrical Engineering Princeton University Princeton, New Jersey 08544 Email:
More informationPerformance Analysis of Multiple Antenna Systems with VQ-Based Feedback
Performance Analysis of Multiple Antenna Systems with VQ-Based Feedback June Chul Roh and Bhaskar D. Rao Department of Electrical and Computer Engineering University of California, San Diego La Jolla,
More informationEs e j4φ +4N n. 16 KE s /N 0. σ 2ˆφ4 1 γ s. p(φ e )= exp 1 ( 2πσ φ b cos N 2 φ e 0
Problem 6.15 : he received signal-plus-noise vector at the output of the matched filter may be represented as (see (5-2-63) for example) : r n = E s e j(θn φ) + N n where θ n =0,π/2,π,3π/2 for QPSK, and
More informationMobile Communications (KECE425) Lecture Note Prof. Young-Chai Ko
Mobile Communications (KECE425) Lecture Note 20 5-19-2014 Prof Young-Chai Ko Summary Complexity issues of diversity systems ADC and Nyquist sampling theorem Transmit diversity Channel is known at the transmitter
More informationDiversity Performance of a Practical Non-Coherent Detect-and-Forward Receiver
Diversity Performance of a Practical Non-Coherent Detect-and-Forward Receiver Michael R. Souryal and Huiqing You National Institute of Standards and Technology Advanced Network Technologies Division Gaithersburg,
More informationA First Course in Digital Communications
A First Course in Digital Communications Ha H. Nguyen and E. Shwedyk February 9 A First Course in Digital Communications 1/46 Introduction There are benefits to be gained when M-ary (M = 4 signaling methods
More informationEE4304 C-term 2007: Lecture 17 Supplemental Slides
EE434 C-term 27: Lecture 17 Supplemental Slides D. Richard Brown III Worcester Polytechnic Institute, Department of Electrical and Computer Engineering February 5, 27 Geometric Representation: Optimal
More informationImproved Detected Data Processing for Decision-Directed Tracking of MIMO Channels
Improved Detected Data Processing for Decision-Directed Tracking of MIMO Channels Emna Eitel and Joachim Speidel Institute of Telecommunications, University of Stuttgart, Germany Abstract This paper addresses
More informationLecture 7 MIMO Communica2ons
Wireless Communications Lecture 7 MIMO Communica2ons Prof. Chun-Hung Liu Dept. of Electrical and Computer Engineering National Chiao Tung University Fall 2014 1 Outline MIMO Communications (Chapter 10
More informationConstrained Detection for Multiple-Input Multiple-Output Channels
Constrained Detection for Multiple-Input Multiple-Output Channels Tao Cui, Chintha Tellambura and Yue Wu Department of Electrical and Computer Engineering University of Alberta Edmonton, AB, Canada T6G
More informationLecture 8: MIMO Architectures (II) Theoretical Foundations of Wireless Communications 1. Overview. Ragnar Thobaben CommTh/EES/KTH
MIMO : MIMO Theoretical Foundations of Wireless Communications 1 Wednesday, May 25, 2016 09:15-12:00, SIP 1 Textbook: D. Tse and P. Viswanath, Fundamentals of Wireless Communication 1 / 20 Overview MIMO
More informationDigital Transmission Methods S
Digital ransmission ethods S-7.5 Second Exercise Session Hypothesis esting Decision aking Gram-Schmidt method Detection.K.K. Communication Laboratory 5//6 Konstantinos.koufos@tkk.fi Exercise We assume
More informationLecture 7: Wireless Channels and Diversity Advanced Digital Communications (EQ2410) 1
Wireless : Wireless Advanced Digital Communications (EQ2410) 1 Thursday, Feb. 11, 2016 10:00-12:00, B24 1 Textbook: U. Madhow, Fundamentals of Digital Communications, 2008 1 / 15 Wireless Lecture 1-6 Equalization
More informationThese outputs can be written in a more convenient form: with y(i) = Hc m (i) n(i) y(i) = (y(i); ; y K (i)) T ; c m (i) = (c m (i); ; c m K(i)) T and n
