Optimality of Beamforming for MIMO Multiple Access Channels via Virtual Representation
|
|
- Eleanore Henderson
- 5 years ago
- Views:
Transcription
1 TO APPAR I TRANSACTIONS ON SIGNAL PROCSSING Optimality of Beamforming for MIMO Multiple Access Channels via Virtual Representation Hong Wan, Rong-Rong Chen, and Yingbin Liang Abstract Ihis paper, we consider the optimality of beamforming for achieving the ergodic capacity of multiple-input multiple-output MIMO multiple access channel MAC via virtual representation VR model. We assume that the receiver nows the channel state information CSI perfectly but that the transmitter nows only partial CSI, i.e., the channel statistics. For the single-user case, we prove that the capacity-achieving beamforming angle c.b.a. is unique, and there exists a signal-to-noise ratio SNR threshold below which beamforming is optimal and above which beamforming is strictly suboptimal. For the multi-user case, we show that the c.b.a is not unique and we obtain explicit conditions that determine the beamforming angles for a special class of correlated MAC-VR models. Under mild conditions, we show that a large class of power allocation schemes can achieve the sum-capacity within a constant as the number of users ihe system becomes large. The beamforming scheme, in particular, is showo be asymptotically capacityachieving only for certain MAC-VR models. I. INTRODUCTION The multiple-input multiple-output MIMO techniques provide powerful means to improve reliability and capacity of wireless channels. Significant amount of wor has been done to study optimal input distributions and the channel capacity of single-user and multi-user MIMO channels see, e.g., 7. Several models have been adopted to capture the spatial correlation between the channel gains corresponding to different transmitreceive antenna pairs. These models include the i.i.d. model, the Kronecer model 2, 8 0, the virtual representation VR model 4,, and the unitaryindependent-unitary UIU model 5. The i.i.d. model assumes that the channel gains are independent and identically distributed i.i.d., and the Kronecer model assumes that the correlation betweehe channel gains The material ihis paper has been presented in part at the I International Symposium on Information Theory ISIT 08. Hong Wan and Rong-Rong Chen are with Department of C, University of Utah, 50 S. Central Campus Dr. Rm. 3280, Salt Lae City, Utah, 842. Tele: , Fax: , mail: {rchen, wan}@ece.utah.edu. Yingbin Liang is with Dept. of CS, Syracuse University, Syracuse, NY mail: yliang06@syr.edu, Tele: can be written ierms of the product of the transmit correlation and the receive correlation. These two models apply only to wireless environments with rich or locally rich scattering at either the transmitter or the receiver. The VR and UIU models are more general, and both transform the MIMO channel to a domain such that the channel gains can be justified to be approximately independent. Ihis paper, we adopt the VR model, which represents the MIMO channel in a virtual angular domain with each channel gain corresponding to one virtual transmit and receive angle pair. The channel gains in the angular domain can be justified to be approximately independent of each other, although not necessarily identically distributed, because they include different signal paths corresponding to different transmit and receive angle pairs with independent random phases. The single-user MIMO channel based on VR was studied in 4. Ihis paper, we generalize this study to the MIMO multiple access channel MAC based on VR, denoted by MAC-VR. We first characterize the optimal input distributiohat achieves the sum-capacity. Then we study the optimality of beamforming, which is a simple scalar coding strategy desirable in practice. We first strengthehe conditions for the optimality of beamforming for the single-user VR model in 4 by proving that there exists a signal-to-noise ratio SNR threshold below which beamforming is optimal and above which beamforming is strictly suboptimal. This result was illustrated in 4 only numerically. For the multi-user case, we present an example to show that the capacity-achieving beamforming angle c.b.a of a given user may vary with SNR and beamforming angles of other users. This is in contrast to the single-user case in which the c.b.a. is independent of SNR. We also derive explicit conditions to determine possible c.b.a. for certain MAC-VR channels. For systems with K users, we show that as K goes to infinity, the sum-rates achieved by a large class of power allocation schemes are within a constant of the sum-capacity, and they grow ihe order of n r logk, where n r is the number of receive antennas. Furthermore, we obtain conditions under which beamforming is asymptotically capacity-
2 TO APPAR I TRANSACTIONS ON SIGNAL PROCSSING 2 achieving. Our study for the single-user case generalizes that in 2, 6 for the Kronecer model, and is different from 2 for the double-scattering model 3. Our study for the MAC-VR also differs from 7 which assumes perfect channel state information at the transmitter, and from 4, which assumes finite feedbac. We also note that the results we derive for the MAC-VR are applicable to the MIMO-MAC Kronecer MAC-Kr model in 9. However, certain results valid for the MAC-Kr may not hold for the MAC-VR as demonstrated in later sections. II. CHANNL MODL AND VIRTUAL RPRSNTATION We consider the K-user MIMO MAC, in which K users transmit to one base station BS with each user equipped with antennas and the BS equipped with n r antennas. The channel between each user and the BS is assumed to be a frequency-flat, MIMO fading channel. The received signal at the BS is ann r -dimensional vector Y C nr and is given by K p Y = H X +W, = where X C nt is the input vector of user that satisfies the power constraint X X, denotes the Hermitian operator, p represents the effective SNR of user at each receive antenna, W C nr is a proper complex Gaussian noise vector that consists of i.i.d. entries with zero-mean and unit-variance, and H C nr nt is the channel matrix of user. The entries of H are identically distributed with unit variance, i.e., H m,j 2 = for all m =,...,n r and j =,...,. In general, these entries are correlated because each channel gain ihe antenna domain corresponding to one transmit and receive antenna pair captures all of the signal paths. For each H, we follow 4 to consider its virtual representation H = A H r A t, where A r and A t are two-dimensional spatial Fourier matrices. The matrix H is referred to as a virtual representation of H. ach element of H, referred to as the virtual coefficient, represents the channel gain corresponding to one transmit and receive virtual angle pair. The virtual coefficients are independent and not identically distributed i.n.d. random variables and each is assumed to be a zero-mean proper complex random variable with a symmetric distribution around the origin. The independency among virtual coefficients can be justified because they correspond to different pairs of transmit and receive angles and thus capture different sets of signal paths with independent random phases. The correlation of the channel gains ihe antenna domain is implicitly determined by the i.n.d. channel gains in virtual domain and the Fourier transform betweehe two domains. A virtual representation of the MIMO MAC channel is given by K p Ỹ = H n X + W, 2 t = where X = A t X, Ỹ = A ry, and W = A rw. Due to the unitarity of A t, the input power constraint ihe virtual domain does not change, i.e., X X. Given H, we define the m,j-th element of the variance matrix V as Vm,j = Var H m,j, for m n r and j, which characterizes the second order statistics of H. Remar : It can be showhat the MAC-Kr also taes the form of 2 under unitary transformations. However, it imposes more constraints on H than MAC- VR does. For MAC-Kr, each element of H is assumed to be Gaussian distributed. This is not required for the MAC-VR. Furthermore, for MAC-VR, the elements of H are i.n.d., and thus elements of V caae any nonnegative value. For MAC-Kr, Vm,j taes on a product form: Vm,j = a m b j, for every m n r and j, 3 where{a m } and{b j } are square-roots of the eigenvalues of the receive correlation and transmit correlation matrix, respectively. III. PRLIMINARIS Ihis section, we present some preliminary results that will be used ihe proofs of the main results in Sections IV and V. Since these preliminary results can be easily derived following techniques in 4, 9, 0, the proofs are omitted for brevity. First, we show that the sum-capacity of MAC-VR is achieved whehe inputs of all users ihe virtual domain are zero-mean proper complex Gaussian and are independent of each other. Let Q = X X be the input covariance matrix of user. The sum-capacity is given by C = max log det I nr + Tr Q =,,K K = p H Q H, 4 We note that a channel matrix with arbitrary correlation in the antenna domain may not necessarily have a meaningful virtual representation with an i.n.d. channel matrix ihe angular domain.
