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...que for arbitrary SNR. Closed-form analytical solution is not feasible due to the complexity of the problem11 . Since the problem is convex, efficient numerical algorithms can be employed to solve it =-=[9]-=-. At high SNR mode, an accurate approximate closed-form solution can be obtained using the Newton-Raphson method. As in the case of BLER-based optimization, the 1st step BER has the dominant effect on...

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...the average conditional error rate at step i, which is the same as the average error rate with (n−m+ i)-th order maximum ratio combining (MRC), and is known in closed form for many modulation formats =-=[18]-=-. Specifically, for BPSK modulation, where P ei = P MRC (n−m+i) (αiγ0) = = [ ]n−m+i 1−μi 2 n−m+i−1 ∑ μi = √ αiγ0 k=0 1+αiγ0 C k n−m+i−1+k , C k n = [ ]k 1+μi 2 n! k!(n − k)! , γ0 =1/σ2 0 and αiγ0 are ...

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...,α) /∂α < 0 (49) This property is supported by the results in [6], [8], and also by extensive results in the literature on the error rate performance of diversity systems with co-channel interference =-=[10]-=--[13] 15 , since the error propagation in V-BLAST effectively “creates” co-channel interference and thus it is similar to diversity combining with interference. Note that since all the Tx powers are i...

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...tion for x: m∑ (4γ0) − i=1 ci = n−m+i n−m+i+1 aixci = m, (n +1)! (n − m +1)!(n − m + i +1) (A3)KOSTINA and LOYKA: ON OPTIMUM POWER ALLOCATION FOR THE V-BLAST 1011 Following the Newton-Raphson method =-=[17]-=-, the zero-order approximate solution to (A3) is found when all only the leading term (i =1)is kept in (A3), x0 = c √ 1 m (4γ0) n−m+1 n−m+2 /a1 (A4) First-order approximate solution can be written as ...

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...is a simpler design of a power amplifier. Note, however, that all the power allocation algorithms discussed in this paper are compatible with 2G and 3G systems, which employ dynamic power control [20]=-=[21]-=-. The proposed algorithms can also accommodate a number of fixed (discrete) power levels, which are used in 2G and 3G systems instead of continuous power allocation, because of algorithms’ robustness,...

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...(a) and 6(b), both gains are close to each other at a practical SNR range. The SNR gain of the optimum power allocation is almost the same, at high SNR, as that of the optimal ordering procedure (see =-=[7]-=- for details). The computational complexity, however, of the former is much less than that of the latter. Hence, the average power optimization can be used instead of the optimal ordering with roughly...

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...rk, by properly re-defining A. 5 While [6] considers the QR-based V-BLAST, it can be shown that its performance is identical to the regular (zero-forcing successive interference cancellation) V-BLAST =-=[14]-=-, [8].KOSTINA and LOYKA: ON OPTIMUM POWER ALLOCATION FOR THE V-BLAST 1001 as [6]-[8], PB =1− m∏ (1 − Pei) (2) k=1 where Pei = Pe (γi) is the instantaneous, i.e. for given channel realization, conditi...

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...or some applications. Since the successive interference cancellation is used, lower detection steps have on average a smaller SNR and thus produce more errors, which further propagate to higher steps =-=[6]-=-, [8] so that the overall error performance may be not satisfactory, especially if no coding is used. A popular approach to improve the error performance of the V-BLAST algorithm is to decrease the er...

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... 2008 IEEE find the transmit (Tx) power allocation that minimizes the instantaneous (i.e. for given channel realization) total error rate (TBER) 2 of the V-BLAST, with or without the optimal ordering =-=[3]-=--[5]. The approximate solutions for the instantaneous Tx power allocation have also been found [3]-[5], based on various approximations. In [2], the instantaneous BLER 2 (rather than the TBER) is cons...

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...me applications. Since the successive interference cancellation is used, lower detection steps have on average a smaller SNR and thus produce more errors, which further propagate to higher steps [6], =-=[8]-=- so that the overall error performance may be not satisfactory, especially if no coding is used. A popular approach to improve the error performance of the V-BLAST algorithm is to decrease the error r...

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...o, Canada, K1N 6N5 (e-mail: sergey.loyka@ieee.org). Digital Object Identifier 10.1109/TCOMM.2008.060517. 1 A different approach to reduce the effect of error propagation has been recently proposed in =-=[22]-=-. 0090-6778/08$25.00 c○ 2008 IEEE find the transmit (Tx) power allocation that minimizes the instantaneous (i.e. for given channel realization) total error rate (TBER) 2 of the V-BLAST, with or withou...

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...exhibits only a minor loss in performance over the practical SNR range. Index Terms—Multi-antenna (MIMO) system, V-BLAST, power allocation, performance analysis. I. INTRODUCTION THE V-BLAST algorithm =-=[1]-=- has attracted in recent years significant attention as a signal processing strategy in the MIMO receiver due to its relative simplicity and also the ability to achieve, under certain conditions, the ...

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...n as well, by noting that Q( √ γ) is a convex function. We note that this result also extends, in a non-trivial way, to any 1-D or 2-D constellation, and also to some multi-dimensional constellations =-=[15]-=-.KOSTINA and LOYKA: ON OPTIMUM POWER ALLOCATION FOR THE V-BLAST 1003 technique for constrained optimization with the following Lagrangian9 , (∑m ) L (α) =P B (α)+λ , (16) the optimum α are found from...

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...i.e. almost all the power goes to the 1st Tx as γ0 →∞,and α opt 1 is quite close to m for finite but large γ0. Referring to 9similar approach to optimization of power allocation has been developed in =-=[19]-=-. 10strictly speaking, an additional constraint αi ≥ 0, i =1...m, is required. However, since our solutions always satisfy it, we do not include it explicitly. (13), this is explained by the fact that...

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...) 2 of the V-BLAST, with or without the optimal ordering [3]-[5]. The approximate solutions for the instantaneous Tx power allocation have also been found [3]-[5], based on various approximations. In =-=[2]-=-, the instantaneous BLER 2 (rather than the TBER) is considered as an optimization criterion, and the optimum Tx power allocation is found numerically for the V-BLAST with two transmitters. Although t...

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...∂α < 0 (49) This property is supported by the results in [6], [8], and also by extensive results in the literature on the error rate performance of diversity systems with co-channel interference [10]-=-=[13]-=- 15 , since the error propagation in V-BLAST effectively “creates” co-channel interference and thus it is similar to diversity combining with interference. Note that since all the Tx powers are increa...

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...considered as an alternative to the optimal ordering, and (ii) the optimal ordering presents serious difficulties for analytical performance evaluation, especially when no approximations are used [8],=-=[16]-=-. Similar approach has been used in [6], where the optimum power and rate allocation technique, based on minimizing the average error rate for fixed total data rate, has been proposed. However, only n...

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...8 IEEE find the transmit (Tx) power allocation that minimizes the instantaneous (i.e. for given channel realization) total error rate (TBER) 2 of the V-BLAST, with or without the optimal ordering [3]-=-=[5]-=-. The approximate solutions for the instantaneous Tx power allocation have also been found [3]-[5], based on various approximations. In [2], the instantaneous BLER 2 (rather than the TBER) is consider...

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...ion is a simpler design of a power amplifier. Note, however, that all the power allocation algorithms discussed in this paper are compatible with 2G and 3G systems, which employ dynamic power control =-=[20]-=-[21]. The proposed algorithms can also accommodate a number of fixed (discrete) power levels, which are used in 2G and 3G systems instead of continuous power allocation, because of algorithms’ robustn...