Binary Codes for synchronous DS-CDMA Stefan Bruck, Ulrich Sorger Institute for Network- and Signal Theory Darmstadt University of Technology Merckstr. 25, 6428 Darmstadt, Germany Tel.: 49 65 629, Fax:
More informationConstellation Precoded Beamforming
Constellation Precoded Beamforming Hong Ju Park and Ender Ayanoglu Center for Pervasive Communications and Computing Department of Electrical Engineering and Computer Science University of California,
More informationThe Gamma Variate with Random Shape Parameter and Some Applications
ITSUBISHI ELECTRIC RESEARCH LABORATORIES http://www.merl.com The Gamma Variate with Random Shape Parameter and Some Applications aaref, A.: Annavajjala, R. TR211-7 December 21 Abstract This letter provides
More informationChapter 4: Continuous channel and its capacity
meghdadi@ensil.unilim.fr Reference : Elements of Information Theory by Cover and Thomas Continuous random variable Gaussian multivariate random variable AWGN Band limited channel Parallel channels Flat
More informationELEC E7210: Communication Theory. Lecture 10: MIMO systems
ELEC E7210: Communication Theory Lecture 10: MIMO systems Matrix Definitions, Operations, and Properties (1) NxM matrix a rectangular array of elements a A. an 11 1....... a a 1M. NM B D C E ermitian transpose
More informationCapacity of multiple-input multiple-output (MIMO) systems in wireless communications
15/11/02 Capacity of multiple-input multiple-output (MIMO) systems in wireless communications Bengt Holter Department of Telecommunications Norwegian University of Science and Technology 1 Outline 15/11/02
More informationELEC546 Review of Information Theory
ELEC546 Review of Information Theory Vincent Lau 1/1/004 1 Review of Information Theory Entropy: Measure of uncertainty of a random variable X. The entropy of X, H(X), is given by: If X is a discrete random
More informationCell throughput analysis of the Proportional Fair scheduler in the single cell environment
Cell throughput analysis of the Proportional Fair scheduler in the single cell environment Jin-Ghoo Choi and Seawoong Bahk IEEE Trans on Vehicular Tech, Mar 2007 *** Presented by: Anh H. Nguyen February
More informationML Detection with Blind Linear Prediction for Differential Space-Time Block Code Systems
ML Detection with Blind Prediction for Differential SpaceTime Block Code Systems Seree Wanichpakdeedecha, Kazuhiko Fukawa, Hiroshi Suzuki, Satoshi Suyama Tokyo Institute of Technology 11, Ookayama, Meguroku,
More informationOn the Multivariate Nakagami-m Distribution With Exponential Correlation
1240 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 51, NO. 8, AUGUST 2003 On the Multivariate Nakagami-m Distribution With Exponential Correlation George K. Karagiannidis, Member, IEEE, Dimitris A. Zogas,
More informationNEW RESULTS ON DIFFERENTIAL AND NON COHERENT TRANSMISSION: MSDD FOR CORRELATED MIMO FADING CHANNELS AND PERFORMANCE ANALYSIS FOR GENERALIZED K FADING
NEW RESULTS ON DIFFERENTIAL AND NON COHERENT TRANSMISSION: MSDD FOR CORRELATED MIMO FADING CHANNELS AND PERFORMANCE ANALYSIS FOR GENERALIZED K FADING by CINDY YUE ZHU B.ASc., The University of British
More informationA New SLNR-based Linear Precoding for. Downlink Multi-User Multi-Stream MIMO Systems
A New SLNR-based Linear Precoding for 1 Downlin Multi-User Multi-Stream MIMO Systems arxiv:1008.0730v1 [cs.it] 4 Aug 2010 Peng Cheng, Meixia Tao and Wenjun Zhang Abstract Signal-to-leaage-and-noise ratio
More informationEstimation of the Capacity of Multipath Infrared Channels
Estimation of the Capacity of Multipath Infrared Channels Jeffrey B. Carruthers Department of Electrical and Computer Engineering Boston University jbc@bu.edu Sachin Padma Department of Electrical and
More informationa) Find the compact (i.e. smallest) basis set required to ensure sufficient statistics.