3 TO APPAR I TRANSACTIONS ON SIGNAL PROCSSING 3 where the expectation is over { H, =,,K}, and the constraint on Q is due to the power constraint for user. Here we assume that { H } changes iime and the receiver nows the perfect channel state information CSI { H }. The transmitter nows only partial CSI, i.e., the channel statistics {V }, which does not change over the time duration of interest. Following techniques of 4, we can prove that the capacity-achieving covariance matrices are diagonal 5. Furthermore, a necessary and sufficient condition for the optimality of the input covariance matrices can be derived following similar approaches of 9, 0. This leads to Theorem below. Theorem : The diagonal covariance matrices { Q, =,,K} achieve the sum-capacity if and only if for every K and j, we have Tr A h j h j H Q H { = 0, if λ j > 0, 0, if λ j = 0, 5 where Q = diagλ,,λ, A = I nr + K l= p l Hl Ql Hl, and h j denotes the j-th column of H. Remar 2: Since the diagonal element λ j, j =,...,, of Q can be interpreted as the amount of transmission power allocated for the j-th virtual transmit angle, computation of the optimal covariance matrices to maximize the ergodic capacity is equivalent to finding the optimal power allocation parameters {λ j }. Although the iterative algorithm in 0 can be applied to compute the optimal power allocation, it has high complexity due to statistical averaging over fading distributions. A low-complexity algorithm that utilizes only the second order statistics of the fading distribution, i.e., the variance matrix V, can be developed for the MAC-VR following similar approaches of 6. When all users perform beamforming, i.e., each user allocates full transmission power to a virtual anglei the beamforming angle, then from 5 we obtain Corollary below that characterizes the optimality of beamforming. It is equivalent to 9, Theorem 2 for the MAC-Kr. Corollary : Consider a K-user MAC-VR in which each user performs beamforming along virtual angle i. Let A = I nr + K p l hl il hl i l. Then beamforming is l= optimal, ierms of achieving the sum-capacity 4, if and only if for every j =,, and =,,K, the following condition is satisfied f j p = h j A h j h i A h i 0. 6 IV. OPTIMALITY OF BAMFORMING A. Single-User Case It is observed in 4 numerically that there exists an SNR threshold below which beamforming is optimal and above which beamforming is suboptimal. Here we provide a mathematical proof of this threshold behavior. The ey step of the proof follows from Lemma below, which characterizes an important property of the beamforming condition f j p in 6. For K =, we assume that the user beamforms to virtual angle i, and thus we have A = I nr + p h i h i, and f jp = h j A hj h i. A hi Lemma : If f j p satisfies f j p 0, then we must have f j p > 0. Proof: Let f j p denote the derivative of f jp with respect to p. We will prove that for every j i, f jp > p +p h i 2 f j p. 7 Once 7 is proved, Lemma immediately follows because +p h 0. To prove 7, we i 2 apply the matrix inversion lemma to write f j p = u j p + v j p, where u j p = hj 2 h i 2 and +p h i 2 v j p = hj 2 h i 2 h j h i 2 p + h i 2. Due to the Cauchy- Schwartz inequality, we have h j 2 h i 2 h j h i 2 > 0 and thus v j p is a positive, strictly increasing function of p with v j p > 0. It follows that f jp > u hi 4 h j 2 h i 2 jp = +p h i 2 2 = p hi 2 h j 2 + p +p h i 2 p h i 2 +p hi 2 2 h j 2 +p hi For the second term of 8, since h j is independent of h i, we apply the inequality /x 2 > /x 2 with x = +p h i 2 to obtain h j 2 +p hi 2 2 > = 2 +p h i 2 +p h i 2 h j 2 h j 2 +p h i 2. 9
4 TO APPAR I TRANSACTIONS ON SIGNAL PROCSSING 4 For the third term of 8, we apply the same inequality to obtain h i 2 +p hi 2 2 = p +p hi 2 2 p +p hi 2 > +p h i 2 hi 2. +p h i 2 0 We then substitute 9 and 0 into 8 to obtain 7. Next, we characterize the threshold behavior of beamforming in Theorem 2. Theorem 2: For a single-user VR channel, the i-th virtual angle is the c.b.a. if and only if a The i-th virtual angle has a sum-variance, defined by n r j= V j,i, that is strictly larger thahe sumvariance of any other virtual angles. This condition implies that the c.b.a. is unique. b The SNR is below a threshold, i.e., p < p s, where p s is a fixed constant. Proof: It follows from Lemma thatf j p is strictly increasing at anypsuch that f j p 0. This implies that i If f j 0 0, then f j p is nonzero over p 0,, and thus we have f j p > 0 for all p > 0. ii If f j 0 < 0, thenf j p has a unique zero pointp j such thatf j p < 0 if and only if p < p j. Hence, if virtual angle i is the c.b.a, i.e., f j p 0 for some p > 0 and j i, then it follows from i that we must have f j 0 < 0. Since f j 0 = h j 2 h i 2, angle i must have the largest sum-variance. This proves Theorem 2 a. Theorem 2 b follows from ii by letting p s = min p j. j i B. Multi-User Case For the multi-user case, we first present an example to show that for the c.b.a. of a particular user is not unique, and it may vary with the SNRs and beamforming angles of other users ihe system. xample : Consider a two-user MAC-VR with = n r = 2. The variance matrices are V = 3 0 0, V 2 = find that, if p,p 2 = 5 db, 0 db, the first virtual angle is the c.b.a. for both users. If p,p 2 = 3 db, 0 db, however, the second virtual angle becomes the c.b.a. for user 2, while the first angle is still the c.b.a. for user. Next, we show in Theorem 3 that whehe variance matrix satisfies certain properties, some of the virtual angles cannot be the c.b.a. of a given user. We first present a useful Lemma. Lemma 2: Assume that there exists virtual angels i,j for a user ihe MAC-VR such that V m,i V m,j for every m =,,n r. Then we have cj c i h +p c i > 0, where c j = j D h j,c i = h i D h i I, and D = nr + K. l pl hl il hl i l Proof: It suffices to show that for any fixed D, we have Ē cj c i +p c i > 0, here Ē denotes the conditional expectation over h j and h i, given D. Since c j and c i are independent given D, we obtain cj c i Ē +p c i = +p Ē c j p +p c i = p Ē+p c j Ē > p Ē+p c j Ē+p c i +p c i = p +p Ēc j +p Ēc i, 2 where the inequality follows from the Jensen s inequality /x > /x. Next, we show that Ēc j Ēc i, and thus the right-hand side of 2 is non-negative. We can write Ēc j Ēc i = Ē h j D h j Ē h i D h i = Tr D Ē h j h j h i h i. It follows from that Ē h j h j h i h i = diagv,j V,i,,V n V r,j n r,i is a diagonal matrix with non-negative entries. This, combined with D being a positive definite Hermitian matrix with positive diagonal entries, imply that Ēc j Ēc i. Theorem 3: Consider user in a K-user MAC-VR. The i-th virtual angle cannot be the c.b.a. of user if there exists another virtual angle j such that holds. Proof: It is sufficient to prove that the beamforming condition 6, with i = i, is violated for any j that satisfies, i.e., fj p > 0. To prove this, we apply the matrix inversion lemma to write. From condition 6 we fj cj c i cj c i h p j = +p + D h i h i D h j c i p +c i cj c i > +p. c i 3 The inequality above is due to the Cauchy-Schwartz inequality that c j c i h j D h i h i D h j > 0. It then follows from Lemma 2 and 3 that fj p > 0. Thus, angle i cannot be the c.b.a. of user.
