各式多天線與多用戶中聯合估計與檢測之容量分析

Abstract

新的無線通訊系統無不朝向更高的傳輸速率發展，以支援行動無線寬頻網際網 路應用，形成了無線傳輸技術迅速發展的主要推力。目前大多數的系統在通道狀 態的量測技術上都是利用「訓練序列」（training sequences）的輔助；而且傳輸資 料的檢測（detection） 的執行都是基於對通道狀態資訊完全瞭解的假設下，而這 樣的方法在非常高速率的傳輸系統中就不太合適，因為過多的訓練序列會造成頻 寬上的浪費。因此，本項計畫將針對聯合估計與檢測（joint estimation and detection）的機制進行研究。 除了原來就具備有更高傳輸速率的優勢外，我們還能用公平的分析方式來探討 系統在理論上的上限，也就是所謂的通道容量（channel capacity）。此處的「公 平」所代表的是在容量分析時一併考慮到了系統估計（estimation）的部分，也就 是說，它考慮到接收器會採取任意型式的方式獲得所需的通道狀態資訊（當然也 包括採用訓練序列的方式！）。而利用此種聯合估計與檢測機制所獲得的系統容 量即為非同調容量 ( non-coherent capacity ) 近年來在衰減通道（fading channels）下的非同調容量研究中發現了一些出乎 意料的結果，這些研究顯示，在高訊雜比（signal-to-noise ratio，SNR）時，非同調 衰減通道的功率效率會變得非常低，因為每多1位元的傳輸速率就會增加所需功率 的平方，此結果與完全瞭解通道資訊條件下的系統容量結果成完全的對比。因此 關鍵之處就在於深入瞭解這些性質並且能估計低效率的發生條件與狀態。另一方 面我們發現，在高訊雜比狀態下通道容量的漸進展開式（asymptotic expansion） 之中的第二項，此處定義為衰減數量（fading number)，可以作為高功率效率低訊 雜比與低功率效率高訊雜比之間界線指標。 根據上述基礎，本項三年計畫首先將集中在分析多輸入多輸出（MIMO）的容 量在非同調的衰減通道，而此目標為推導出衰減數量在記憶型（memory）下多輸 入單輸出 （MISO）衰減通道與無記憶型（memoryless）多輸入多輸出（MIMO） 衰減通道，和一般記憶型（memory）多輸入多輸出（MIMO）衰減通道。 第二個部分是將分析的範圍延伸到多用戶的衰減通道和其它普遍化的層面。而 主要目的還是推導出衰減數量。 最後，本計畫所獲得的知識、技術和工具將有助於發展通訊上面的其它議 題，例如：寬頻衰減通道、衰減中繼通道、還有衰減通道在迴授、衰減網路和光 學無線傳輸等研究。

The demand of new wireless communication systems with much higher data rates that allow, e.g., mobile wireless broadband Internet connections inspires a quick advance in wireless transmission technology. So far most systems rely on an approach where the channel state is measured with the help of regularly transmitted training sequences. The detection of the transmitted data is then done under the assumption of perfect knowledge of the channel state. This approach will not be sufficient anymore for very high data rate systems since the loss of bandwidth due to the training sequences is too large. Therefore, the research interest on joint estimation and detection schemes has been increased considerably. Apart from potentially higher data rates a further advantage of such a system is that it allows for a fair analysis of the theoretical upper limit, the so-called channel capacity. 「Fair」 is used here in the sense that the capacity analysis does not ignore the estimation part of the system, i.e., it takes into account the need of the receiver to gain some knowledge about the channel state without restricting it to assume any particular form (particularly, this approach does also include the approach with training sequences!). The capacity of such a joint estimation and detection scheme is often also known as non-coherent capacity. Recent studies investigating the non-coherent capacity of fading channels have shown very unexpected results. In stark contrast to the capacity with perfect chan- nel knowledge at the receiver, it has been shown that non-coherent fading channels become very power-inefficient in the high signal-to-noise (SNR) regime in the sense that increasing the transmission rate by an additional bit requires squaring the neces- sary power. Since transmission in such a regime will be highly inefficient, it is crucial to better understand this behavior and to be able to give an estimation as to where the inefficient regime starts. One parameter that provides a good approximation to such a threshold between the power-efficient low-SNR and the power-inefficient high-SNR regime is the so-called fading number which is defined as the second term in the high-SNR asymptotic expansion of channel capacity. Based on this insight, this three-years project will focus in a first step on the anal- ysis of the non-coherent capacity of multiple-input multiple-output fading channels. The goal is to derive the fading number for multiple-input single-output (MISO) fading channels with memory, memoryless multiple-input multiple-output (MIMO) fading channels and general MIMO fading channels with memory. In a second step the analysis will be extended to multiple-user fading channels and various other generalizations thereof. Again the goal is to derive the fading number. Finally, the gained knowledge, techniques, and tools will be used to investigate other communication scenarios, like, e.g., broadcast fading channels, fading relay channels, fading channels that include some feedback, fading networks, and optical wireless communication.