Digital Modulation and Coding Tutorial-1 1. Consider the signal set shown below in Fig.1 a) Find the compact (i.e. smallest) basis set required to ensure sufficient statistics. b) What is the minimum Euclidean
More informationPERFORMANCE ANALYSIS OF DPSK SYSTEMS WITH MIMO EMPLOYING EGC OVER WIRELESS FADING CHANNELS
PERFORMANCE ANALYSIS OF DPSK SYSTEMS WITH MIMO EMPLOYING EGC OVER WIRELESS FADING CHANNELS by IYAD ABDELRAZZAQE AL FALUJAH A Dissertation Presented to the Faculty of the Graduate School of The University
More informationThis examination consists of 10 pages. Please check that you have a complete copy. Time: 2.5 hrs INSTRUCTIONS
THE UNIVERSITY OF BRITISH COLUMBIA Department of Electrical and Computer Engineering EECE 564 Detection and Estimation of Signals in Noise Final Examination 08 December 2009 This examination consists of
More informationLIKELIHOOD RECEIVER FOR FH-MFSK MOBILE RADIO*
LIKELIHOOD RECEIVER FOR FH-MFSK MOBILE RADIO* Item Type text; Proceedings Authors Viswanathan, R.; S.C. Gupta Publisher International Foundation for Telemetering Journal International Telemetering Conference
More informationLecture 9: Diversity-Multiplexing Tradeoff Theoretical Foundations of Wireless Communications 1
: Diversity-Multiplexing Tradeoff Theoretical Foundations of Wireless Communications 1 Rayleigh Friday, May 25, 2018 09:00-11:30, Kansliet 1 Textbook: D. Tse and P. Viswanath, Fundamentals of Wireless
More informationSummary: SER formulation. Binary antipodal constellation. Generic binary constellation. Constellation gain. 2D constellations
TUTORIAL ON DIGITAL MODULATIONS Part 8a: Error probability A [2011-01-07] 07] Roberto Garello, Politecnico di Torino Free download (for personal use only) at: www.tlc.polito.it/garello 1 Part 8a: Error
More informationDetecting Parametric Signals in Noise Having Exactly Known Pdf/Pmf
Detecting Parametric Signals in Noise Having Exactly Known Pdf/Pmf Reading: Ch. 5 in Kay-II. (Part of) Ch. III.B in Poor. EE 527, Detection and Estimation Theory, # 5c Detecting Parametric Signals in Noise
More informationLecture 5: Antenna Diversity and MIMO Capacity Theoretical Foundations of Wireless Communications 1. Overview. CommTh/EES/KTH
: Antenna Diversity and Theoretical Foundations of Wireless Communications Wednesday, May 4, 206 9:00-2:00, Conference Room SIP Textbook: D. Tse and P. Viswanath, Fundamentals of Wireless Communication
More informationLecture 9: Diversity-Multiplexing Tradeoff Theoretical Foundations of Wireless Communications 1. Overview. Ragnar Thobaben CommTh/EES/KTH
: Diversity-Multiplexing Tradeoff Theoretical Foundations of Wireless Communications 1 Rayleigh Wednesday, June 1, 2016 09:15-12:00, SIP 1 Textbook: D. Tse and P. Viswanath, Fundamentals of Wireless Communication
More informationExploiting Partial Channel Knowledge at the Transmitter in MISO and MIMO Wireless
Exploiting Partial Channel Knowledge at the Transmitter in MISO and MIMO Wireless SPAWC 2003 Rome, Italy June 18, 2003 E. Yoon, M. Vu and Arogyaswami Paulraj Stanford University Page 1 Outline Introduction
More informationLecture 4. Capacity of Fading Channels
1 Lecture 4. Capacity of Fading Channels Capacity of AWGN Channels Capacity of Fading Channels Ergodic Capacity Outage Capacity Shannon and Information Theory Claude Elwood Shannon (April 3, 1916 February
More informationA SEMI-BLIND TECHNIQUE FOR MIMO CHANNEL MATRIX ESTIMATION. AdityaKiran Jagannatham and Bhaskar D. Rao
A SEMI-BLIND TECHNIQUE FOR MIMO CHANNEL MATRIX ESTIMATION AdityaKiran Jagannatham and Bhaskar D. Rao Department of Electrical and Computer Engineering University of California, San Diego La Jolla, CA 9093-0407
More informationA REDUCED COMPLEXITY TWO-DIMENSIONAL BCJR DETECTOR FOR HOLOGRAPHIC DATA STORAGE SYSTEMS WITH PIXEL MISALIGNMENT
A REDUCED COMPLEXITY TWO-DIMENSIONAL BCJR DETECTOR FOR HOLOGRAPHIC DATA STORAGE SYSTEMS WITH PIXEL MISALIGNMENT 1 S. Iman Mossavat, 2 J.W.M.Bergmans 1 iman@nus.edu.sg 1 National University of Singapore,
More informationChapter [4] "Operations on a Single Random Variable"