5 TO APPAR I TRANSACTIONS ON SIGNAL PROCSSING 5 xample 2: Assume that V = Since is satisfied for i = and j = 2, it follows from Theorem 3 that the first virtual angle cannot be the c.b.a for user. This result holds independent of the SNR and other users beamforming angles. An immediate corollary of Theorem 3 is as follows: Corollary 2: If there exists a virtual angle i such that Vm,i > Vm,j, for every m n r and j i, then angle i is the only possible c.b.a. Corollary 2 is applicable to both MAC-VR and MAC- Kr. For MAC-Kr, we see that the c.b.a. of user is the i-th angle that maximizes {b j,j =,,} defined in 3, and thus the c.b.a is unique. In comparison, the c.b.a. is not unique for MAC-VR. Such differences arise because the variance matrix for MAC-VR taes a general form, while that of MAC-Kr is restricted to the product form 3. V. POWR ALLOCATION FOR LARG SYSTMS Ihis section, we show that under mild conditions, the sum-capacity of a K-user system, denoted by CK, grows ihe order of n r logk. Furthermore, we present conditions under which the sum-rate achieved by a power allocation scheme λ is within a constant of CK as K goes to infinity. Given a power allocation λ = {λ j, =,,K,j =,, }, let A K = I nr + K K =j= p = p H Q H = I nr + λ j h j h j. The sum-rate achieved by λ is given by Iλ,K = logdeta K. We apply Jensen s inequality to obtain an upper bound Īλ,K such that Iλ,K = logdeta K logdeta K n r K p = log + λ j n V m,j t = m= = j= Īλ,K. 4 Proposition below shows that under mild conditions, Īλ,K is asymptotically tight as K. Proposition : Assume that M 4 = sup m,j, p 2 h m,j 4 <. If there exists a constant c > 0 such that λ satisfies min liminf m n r K K = j= p λ j n V m,j c > 0, 5 t then we have Iλ,K = Īλ,K + o, where o converges to zero as K. Proof. First, we write Iλ,K Īλ,K = log deta K deta K deta K = log n r + K p λ j V m,j ÃK m,i = m= = logdetãk, =j= where the m,i-th element ofãk, denoted by ÃK m,i, is given by + K p λ j h m,j h i,j = =j= + K + K =j= =j= + K =j= p λ j V m,j p λ j h m,j h i,j p λ j V m,j /+K /+K. 6 We let S K denote the numerator ihe second fraction of 6, which equals the average of the summation of independent random variables. It follows from the Strong Law of Large Number SLLN and 5 that 0= lim S K S K =limsup S K S K S K lim inf S K lim sup S K S K c limsup S K S K. Thus, for m = i we obtain lim ÃK i,i = lim SK / S K =. For m i, since S K = 0, it follows from 5 and the SLLN that lim ÃK m,i c lim S K = 0. This proves that SK S K = c lim à K converges to the identity matrix and thus lim logdet à K = 0. Assume that the distributions of the random vectors { h j } are sufficiently smooth to facilitate exchange of the limit and the expectation operator, we obtain lim Iλ,K Īλ,K = lim logdet à K = lim logdetãk = 0. Note that although both proofs apply the SLLN, the proof of Proposition differs from that of 9, Lemma 2 for the MAC-Kr ihat we provide a sufficient condition 5, which guarantees that 7 holds. From Proposition we obtain Corollary 3 below. Corollary 3: For any λ that satisfies 5, we have Iλ,K = CK+O = n r logk+o, whereo
6 TO APPAR I TRANSACTIONS ON SIGNAL PROCSSING 6 denotes a bounded quantity as K. Hence, Iλ,K grows ihe order of n r logk, and asymptotically it differs from the sum-capacity CK by only a constant. Setch of proof. It is sufficient to show that there exists constants u and u c such that n r logk +u c +o Iλ,K CK maxīλ,k n r logk +u +o. 7 λ From 5 we can find u c such that Īλ,K n r logk+u c. This, combined with Proposition, leads to the first inequality of 7. The last inequality of 7 utilizes M 2 = sup m,j, p Vm,j <. Next, we consider a simple example for which we can characterize the term O in Corollary 3 for various λ. The accuracy of these computations will be verified in Section VI. xample 3: Assume that all users have the samep = 2 and the same variance matrix V =. The virtual elements in H are complex Gaussian distributed. Assume that each user adopts the same power allocation λ = λ,λ 2 such that λ + λ 2 = 2. For each λ that satisfies the assumptions of Proposition, we have Iλ,K = Īλ,K+o = 2logK+log2λ +0.5 λ 2 + log0.5 λ +λ 2 +o. 8 Consider the following three power allocations for which Proposition and Corollary 3 are applicable. The beamforming scheme λ BF where each user beamforms to the first virtual angle which has the largest sum-variance. Since λ = 2,λ 2 = 0, it follows from 8 that Iλ BF,K = Īλ BF,K+o = 2logK +log4+o. 9 2 The equal power allocation λ q such that λ = λ 2 =. From 8 we have Iλ q,k = Īλ q,k+o = 2logK +log5/4 +o = 2logK o We can choose λ,λ 2 to maximize the summation of the two constant terms in 8. This yields the optimized solution λ = λ,λ 2 = 5/3,/3. Hence, from 8 we have Iλ,K = Īλ,K+o = 2logK +log49/2 +o = 2logK o. 2 The constant term in 2 is slightly greater thahat of λ BF in 9 and that ofλ q in 20. This example demonstrates that beamforming may not be asymptotically optimal for the MAC-VR, evehough it is asymptotically optimal for MAC-Kr 9, Theorem 7. Corollary 4 below provides a sufficient condition under which beamforming is asymptotically optimal for MAC-VR. Corollary 4: Beamforming is asymptotically optimal for the MAC-VR: Iλ BF,K = CK+o, as K, if each user beamforms to a virtual angle i that satisfies V m,i V m,j for every m n r and j, and there exists a constant c > 0 such that min liminf m n r K K p Vm,i c > = Setch of proof. Given Vm,i Vm,j, one can show that CK Īλ BF,K. Condition 22 ensures that Iλ BF,K = Īλ BF,K + o. Thus Corollary 4 follows. Considering a special case of Corollary 4 in which we let i be the virtual angle that maximizes {b j,j =,, }, then we obtaihe same result as 9, Theorem 7 that beamforming is always asymptotically optimal for MAC-Kr. In comparison, as shown in xample 3, there exists MAC-VR such that beamforming is not asymptotically optimal. This difference, again, is due to the general structure of the variance matrix for MAC- VR. VI. NUMRICAL RSULTS Ihis section, we present numerical examples to illustrate the theoretical results given in previous sections. Four power allocation schemes are considered: the equal power allocation λ q, the beamforming scheme λ BF, the optimal power allocation λ Opt found by the algorithm of 0, and a low-complexity power allocation algorithm derived based on 6 λ Low. Let Iλ denote the sum-rate achieved by λ. We first consider a singleuser system with n r = = 5. The virtual coefficients in H are assumed to be complex Gaussian distributed with the same variance matrix as the one in 4, given by V = Please refer to 4 for the physical meaning of such a variance matrix. The third virtual angle is the beamforming angle because it has the largest sum-variance. Fig.
