位元交錯編碼調變合作中繼網路之效能分析與功率分配

Abstract

位元交錯編碼調變合作中繼網路(BICM-coded cooperative relaying network)是下世代無線通訊系統所使用的關鍵技術；它承襲了位元交錯編碼調變(bit-interleaved coded modulation, BICM)的頻寬與功率的高使用效率，並得益於合作式傳輸的使用，使得它可以在不需要實際裝置多天線的前提下，即能達到空間分集(space diversity)的效果。在本論文中，我們將探討此系統的效能分析與功率分配。 位元交錯編碼調變合作中繼網路的效能分析至今仍尚未有完整的探討，特別是針對選擇性解碼-轉傳(Selection decode-and-forward，S-DF)技術。S-DF被認為是一實際的轉傳方式，因為它在可行的複雜度下，能提供比固定式解碼轉傳(Fixed DF)更好的效能。在現有的文獻中已有S-DF的相關分析結果，但皆僅侷限於無通道編碼的系統，並且皆採用一種以符元為單位的轉傳策略。在此策略中，各符元是分別地被檢測，而僅有正確的符元才允許被轉傳。實際上，此策略可能不適用於現今真實的系統上，因為它與循環冗餘校驗(cyclic redundancy check)本身特性有所矛盾，況且又需大量額外的信令耗損(signaling overhead)。本論文考慮的是一種以封包為單位的轉傳策略；包含了兩種S-DF方式：S-DF/RT(S-DF with source retransmission) 與S-DF/Idle (S-DF with source idle) (依訊源端(source)是否在中繼站解碼失敗時重傳封包來做區分)。在快速衰退(fast-fading)和區塊衰退(block-fading)的Nakagami-m通道下，本論文提出了在目的端(destination)的位元錯誤率(bit-error-rate，BER)分析，並且推導了該網路的分集階數(diversity order)，同時，也提供了模擬的結果來證實：在不同的調變、中繼站數量、及通道狀況下，所提出的分析方法的準確性。 在功率分配的部分，本論文考慮了四種的合作中繼模式：放大-轉傳(amplify-and-forward，AF)、S-DF/RT、S-DF/Idle與S-DF/AF，其中S-DF/AF代表中繼站在解碼失敗時，切換成以AF的模式進行轉傳。本論文的目標為：根據完美的通道狀態資訊(channel state information)，透過功率分配來最小化目的端的BER。在AF模式中，本論文提出了一近似的BER，並證明其為等效通道(equivalent channel)之嚴格遞減函數，因而可將此等效通道視為成本函數(cost function)來進行最佳化。在S-DF模式下，則提出了PA-ABER與PA-MGEC兩種功率分配的方式。PA-ABER是採用近似的BER做為成本函數，經由證明得知此成本函數對於S-DF下的任一種中繼模式而言，皆是convex函數，因此可使用gradient method來對其進行最佳化。本論文又提出了PA-MGEC來進一步減化計算的複雜度，它將原本在PA-ABER的最佳化問題轉換成了一個max-min的問題，然後採用了最小廣義等效通道 (minimum generalized equivalent channel，MGEC)為其成本函數。對於不同的S-DF模式，我們皆提出了PA-MGEC下的特定解法。此外，本論文亦證明了PA-ABER與PA-MGEC皆可以被應用在解碼-重映射-轉傳(decode-remap-and-forward，DRF)的合作中繼系統上。其中DRF代表中繼站被允許使用與source不同的星座映射(constellation mapping)方式，來得到重映射的好處。本論文提供了數值的結果來證實，所提出的方法在效能上的確大幅地超越了等增益功率分配(equal gain power allocation)。

BICM (bit-interelaved coded modulation)-coded cooperative relaying network is one of the key technologies for the next-generation wireless communication systems. It inherits the bandwidth and power efficiency from BICM and also benefits from cooperative transmission for gaining space diversity yet without using multiple physical antennas. This dissertation investigates such a system from the aspects of performance analysis and power allocation. The performance analysis of BICM-coded cooperative relaying network has not yet been fully explored, especially for selection decode-and-forward (S-DF) which has been regarded as a promising scheme that provides better performance over fixed DF with practical complexities. In fact, existing works are limited to un-coded S-DF with a symbol-by-symbol forwarding strategy, in which each symbol is detected separately, and only the correct symbols are forwarded. Unfortunately, this strategy may not be applicable to nowadays real systems due to the limitation of cyclic redundancy check and the requirement of additional signaling overhead. This dissertation is the first work that considers BICM-coded cooperative relaying network with a packet-by-packet forwarding strategy. In addition, two types of S-DF modes are investigated: S-DF/RT and S-DF/Idle, depending on whether or not the source re-transmits the packet again when the relay fails to decode. The analysis of bit-error-rate (BER) at the destination and derivation of the diversity orders of the network are proposed for both fast-fading and block-fading Nakagami-m channels. Simulation results are given to show the effectiveness of our analyses in different modulations, number of relays and channel condi-tions. This dissertation also provides a comprehensive investigation on transmit power allocation including 4 relaying modes, namely, amplify-and-forward (AF), S-DF/Idle, S-DF/RT and S-DF/AF in which the relay uses AF upon decoding failure. Based on perfect channel state information, the target is to allocate power to minimize the BER at the destination. To avoid the cumbersome (if not impossible) evaluation of the exact BER and an inefficient exhaustive search of the optimal power, this dissertation provides, for individual modes, a simplified cost function which can be optimized efficiently through existing algorithms. For AF, it is shown that the approximate BER monotonically decreases with the equivalent channel, which is then adopted as the cost function for optimization. For S-DF, two power allocation methods are pro-posed. The first, called PA-ABER, employs an approximate BER as a cost function, which is then proved to be convex for each relaying mode and then optimized through the gradient method. To further reduce the computation complexity, the second method, called PA-MGEC, first transforms PA-ABER to a max-min problem, and the cost function is named minimum generalized equivalent channel (MGEC) which can be optimized with existing algorithms for the 3 relaying schemes. Furthermore, this dissertation shows that these two methods are applicable to the network with decode-remap-and-forward (DRF) relays, which are allowed to choose different constellation mappings from that of source so as to obtain a remapping gain. Numerical results show that both of the proposed methods outperform the equal gain power allocation by large margins with or without remapping.