Chapter [4] "Operations on a Single Random Variable" 4.1 Introduction In our study of random variables we use the probability density function or the cumulative distribution function to provide a complete
More informationMulti-Input Multi-Output Systems (MIMO) Channel Model for MIMO MIMO Decoding MIMO Gains Multi-User MIMO Systems
Multi-Input Multi-Output Systems (MIMO) Channel Model for MIMO MIMO Decoding MIMO Gains Multi-User MIMO Systems Multi-Input Multi-Output Systems (MIMO) Channel Model for MIMO MIMO Decoding MIMO Gains Multi-User
More informationECE 564/645 - Digital Communications, Spring 2018 Homework #2 Due: March 19 (In Lecture)
ECE 564/645 - Digital Communications, Spring 018 Homework # Due: March 19 (In Lecture) 1. Consider a binary communication system over a 1-dimensional vector channel where message m 1 is sent by signaling
More informationAnalysis of Random Radar Networks
Analysis of Random Radar Networks Rani Daher, Ravira Adve Department of Electrical and Computer Engineering, University of Toronto 1 King s College Road, Toronto, ON M5S3G4 Email: rani.daher@utoronto.ca,
More informationHomework 5 Solutions. Problem 1
Homework 5 Solutions Problem 1 (a Closed form Chernoff upper-bound for the uncoded 4-QAM average symbol error rate over Rayleigh flat fading MISO channel with = 4, assuming transmit-mrc The vector channel
More informationSimultaneous SDR Optimality via a Joint Matrix Decomp.
Simultaneous SDR Optimality via a Joint Matrix Decomposition Joint work with: Yuval Kochman, MIT Uri Erez, Tel Aviv Uni. May 26, 2011 Model: Source Multicasting over MIMO Channels z 1 H 1 y 1 Rx1 ŝ 1 s
More informationImproved Multiple Feedback Successive Interference Cancellation Algorithm for Near-Optimal MIMO Detection
Improved Multiple Feedback Successive Interference Cancellation Algorithm for Near-Optimal MIMO Detection Manish Mandloi, Mohammed Azahar Hussain and Vimal Bhatia Discipline of Electrical Engineering,
More informationAn Efficient Approach to Multivariate Nakagami-m Distribution Using Green s Matrix Approximation
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL 2, NO 5, SEPTEMBER 2003 883 An Efficient Approach to Multivariate Nakagami-m Distribution Using Green s Matrix Approximation George K Karagiannidis, Member,
More informationFlat Rayleigh fading. Assume a single tap model with G 0,m = G m. Assume G m is circ. symmetric Gaussian with E[ G m 2 ]=1.
Flat Rayleigh fading Assume a single tap model with G 0,m = G m. Assume G m is circ. symmetric Gaussian with E[ G m 2 ]=1. The magnitude is Rayleigh with f Gm ( g ) =2 g exp{ g 2 } ; g 0 f( g ) g R(G m
More informationThe Performance of Quaternary Amplitude Modulation with Quaternary Spreading in the Presence of Interfering Signals
Clemson University TigerPrints All Theses Theses 1-015 The Performance of Quaternary Amplitude Modulation with Quaternary Spreading in the Presence of Interfering Signals Allison Manhard Clemson University,
More informationEE4512 Analog and Digital Communications Chapter 4. Chapter 4 Receiver Design
Chapter 4 Receiver Design Chapter 4 Receiver Design Probability of Bit Error Pages 124-149 149 Probability of Bit Error The low pass filtered and sampled PAM signal results in an expression for the probability
More informationResidual Versus Suppressed-Carrier Coherent Communications
TDA Progress Report -7 November 5, 996 Residual Versus Suppressed-Carrier Coherent Communications M. K. Simon and S. Million Communications and Systems Research Section This article addresses the issue
More informationBASICS OF DETECTION AND ESTIMATION THEORY
BASICS OF DETECTION AND ESTIMATION THEORY 83050E/158 In this chapter we discuss how the transmitted symbols are detected optimally from a noisy received signal (observation). Based on these results, optimal
More informationPerformance Analysis of Multi-User Massive MIMO Systems Subject to Composite Shadowing-Fading Environment
Performance Analysis of Multi-User Massive MIMO Systems Subject to Composite Shadowing-Fading Environment By Muhammad Saad Zia NUST201260920MSEECS61212F Supervisor Dr. Syed Ali Hassan Department of Electrical