7 TO APPAR I TRANSACTIONS ON SIGNAL PROCSSING 7 K=, n =5, n =5 t r 4 sum rate bits/s/hz optimum low complexity Alg. equal power beamforming db f p f 4 p SNRdB a Single-user system with = n r = SNRdB b Beamforming conditions, SNR threshold is at 0.29 db 2.3 =2, n r =2, SNR=3dB 40 =5, n r =5, SNR=5dB sum rate 2logK b/s/hz beamforming 20 equal power 2 optimized 22 sum rate b/s/hz equal power beamforming low compleixty Alg. upper bound.9 Fig K, the number of users c Numerical verification of xample 3. Optimality of beamforming for MAC-VR K, the number of users d Optimality of beamforming for large systems a shows that Iλ Low is very close to Iλ Opt for the entire range of SNRs considered. Iλ q is near optimal only at high SNR and Iλ BF is optimal only when SNR is below the threshold of 0.29 db. This is consistent with the threshold behavior proved in Theorem 2. In Fig. b, we plot the beamforming conditions defined in Section IV-A for the third virtual angle i = 3. Since f 2 p = f p and f 5 p = f 4 p, Fig. b plots f p and f 4 p and shows that when SNR is below 0.29 db, both functions are negative and thus beamforming to the third virtual angle is optimal. In Fig. c, we examine the accuracy of Proposition and Corollary 3 by comparing the asymptotic expressions 9-2 in xample 3 with numerical values of Iλ, K obtained through Monte Carlo integration. Three functions Iλ BF,K 2logK, Iλ q,k 2logK, and Iλ,K 2logK are plotted to confirm that as K increases, they indeed converge to the predicted constants 2,.9069, and , respectively. Fig. d considers a multi-user system in which each V is generated independently, taing a form similar to 23. The beamforming angle of user is chosen to be the virtual angle with the largest sum-variance. Because {V } satisfy conditions of Corollary 4, λ BF is asymptotically optimal. This is confirmed in Fig. d. The curve for Iλ Opt,K is not shown due to high complexity for computing λ Opt. Instead, we provide a simple sum-capacity upper bound CK n r log+km 2 as a performance benchmar for large K. Hence, the gap between Iλ BF,K and CK is less thahe small gap shown in Fig. d between Iλ BF,K and the upper bound. The gap becomes negligible as K increases, confirming the optimality of beamforming. For small K, Iλ Low,K closely approximates Iλ Opt,K not shown. For large K, Iλ Low,K and Iλ BF,K merge quicly and become indistinguishable after K 30. We note that Iλ q,k is inferior to Iλ BF,K by roughly a constant, evehough it achieves the same asymptote of n r logk = 5logK. This is consistent with Corollary 3.
8 TO APPAR I TRANSACTIONS ON SIGNAL PROCSSING 8 VII. CONCLUSION Ihis paper, we study the optimality of beamforming for the MAC-VR. For the single-user case, we provide a mathematical proof of the threshold behavior for the optimality of beamforming which is applicable to both Kronecer model and VR model. We present useful criteria in determining the capacity-achieving beamforming angles for a class of MAC-VR models. Due to the generality of the VR model, we demonstrate by examples that existing results for the MAC-Kr may not be valid for the MAC-VR. These include the uniqueness of the capacity-achieving beamforming angle, and the optimality of beamforming for systems with large number of users. 4 W. Dai, B. Rider, and Y. Liu, Joint beamforming for multiaccess MIMO systems with finite rate feedbac, I Transactions on Wireless Communications, vol. 8, no. 5, pp , May H. Wan, R.-R. Chen, and Y. Liang, Optimality of beamforming in MIMO multi-access channels via virtual representation, in Proc. I International Symposium on Information Theory ISIT 08, pp , July, S. Lasaulce, A. Suarez, M. Debbah, and L. Cottatellucci, Power allocation game for fading MIMO multiple access channels with antenna correlation, Conference on GameComm, Oct RFRNCS I.. Telatar, Capacity of multi-antenna Gaussian channels, ur. Trans. Telecom, vol. 0, pp , Nov S. Jafar and A. Goldsmith, Transmitter optimization and optimality of beamforming for multiple antenna systems, I Trans. Wireless Commun., vol. 3, pp , July Z. Wang and G. B. Giannais, Outage mutual information rate of space-time MIMO channels, I Trans. on Information Theory, vol. 50, no. 4, pp , Sep V. V. Veeravalli, Y. Liang, and A. M. Sayeed, Correlated MIMO wireless channels: Capacity, optimal signaling, and asymptotics, I Transactions on informatioheory, vol. 5, pp , A. M.Tulino, A. Lozano, and S. Verdu, Impact of antenna correlation ohe capacity of multiantenna channels, I Trans. on Information Theory, vol. 5, pp , July Jorswiec and H. Boche, Channel capacity and capacity range of beamforming in MIMO wireless systems under correlated fading with covariance feedbac, I Trans. on Wireless Commu., vol. 3, pp , Sep W. Rhee, W. Yu, and J. M. Cioffi, The optimality of beamforming in uplin multiuser wireless systems, I Trans. on Wireless Commu., vol. 3, no., pp , Jan H. Shin and J. H. Lee, Capacity of multiple-antenna fading channels: Spatial fading correlation, double scattering, and eyhole, I Trans. on Info. Theory, vol. 49, pp , Oct A. Soysal and S. Uluus, Optimality of beamforming in fading multiple access channels, I Trans. on Communications, pp. 7 83, April, , Optimum power allocation for single-user MIMO and multi-user MIMO-MAC with partial CSI, I Trans. on Selected Areas in Communication, no. 7, pp , Sep A. M. Sayeed, Deconstructing multi-antenna fading channels, I Trans. Signal Processing, pp , Oct, X. Li, S. Jin, X. Gao, M. Mcay, and K. Wong, Transmitter optimization and beamforming optimality conditions for doublescattering MIMO channels, I Trans. Wireless Commun., vol. 7, no. 9, pp , Sep D. Gesbert, H. Bolcsei, D. A. Gore, and A. J. Paulraj, Ourdoor MIMO wireless channels: Models and performance prediction, I Trans. Commun., vol. 50, no. 2, pp , Dec
Optimum Power Allocation in Fading MIMO Multiple Access Channels with Partial CSI at the Transmitters
Optimum Power Allocation in Fading MIMO Multiple Access Channels with Partial CSI at the Transmitters Alkan Soysal Sennur Ulukus Department of Electrical and Computer Engineering University of Maryland,
More informationTransmit Directions and Optimality of Beamforming in MIMO-MAC with Partial CSI at the Transmitters 1
2005 Conference on Information Sciences and Systems, The Johns Hopkins University, March 6 8, 2005 Transmit Directions and Optimality of Beamforming in MIMO-MAC with Partial CSI at the Transmitters Alkan
More informationUSING multiple antennas has been shown to increase the
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 55, NO. 1, JANUARY 2007 11 A Comparison of Time-Sharing, DPC, and Beamforming for MIMO Broadcast Channels With Many Users Masoud Sharif, Member, IEEE, and Babak
More informationDirty Paper Coding vs. TDMA for MIMO Broadcast Channels
TO APPEAR IEEE INTERNATIONAL CONFERENCE ON COUNICATIONS, JUNE 004 1 Dirty Paper Coding vs. TDA for IO Broadcast Channels Nihar Jindal & Andrea Goldsmith Dept. of Electrical Engineering, Stanford University
More informationUpper Bounds on MIMO Channel Capacity with Channel Frobenius Norm Constraints
Upper Bounds on IO Channel Capacity with Channel Frobenius Norm Constraints Zukang Shen, Jeffrey G. Andrews, Brian L. Evans Wireless Networking Communications Group Department of Electrical Computer Engineering
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 informationMorning Session Capacity-based Power Control. Department of Electrical and Computer Engineering University of Maryland
Morning Session Capacity-based Power Control Şennur Ulukuş Department of Electrical and Computer Engineering University of Maryland So Far, We Learned... Power control with SIR-based QoS guarantees Suitable
More informationJoint FEC Encoder and Linear Precoder Design for MIMO Systems with Antenna Correlation
Joint FEC Encoder and Linear Precoder Design for MIMO Systems with Antenna Correlation Chongbin Xu, Peng Wang, Zhonghao Zhang, and Li Ping City University of Hong Kong 1 Outline Background Mutual Information
More informationCapacity optimization for Rician correlated MIMO wireless channels
Capacity optimization for Rician correlated MIMO wireless channels Mai Vu, and Arogyaswami Paulraj Information Systems Laboratory, Department of Electrical Engineering Stanford University, Stanford, CA
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 informationErgodic and Outage Capacity of Narrowband MIMO Gaussian Channels
Ergodic and Outage Capacity of Narrowband MIMO Gaussian Channels Yang Wen Liang Department of Electrical and Computer Engineering The University of British Columbia April 19th, 005 Outline of Presentation
More informationOn the Optimality of Multiuser Zero-Forcing Precoding in MIMO Broadcast Channels
On the Optimality of Multiuser Zero-Forcing Precoding in MIMO Broadcast Channels Saeed Kaviani and Witold A. Krzymień University of Alberta / TRLabs, Edmonton, Alberta, Canada T6G 2V4 E-mail: {saeed,wa}@ece.ualberta.ca
More informationTight Lower Bounds on the Ergodic Capacity of Rayleigh Fading MIMO Channels
Tight Lower Bounds on the Ergodic Capacity of Rayleigh Fading MIMO Channels Özgür Oyman ), Rohit U. Nabar ), Helmut Bölcskei 2), and Arogyaswami J. Paulraj ) ) Information Systems Laboratory, Stanford
More informationMultiple Antennas in Wireless Communications
Multiple Antennas in Wireless Communications Luca Sanguinetti Department of Information Engineering Pisa University luca.sanguinetti@iet.unipi.it April, 2009 Luca Sanguinetti (IET) MIMO April, 2009 1 /
More informationThe Optimality of Beamforming: A Unified View
The Optimality of Beamforming: A Unified View Sudhir Srinivasa and Syed Ali Jafar Electrical Engineering and Computer Science University of California Irvine, Irvine, CA 92697-2625 Email: sudhirs@uciedu,
More informationOn the Rate Duality of MIMO Interference Channel and its Application to Sum Rate Maximization
On the Rate Duality of MIMO Interference Channel and its Application to Sum Rate Maximization An Liu 1, Youjian Liu 2, Haige Xiang 1 and Wu Luo 1 1 State Key Laboratory of Advanced Optical Communication
More informationMIMO Capacity in Correlated Interference-Limited Channels
MIMO Capacity in Correlated Interference-Limited Channels Jin Sam Kwak LG Electronics Anyang 431-749, Korea Email: sami@lge.com Jeffrey G. Andrews The University of Texas at Austin AustiX 78712, USA Email:
More informationOptimal Transmit Strategies in MIMO Ricean Channels with MMSE Receiver
Optimal Transmit Strategies in MIMO Ricean Channels with MMSE Receiver E. A. Jorswieck 1, A. Sezgin 1, H. Boche 1 and E. Costa 2 1 Fraunhofer Institute for Telecommunications, Heinrich-Hertz-Institut 2
More informationTransmitter optimization for distributed Gaussian MIMO channels
Transmitter optimization for distributed Gaussian MIMO channels Hon-Fah Chong Electrical & Computer Eng Dept National University of Singapore Email: chonghonfah@ieeeorg Mehul Motani Electrical & Computer
More informationOn the Capacity of Distributed Antenna Systems Lin Dai
On the apacity of Distributed Antenna Systems Lin Dai ity University of Hong Kong JWIT 03 ellular Networs () Base Station (BS) Growing demand for high data rate Multiple antennas at the BS side JWIT 03
More informationMULTIPLE-input multiple-output (MIMO) wireless systems,
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 55, NO. 8, AUGUST 2009 3735 Statistical Eigenmode Transmission Over Jointly Correlated MIMO Channels Xiqi Gao, Senior Member, IEEE, Bin Jiang, Student Member,
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 informationMULTIPLE-INPUT multiple-output (MIMO) systems
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 56, NO. 10, OCTOBER 2010 4793 Maximum Mutual Information Design for MIMO Systems With Imperfect Channel Knowledge Minhua Ding, Member, IEEE, and Steven D.
More informationWhat is the Value of Joint Processing of Pilots and Data in Block-Fading Channels?