More informationComparison of DPSK and MSK bit error rates for K and Rayleigh-lognormal fading distributions
Comparison of DPSK and MSK bit error rates for K and Rayleigh-lognormal fading distributions Ali Abdi and Mostafa Kaveh ABSTRACT The composite Rayleigh-lognormal distribution is mathematically intractable
More informationMulti-Branch MMSE Decision Feedback Detection Algorithms. with Error Propagation Mitigation for MIMO Systems
Multi-Branch MMSE Decision Feedback Detection Algorithms with Error Propagation Mitigation for MIMO Systems Rodrigo C. de Lamare Communications Research Group, University of York, UK in collaboration with
More informationLecture 12. Block Diagram
Lecture 12 Goals Be able to encode using a linear block code Be able to decode a linear block code received over a binary symmetric channel or an additive white Gaussian channel XII-1 Block Diagram Data
More informationMultiuser Capacity in Block Fading Channel
Multiuser Capacity in Block Fading Channel April 2003 1 Introduction and Model We use a block-fading model, with coherence interval T where M independent users simultaneously transmit to a single receiver
More informationMax-Min Relay Selection for Legacy Amplify-and-Forward Systems with Interference
1 Max-Min Relay Selection for Legacy Amplify-and-Forward Systems with Interference Ioannis Kriidis, Member, IEEE, John S. Thompson, Member, IEEE, Steve McLaughlin, Senior Member, IEEE, and Norbert Goertz,
More informationDigital Modulation 1
Digital Modulation 1 Lecture Notes Ingmar Land and Bernard H. Fleury Navigation and Communications () Department of Electronic Systems Aalborg University, DK Version: February 5, 27 i Contents I Basic
More informationA Thesis for the Degree of Master. An Improved LLR Computation Algorithm for QRM-MLD in Coded MIMO Systems
A Thesis for the Degree of Master An Improved LLR Computation Algorithm for QRM-MLD in Coded MIMO Systems Wonjae Shin School of Engineering Information and Communications University 2007 An Improved LLR
More informationAdvanced 3 G and 4 G Wireless Communication Prof. Aditya K Jagannathan Department of Electrical Engineering Indian Institute of Technology, Kanpur
Advanced 3 G and 4 G Wireless Communication Prof. Aditya K Jagannathan Department of Electrical Engineering Indian Institute of Technology, Kanpur Lecture - 19 Multi-User CDMA Uplink and Asynchronous CDMA
More informationEstimation of the Optimum Rotational Parameter for the Fractional Fourier Transform Using Domain Decomposition
Estimation of the Optimum Rotational Parameter for the Fractional Fourier Transform Using Domain Decomposition Seema Sud 1 1 The Aerospace Corporation, 4851 Stonecroft Blvd. Chantilly, VA 20151 Abstract
More informationOutline. Digital Communications. Lecture 12 Performance over Fading Channels and Diversity Techniques. Flat-Flat Fading. Intuition
Digital Counications Lecture 2 Perforance over Fading Channels and Diversity Techniques Pierluigi SALVO ROSSI Outline Noncoherent/Coherent Detection 2 Channel Estiation Departent of Industrial and Inforation
More informationReliability of Radio-mobile systems considering fading and shadowing channels
Reliability of Radio-mobile systems considering fading and shadowing channels Philippe Mary ETIS UMR 8051 CNRS, ENSEA, Univ. Cergy-Pontoise, 6 avenue du Ponceau, 95014 Cergy, France Philippe Mary 1 / 32
More informationPerformance Analysis and Code Optimization of Low Density Parity-Check Codes on Rayleigh Fading Channels
Performance Analysis and Code Optimization of Low Density Parity-Check Codes on Rayleigh Fading Channels Jilei Hou, Paul H. Siegel and Laurence B. Milstein Department of Electrical and Computer Engineering
More informationA Simple Example Binary Hypothesis Testing Optimal Receiver Frontend M-ary Signal Sets Message Sequences. possible signals has been transmitted.
Introduction I We have focused on the problem of deciding which of two possible signals has been transmitted. I Binary Signal Sets I We will generalize the design of optimum (MPE) receivers to signal sets
More informationthat efficiently utilizes the total available channel bandwidth W.