What is the Value of Joint Processing of Pilots Data in Block-Fading Channels? Nihar Jindal University of Minnesota Minneapolis, MN 55455 Email: nihar@umn.edu Angel Lozano Universitat Pompeu Fabra Barcelona
More informationDuality, Achievable Rates, and Sum-Rate Capacity of Gaussian MIMO Broadcast Channels
2658 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL 49, NO 10, OCTOBER 2003 Duality, Achievable Rates, and Sum-Rate Capacity of Gaussian MIMO Broadcast Channels Sriram Vishwanath, Student Member, IEEE, Nihar
More informationOn the Fluctuation of Mutual Information in Double Scattering MIMO Channels
Research Collection Conference Paper On the Fluctuation of Mutual Information in Double Scattering MIMO Channels Author(s): Zheng, Zhong; Wei, Lu; Speicher, Roland; Müller, Ralf; Hämäläinen, Jyri; Corander,
More informationParallel Additive Gaussian Channels
Parallel Additive Gaussian Channels Let us assume that we have N parallel one-dimensional channels disturbed by noise sources with variances σ 2,,σ 2 N. N 0,σ 2 x x N N 0,σ 2 N y y N Energy Constraint:
More informationA Proof of the Converse for the Capacity of Gaussian MIMO Broadcast Channels
A Proof of the Converse for the Capacity of Gaussian MIMO Broadcast Channels Mehdi Mohseni Department of Electrical Engineering Stanford University Stanford, CA 94305, USA Email: mmohseni@stanford.edu
More informationUnder sum power constraint, the capacity of MIMO channels
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL 6, NO 9, SEPTEMBER 22 242 Iterative Mode-Dropping for the Sum Capacity of MIMO-MAC with Per-Antenna Power Constraint Yang Zhu and Mai Vu Abstract We propose an
More informationCharacterizing the Capacity for MIMO Wireless Channels with Non-zero Mean and Transmit Covariance
Characterizing the Capacity for MIMO Wireless Channels with Non-zero Mean and Transmit Covariance Mai Vu and Arogyaswami Paulraj Information Systems Laboratory, Department of Electrical Engineering Stanford
More information12.4 Known Channel (Water-Filling Solution)
ECEn 665: Antennas and Propagation for Wireless Communications 54 2.4 Known Channel (Water-Filling Solution) The channel scenarios we have looed at above represent special cases for which the capacity
More informationSchur-convexity of the Symbol Error Rate in Correlated MIMO Systems with Precoding and Space-time Coding
Schur-convexity of the Symbol Error Rate in Correlated MIMO Systems with Precoding and Space-time Coding RadioVetenskap och Kommunikation (RVK 08) Proceedings of the twentieth Nordic Conference on Radio
More informationOn the Impact of Quantized Channel Feedback in Guaranteeing Secrecy with Artificial Noise
On the Impact of Quantized Channel Feedback in Guaranteeing Secrecy with Artificial Noise Ya-Lan Liang, Yung-Shun Wang, Tsung-Hui Chang, Y.-W. Peter Hong, and Chong-Yung Chi Institute of Communications
More informationDiversity Multiplexing Tradeoff in Multiple Antenna Multiple Access Channels with Partial CSIT
1 Diversity Multiplexing Tradeoff in Multiple Antenna Multiple Access Channels with artial CSIT Kaushi Josiam, Dinesh Rajan and Mandyam Srinath, Department of Electrical Engineering, Southern Methodist
More informationAlgebraic Multiuser Space Time Block Codes for 2 2 MIMO
Algebraic Multiuser Space Time Bloc Codes for 2 2 MIMO Yi Hong Institute of Advanced Telecom. University of Wales, Swansea, UK y.hong@swansea.ac.u Emanuele Viterbo DEIS - Università della Calabria via
More informationImproved Sum-Rate Optimization in the Multiuser MIMO Downlink
Improved Sum-Rate Optimization in the Multiuser MIMO Downlin Adam J. Tenenbaum and Raviraj S. Adve Dept. of Electrical and Computer Engineering, University of Toronto 10 King s College Road, Toronto, Ontario,
More informationErgodic and Outage Capacity of Narrowband MIMO Gaussian Channels
Ergodic and Outage Capacity of Narrowband MIMO Gaussian Channels Yang Wen Liang Department of Electrical and Computer Engineering The University of British Columbia, Vancouver, British Columbia Email:
More informationRate-Optimum Beamforming Transmission in MIMO Rician Fading Channels
Rate-Optimum Beamforming Transmission in MIMO Rician Fading Channels Dimitrios E. Kontaxis National and Kapodistrian University of Athens Department of Informatics and telecommunications Abstract In this
More informationSingle-User MIMO systems: Introduction, capacity results, and MIMO beamforming
Single-User MIMO systems: Introduction, capacity results, and MIMO beamforming Master Universitario en Ingeniería de Telecomunicación I. Santamaría Universidad de Cantabria Contents Introduction Multiplexing,
More informationOptimum Transmission Scheme for a MISO Wireless System with Partial Channel Knowledge and Infinite K factor
Optimum Transmission Scheme for a MISO Wireless System with Partial Channel Knowledge and Infinite K factor Mai Vu, Arogyaswami Paulraj Information Systems Laboratory, Department of Electrical Engineering
More informationVector Channel Capacity with Quantized Feedback
Vector Channel Capacity with Quantized Feedback Sudhir Srinivasa and Syed Ali Jafar Electrical Engineering and Computer Science University of California Irvine, Irvine, CA 9697-65 Email: syed@ece.uci.edu,
More informationMULTI-INPUT multi-output (MIMO) channels, usually
3086 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 57, NO. 8, AUGUST 2009 Worst-Case Robust MIMO Transmission With Imperfect Channel Knowledge Jiaheng Wang, Student Member, IEEE, and Daniel P. Palomar,
More informationMultiple Antennas for MIMO Communications - Basic Theory
Multiple Antennas for MIMO Communications - Basic Theory 1 Introduction The multiple-input multiple-output (MIMO) technology (Fig. 1) is a breakthrough in wireless communication system design. It uses
More informationOn the Capacity of Fading MIMO Broadcast Channels with Imperfect Transmitter Side-Information
To be presented at the 43rd Annual Allerton Conference on Communication, Control, and Computing, September 8 30, 005. (Invited Paper) DRAFT On the Capacity of Fading MIMO Broadcast Channels with Imperfect
More informationAchievable Outage Rate Regions for the MISO Interference Channel
Achievable Outage Rate Regions for the MISO Interference Channel Johannes Lindblom, Eleftherios Karipidis and Erik G. Larsson Linköping University Post Print N.B.: When citing this work, cite the original
More informationWideband Fading Channel Capacity with Training and Partial Feedback
Wideband Fading Channel Capacity with Training and Partial Feedback Manish Agarwal, Michael L. Honig ECE Department, Northwestern University 145 Sheridan Road, Evanston, IL 6008 USA {m-agarwal,mh}@northwestern.edu
More informationWE study the capacity of peak-power limited, single-antenna,
1158 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 56, NO. 3, MARCH 2010 Gaussian Fading Is the Worst Fading Tobias Koch, Member, IEEE, and Amos Lapidoth, Fellow, IEEE Abstract The capacity of peak-power
More informationAn Uplink-Downlink Duality for Cloud Radio Access Network
An Uplin-Downlin Duality for Cloud Radio Access Networ Liang Liu, Prati Patil, and Wei Yu Department of Electrical and Computer Engineering University of Toronto, Toronto, ON, 5S 3G4, Canada Emails: lianguotliu@utorontoca,
More informationUniform Power Allocation in MIMO Channels: A Game-Theoretic Approach
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 49, NO. 7, JULY 2003 1707 Uniform Power Allocation in MIMO Channels: A Game-Theoretic Approach Daniel Pérez Palomar, Student Member, IEEE, John M. Cioffi,
More information1402 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 25, NO. 7, SEPTEMBER 2007
40 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 5, NO. 7, SEPTEMBER 007 Optimum Power Allocation for Single-User MIMO and Multi-User MIMO-MAC with Partial CSI Alkan Soysal, Student Member, IEEE,
More informationErgodic Capacity, Capacity Distribution and Outage Capacity of MIMO Time-Varying and Frequency-Selective Rayleigh Fading Channels
Ergodic Capacity, Capacity Distribution and Outage Capacity of MIMO Time-Varying and Frequency-Selective Rayleigh Fading Channels Chengshan Xiao and Yahong R. Zheng Department of Electrical & Computer
More informationWIRELESS networking constitutes an important component
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 51, NO. 1, JANUARY 2005 29 On the Capacity of MIMO Relay Channels Bo Wang, Student Member, IEEE, Junshan Zhang, Member, IEEE, and Anders Høst-Madsen, Senior
More informationGame Theoretic Solutions for Precoding Strategies over the Interference Channel
Game Theoretic Solutions for Precoding Strategies over the Interference Channel Jie Gao, Sergiy A. Vorobyov, and Hai Jiang Department of Electrical & Computer Engineering, University of Alberta, Canada
More information5032 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 55, NO. 11, NOVEMBER /$ IEEE
5032 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 55, NO. 11, NOVEMBER 2009 On the Information Rate of MIMO Systems With Finite Rate Channel State Feedback Using Beamforming Power On/Off Strategy Wei
More informationSpatial and Temporal Power Allocation for MISO Systems with Delayed Feedback
Spatial and Temporal ower Allocation for MISO Systems with Delayed Feedback Venkata Sreekanta Annapureddy and Srikrishna Bhashyam Department of Electrical Engineering Indian Institute of Technology Madras
More informationDegrees-of-Freedom Robust Transmission for the K-user Distributed Broadcast Channel
/33 Degrees-of-Freedom Robust Transmission for the K-user Distributed Broadcast Channel Presented by Paul de Kerret Joint work with Antonio Bazco, Nicolas Gresset, and David Gesbert ESIT 2017 in Madrid,
More informationSecure Degrees of Freedom of the MIMO Multiple Access Wiretap Channel
Secure Degrees of Freedom of the MIMO Multiple Access Wiretap Channel Pritam Mukherjee Sennur Ulukus Department of Electrical and Computer Engineering University of Maryland, College Park, MD 074 pritamm@umd.edu
More informationDegrees of Freedom Region of the Gaussian MIMO Broadcast Channel with Common and Private Messages
Degrees of Freedom Region of the Gaussian MIMO Broadcast hannel with ommon and Private Messages Ersen Ekrem Sennur Ulukus Department of Electrical and omputer Engineering University of Maryland, ollege
More informationLinear Processing for the Downlink in Multiuser MIMO Systems with Multiple Data Streams
Linear Processing for the Downlin in Multiuser MIMO Systems with Multiple Data Streams Ali M. Khachan, Adam J. Tenenbaum and Raviraj S. Adve Dept. of Electrical and Computer Engineering, University of
More informationOptimal Data and Training Symbol Ratio for Communication over Uncertain Channels
Optimal Data and Training Symbol Ratio for Communication over Uncertain Channels Ather Gattami Ericsson Research Stockholm, Sweden Email: athergattami@ericssoncom arxiv:50502997v [csit] 2 May 205 Abstract
More informationChannel Capacity Estimation for MIMO Systems with Correlated Noise
Channel Capacity Estimation for MIMO Systems with Correlated Noise Snezana Krusevac RSISE, The Australian National University National ICT Australia ACT 0200, Australia snezana.krusevac@rsise.anu.edu.au
More informationCapacity of Block Rayleigh Fading Channels Without CSI
Capacity of Block Rayleigh Fading Channels Without CSI Mainak Chowdhury and Andrea Goldsmith, Fellow, IEEE Department of Electrical Engineering, Stanford University, USA Email: mainakch@stanford.edu, andrea@wsl.stanford.edu
More informationOn the Required Accuracy of Transmitter Channel State Information in Multiple Antenna Broadcast Channels
On the Required Accuracy of Transmitter Channel State Information in Multiple Antenna Broadcast Channels Giuseppe Caire University of Southern California Los Angeles, CA, USA Email: caire@usc.edu Nihar
More informationDiversity-Multiplexing Tradeoff in MIMO Channels with Partial CSIT. ECE 559 Presentation Hoa Pham Dec 3, 2007
Diversity-Multiplexing Tradeoff in MIMO Channels with Partial CSIT ECE 559 Presentation Hoa Pham Dec 3, 2007 Introduction MIMO systems provide two types of gains Diversity Gain: each path from a transmitter
More informationto reprint/republish this material for advertising or promotional purposes
c 8 IEEE Personal use of this material is permitted However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution
More informationCHANNEL FEEDBACK QUANTIZATION METHODS FOR MISO AND MIMO SYSTEMS
CHANNEL FEEDBACK QUANTIZATION METHODS FOR MISO AND MIMO SYSTEMS June Chul Roh and Bhaskar D Rao Department of Electrical and Computer Engineering University of California, San Diego La Jolla, CA 9293 47,
More informationInformation Theory for Wireless Communications, Part II:
Information Theory for Wireless Communications, Part II: Lecture 5: Multiuser Gaussian MIMO Multiple-Access Channel Instructor: Dr Saif K Mohammed Scribe: Johannes Lindblom In this lecture, we give the
More informationOn the Optimality of Beamformer Design for Zero-forcing DPC with QR Decomposition
IEEE ICC 2012 - Communications Theory On the Optimality of Beamformer Design for Zero-forcing DPC with QR Decomposition Le-Nam Tran, Maru Juntti, Mats Bengtsson, and Björn Ottersten Centre for Wireless
More informationA deterministic equivalent for the capacity analysis of correlated multi-user MIMO channels
A deterministic equivalent for the capacity analysis of correlated multi-user MIMO channels Romain Couillet,, Mérouane Debbah, Jac Silverstein Abstract This paper provides the analysis of capacity expressions
More informationOptimization of Multiuser MIMO Networks with Interference
Optimization of Multiuser MIMO Networks with Interference Jia Liu, Y. Thomas Hou, Yi Shi, and Hanif D. Sherali Department of Electrical and Computer Engineering Department of Industrial and Systems Engineering
More informationOptimal Power Control in Decentralized Gaussian Multiple Access Channels
1 Optimal Power Control in Decentralized Gaussian Multiple Access Channels Kamal Singh Department of Electrical Engineering Indian Institute of Technology Bombay. arxiv:1711.08272v1 [eess.sp] 21 Nov 2017
More informationWeighted Sum Rate Optimization for Cognitive Radio MIMO Broadcast Channels
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS (SUBMITTED) Weighted Sum Rate Optimization for Cognitive Radio MIMO Broadcast Channels Lan Zhang, Yan Xin, and Ying-Chang Liang Abstract In this paper, we consider