Signal Design for Band-Limited Channels Wireless Information Transmission System Lab. Institute of Communications Engineering g National Sun Yat-sen University Introduction We consider the problem of signal
More informationLECTURE 18. Lecture outline Gaussian channels: parallel colored noise inter-symbol interference general case: multiple inputs and outputs
LECTURE 18 Last time: White Gaussian noise Bandlimited WGN Additive White Gaussian Noise (AWGN) channel Capacity of AWGN channel Application: DS-CDMA systems Spreading Coding theorem Lecture outline Gaussian
More informationSignal Design for Band-Limited Channels
Wireless Information Transmission System Lab. Signal Design for Band-Limited Channels Institute of Communications Engineering National Sun Yat-sen University Introduction We consider the problem of signal
More informationUTA EE5362 PhD Diagnosis Exam (Spring 2011)
EE5362 Spring 2 PhD Diagnosis Exam ID: UTA EE5362 PhD Diagnosis Exam (Spring 2) Instructions: Verify that your exam contains pages (including the cover shee. Some space is provided for you to show your
More informationA Systematic Description of Source Significance Information
A Systematic Description of Source Significance Information Norbert Goertz Institute for Digital Communications School of Engineering and Electronics The University of Edinburgh Mayfield Rd., Edinburgh
More informationOn Design Criteria and Construction of Non-coherent Space-Time Constellations
On Design Criteria and Construction of Non-coherent Space-Time Constellations Mohammad Jaber Borran, Ashutosh Sabharwal, and Behnaam Aazhang ECE Department, MS-366, Rice University, Houston, TX 77005-89
More informationExpected Error Based MMSE Detection Ordering for Iterative Detection-Decoding MIMO Systems
Expected Error Based MMSE Detection Ordering for Iterative Detection-Decoding MIMO Systems Lei Zhang, Chunhui Zhou, Shidong Zhou, Xibin Xu National Laboratory for Information Science and Technology, Tsinghua
More informationMemo of J. G. Proakis and M Salehi, Digital Communications, 5th ed. New York: McGraw-Hill, Chenggao HAN
Memo of J. G. Proakis and M Salehi, Digital Communications, 5th ed. New York: McGraw-Hill, 007 Chenggao HAN Contents 1 Introduction 1 1.1 Elements of a Digital Communication System.....................
More informationIEEE C80216m-09/0079r1
Project IEEE 802.16 Broadband Wireless Access Working Group Title Efficient Demodulators for the DSTTD Scheme Date 2009-01-05 Submitted M. A. Khojastepour Ron Porat Source(s) NEC
More informationUsing Noncoherent Modulation for Training
EE8510 Project Using Noncoherent Modulation for Training Yingqun Yu May 5, 2005 0-0 Noncoherent Channel Model X = ρt M ΦH + W Rayleigh flat block-fading, T: channel coherence interval Marzetta & Hochwald
More informationMIMO Zero-Forcing Receivers Part I: Multivariate Statistical Analysis
TRANSACTIONS ON INFORMATION THEORY, VOL.,NO., JANUAR MIMO Zero-Forcing Receivers Part I: Multivariate Statistical Analysis Mario Kießling, Member, IEEE Abstract In this paper, we analyze the signal to
More informationA Design of High-Rate Space-Frequency Codes for MIMO-OFDM Systems
A Design of High-Rate Space-Frequency Codes for MIMO-OFDM Systems Wei Zhang, Xiang-Gen Xia and P. C. Ching xxia@ee.udel.edu EE Dept., The Chinese University of Hong Kong ECE Dept., University of Delaware
More informationSOLUTIONS TO ECE 6603 ASSIGNMENT NO. 6
SOLUTIONS TO ECE 6603 ASSIGNMENT NO. 6 PROBLEM 6.. Consider a real-valued channel of the form r = a h + a h + n, which is a special case of the MIMO channel considered in class but with only two inputs.
More informationCoding theory: Applications
INF 244 a) Textbook: Lin and Costello b) Lectures (Tu+Th 12.15-14) covering roughly Chapters 1,9-12, and 14-18 c) Weekly exercises: For your convenience d) Mandatory problem: Programming project (counts
More informationSecond-Order Statistics of MIMO Rayleigh Interference Channels: Theory, Applications, and Analysis
Second-Order Statistics of MIMO Rayleigh Interference Channels: Theory, Applications, and Analysis Ahmed O.. Ali, Cenk M. Yetis, Murat Torlak epartment of Electrical Engineering, University of Texas at
More informationOptimum Relay Position for Differential Amplify-and-Forward Cooperative Communications
Optimum Relay Position for Differential Amplify-and-Forard Cooperative Communications Kazunori Hayashi #1, Kengo Shirai #, Thanongsak Himsoon 1, W Pam Siriongpairat, Ahmed K Sadek 3,KJRayLiu 4, and Hideaki
More information