More informationNash Bargaining in Beamforming Games with Quantized CSI in Two-user Interference Channels
Nash Bargaining in Beamforming Games with Quantized CSI in Two-user Interference Channels Jung Hoon Lee and Huaiyu Dai Department of Electrical and Computer Engineering, North Carolina State University,
More informationPilot Optimization and Channel Estimation for Multiuser Massive MIMO Systems
1 Pilot Optimization and Channel Estimation for Multiuser Massive MIMO Systems Tadilo Endeshaw Bogale and Long Bao Le Institute National de la Recherche Scientifique (INRS) Université de Québec, Montréal,
More informationAsymptotically Optimal Power Allocation for Massive MIMO Uplink
Asymptotically Optimal Power Allocation for Massive MIMO Uplin Amin Khansefid and Hlaing Minn Dept. of EE, University of Texas at Dallas, Richardson, TX, USA. Abstract This paper considers massive MIMO
More informationThroughput analysis for MIMO systems in the high SNR regime
ISIT 2006, Seattle, USA, July 9-4, 2006 Throughput analysis for MIMO systems in the high SNR regime Narayan Prasad and Mahesh K. Varanasi Electrical & Computer Engineering Department University of Colorado,
More informationSum-Power Iterative Watefilling Algorithm
Sum-Power Iterative Watefilling Algorithm Daniel P. Palomar Hong Kong University of Science and Technolgy (HKUST) ELEC547 - Convex Optimization Fall 2009-10, HKUST, Hong Kong November 11, 2009 Outline
More informationMULTIPLE-INPUT Multiple-Output (MIMO) systems
488 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 2, FEBRUARY 2008 On the Capacity of Multiuser MIMO Networks with Interference Jia Liu, Student Member, IEEE, Y. Thomas Hou, Senior Member,
More informationONE of the key motivations for the use of multiple antennas
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL 57, NO 7, JULY 2011 4123 On the Ergodic Capacity of Correlated Rician Fading MIMO Channels With Interference Giorgio Taricco, Fellow, IEEE, and Erwin Riegler,
More informationCapacity Bounds of Downlink Network MIMO Systems with Inter-Cluster Interference
Capacity Bounds of Downlink Network MIMO Systems with Inter-Cluster Interference Zhiyuan Jiang, Sheng Zhou, Zhisheng Niu Tsinghua National Laboratory for Information Science and Technology Department of
More informationCapacity Region of the Two-Way Multi-Antenna Relay Channel with Analog Tx-Rx Beamforming
Capacity Region of the Two-Way Multi-Antenna Relay Channel with Analog Tx-Rx Beamforming Authors: Christian Lameiro, Alfredo Nazábal, Fouad Gholam, Javier Vía and Ignacio Santamaría University of Cantabria,
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 informationUser Selection Criteria for Multiuser Systems With Optimal and Suboptimal LR Based Detectors REFERENCES. Jinho Choi and Fumiyuki Adachi
IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 58, NO. 10, OCTOBER 2010 5463 REFERENCES [1] I. E. Telatar, Capacity of multi-antenna Gaussian channels, Eur. Trans. Telecommun., vol. 10, pp. 585 595, Nov.
More informationOn the Capacity of the Multiple Antenna Broadcast Channel
DIMACS Series in Discrete Mathematics and Theoretical Computer Science On the Capacity of the Multiple Antenna Broadcast Channel David Tse and Pramod Viswanath Abstract. The capacity region of the multiple
More informationMinimum Mean Squared Error Interference Alignment
Minimum Mean Squared Error Interference Alignment David A. Schmidt, Changxin Shi, Randall A. Berry, Michael L. Honig and Wolfgang Utschick Associate Institute for Signal Processing Technische Universität
More informationOptimal Power Allocation for Cognitive Radio under Primary User s Outage Loss Constraint
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 29 proceedings Optimal Power Allocation for Cognitive Radio
More informationASPECTS OF FAVORABLE PROPAGATION IN MASSIVE MIMO Hien Quoc Ngo, Erik G. Larsson, Thomas L. Marzetta
ASPECTS OF FAVORABLE PROPAGATION IN MASSIVE MIMO ien Quoc Ngo, Eri G. Larsson, Thomas L. Marzetta Department of Electrical Engineering (ISY), Linöping University, 58 83 Linöping, Sweden Bell Laboratories,
More informationPROMPTED by recent results suggesting possible extraordinary
1102 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 3, MAY 2005 On the Capacity of Multiple-Antenna Systems in Rician Fading Sudharman K. Jayaweera, Member, IEEE, and H. Vincent Poor, Fellow,
More informationOVER the past ten years, research (see the references in
766 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 54, NO. 2, FEBRUARY 2006 Duplex Distortion Models for Limited Feedback MIMO Communication David J. Love, Member, IEEE Abstract The use of limited feedback
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 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 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 informationOn the Capacity of MIMO Rician Broadcast Channels
On the Capacity of IO Rician Broadcast Channels Alireza Bayesteh Email: alireza@shannon2.uwaterloo.ca Kamyar oshksar Email: kmoshksa@shannon2.uwaterloo.ca Amir K. Khani Email: khani@shannon2.uwaterloo.ca
More informationSum-Rate Capacity of Poisson MIMO Multiple-Access Channels
1 Sum-Rate Capacity of Poisson MIMO Multiple-Access Channels Ain-ul-Aisha, Lifeng Lai, Yingbin Liang and Shlomo Shamai (Shitz Abstract In this paper, we analyze the sum-rate capacity of two-user Poisson
More informationVECTOR QUANTIZATION TECHNIQUES FOR MULTIPLE-ANTENNA CHANNEL INFORMATION FEEDBACK
VECTOR QUANTIZATION TECHNIQUES FOR MULTIPLE-ANTENNA CHANNEL INFORMATION FEEDBACK June Chul Roh and Bhaskar D. Rao Department of Electrical and Computer Engineering University of California, San Diego La
More informationInformation Theory Meets Game Theory on The Interference Channel
Information Theory Meets Game Theory on The Interference Channel Randall A. Berry Dept. of EECS Northwestern University e-mail: rberry@eecs.northwestern.edu David N. C. Tse Wireless Foundations University
More informationCooperative Interference Alignment for the Multiple Access Channel
1 Cooperative Interference Alignment for the Multiple Access Channel Theodoros Tsiligkaridis, Member, IEEE Abstract Interference alignment (IA) has emerged as a promising technique for the interference
More informationMutual Information and Eigenvalue Distribution of MIMO Ricean Channels
International Symposium on Informatioheory and its Applications, ISITA24 Parma, Italy, October 1 13, 24 Mutual Information and Eigenvalue Distribution of MIMO Ricean Channels Giuseppa ALFANO 1, Angel LOZANO
More informationQuantifying the Performance Gain of Direction Feedback in a MISO System
Quantifying the Performance Gain of Direction Feedback in a ISO System Shengli Zhou, Jinhong Wu, Zhengdao Wang 3, and ilos Doroslovacki Dept. of Electrical and Computer Engineering, University of Connecticut
More informationCapacity Analysis of MIMO Systems with Unknown Channel State Information
Capacity Analysis of MIMO Systems with Unknown Channel State Information Jun Zheng an Bhaskar D. Rao Dept. of Electrical an Computer Engineering University of California at San Diego e-mail: juzheng@ucs.eu,
More information