多天線多通道多模多速率無線網狀網路之設計與實作-子計畫二：M4 無線網狀網路之存取控制協定及繞徑設計(I)

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(1)行政院國家科學委員會專題研究計畫. 期中進度報告. 子計畫二：M4 無線網狀網路之存取控制協定及繞徑設計 (1/3). 計畫類別：整合型計畫計畫編號： NSC94-2219-E-009-005執行期間： 94 年 08 月 01 日至 95 年 07 月 31 日執行單位：國立交通大學資訊科學學系(所). 計畫主持人：簡榮宏計畫參與人員：鄭安凱、李奇育、張瑋倫、詹雯甄. 報告類型：完整報告報告附件：出席國際會議研究心得報告及發表論文處理方式：本計畫可公開查詢. 中. 華民國 95 年 7 月 24 日.

(2) 行政院國家科學委員會專題研究計畫期末報告多天線多模多通道多速率無線網狀路—子計劃二：M4無線網狀網路之存取控制協定及繞徑設計（1/3） Media Access Control and Routing Protocols for M4 Mesh Networks 計畫編號：NSC 94－2219－E－009－005 執行期限：94 年 8 月 1 日至 95 年 7 月 31 日主持人：簡榮宏國立交通大學資訊工程系計畫參與人員：鄭安凱、李奇育、張瑋倫、詹雯甄國立交通大學資訊工程系中文摘要無線網狀網路技術提升了無線網路存取範圍提升，而多重通道多重天線架構更可大幅增進網路效能。在本年度的計畫中，我們針對無線網路架構設計適用於多通道多天線環境的存取控制協定，使網路節點可於鏈結層中順利的傳遞訊息而不會造成過多的碰撞。為了進一步提升網路輸出，我們為通道使用方式進行最佳化的配置，設計可於效能和品質之間達到平衡的混合式通道指定演算法。此外我們以 VoIP 為應用，對 IEEE 802.11e 標準提出了跨層次的品質保證控制架構，使得 VoIP 有效地應用於此網路。關鍵詞：無線網狀網路、存取控制，通道指定、服務品質保證，VoIP. Abstract. Wireless mesh network extends the wireless network’s coverage. By equipping mesh nodes with multiple antennas, they can further utilize the benefits from multiple channels. In this project, we have investigated a media access control protocol for this multi-channel multi-antenna environment. It can avoid considerable collision at link layer. To further increasing the network throughput, we address the optimization issue and proposed approximating algorithms. Finally, the application of VoIP has been applied to this network. To achieve better performance, we designed a cross-layer control scheme for M4 mesh networks with IEEE 802.11e interfaces.. Keywords: Wireless Mesh Network, Media Access Control, Channel Assignment, QoS, VoIP I.

(3) 目錄一、前言……………………………………………………………………1 二、研究目的………………………………………………………………2 三、文獻探討………………………………………………………………4 四、研究方法………………………………………………………………6 五、結果與討論……………………………………………………………10 六、第二年工作計畫………………………………………………………12 六、參考文獻……………………………………………………………...13 附錄: 本年度本計畫衍生的論文附件一附件二附件三附件四. II.

(4) 一、前言近幾年，由於無線行動裝置的普及化以及對多媒體傳輸的需求，使得使無線寬頻技術的發展持續受到關注，而無線網狀網路(wireless mesh network)，則是預期將被整合進無線寬頻網路的重要技術之一。無線網狀網路是使用無線傳輸介面當網路主幹，因此不需要任何網路佈線等建設成本，有佈建快速及不受地形限制等優點，可將無線區域網路之涵蓋範圍快速的延伸至企業、校園以至於更大規模之無線都會網路 (wireless metropolitan networks)。雖然網路資源的存取變得便為便利，但在傳輸速率上仍然無法達到有線網路相同的水準，主要的原因就在於無線媒介的本質，無法將干擾隔絕於外，而正常的載波亦會影響鄰近節點的傳輸效能[1]，因此 IEEE802.11a/b/g 標準提供了多通道(multi-channels)的機制，使得鄰近的節點可透過非重疊的通道(non-overlapping)同時傳輸，避免彼此的干擾，進而提升整體網路的聚合頻寬(aggregated bandwidth)[2, 3]。這樣的技術，非常適用於節點間獨立運作的基礎架構型網路(infrastructure networks)[4]，但在隨意網路(ad hoc network)架構下，傳輸必需透過節點間相互的轉送(relay)方可達成，而相鄰的兩點亦需透過相同的通道方可收送，因此多重通道的使用必需在干擾程度(interference)與網路連接性(connectivity)上取得平衡[5]。而在無線網狀網路(wireless mesh network)架構中，網路更強調多點對多點(multipoint-to-multipoint) 同時傳輸的能力，因此每個節點都必需有能力協調來自四面八方的傳遞，而干擾模式與通道資源的利用也將變的更為複雜[6, 7]。無線網路透過半雙工的天線於特定頻道上收送載波，而為了在減低干擾的同時，維持網路的連通性，節點可裝配數個天線(multi-antenna)[8, 9, 10]，如圖一(a)所示，上下兩對節點以不同的頻道傳輸彼此干擾，但卻斷為兩個子網路，若每個節點皆裝配兩個天線，圖一(b)，則可維持所有節點的暢通，而每個節點的 throughput 也可因此而倍增[5]。 1. 1 3. 2. 2. 4. (a) (b) 圖一:多通道多天線. 此外在無線網路中，通道的位元錯誤率(bit error rate)會受到各種因素而變動，而且會隨著傳輸距離的增加而加劇[11, 12]，因此對鄰近來源端的節點，通常可以使用較高層級的變調機制(high level modulation scheme)來增加傳輸速率，反之則必需以較低層的變 III.

(5) 調機制來處雜訊率(single noise rate)而降低速率[13]，以 802.11b為例，會因傳輸距離的不同有不同的傳輸速率，如 10m, 30m和 100m的距離內最高速率分別為 11Mbps, 5.5Mbps, 和 2 Mbps三種 [14]。除了 802.11b外，尚有a, g等標準，在不同的頻帶上以不同的速率、相容性、延遲、耗電量等提供多重的傳輸模式[15]，而目前的技術以可將多重模式以單一晶片和相同規格的天線，結合於無線設備上[16,17]。結合上述之特性、優點及可行性，本計畫以多天線、多通道、多速率、多模(multi-antenna multi-channel multi-rate multi-mode, M4)作為無線網狀網路研究之基礎架構。本研究為總計畫「多天線多模多通道多速率無線網狀路」之第二子計畫，共為期三年，主要探討M4無線網狀網路之存取控制協定及繞徑設計。在第一年的進度中，我們針對無線網路架構設計適用於多通道多天線環境的存取控制協定(multi-channel multi-radio media access control )，使網路節點可於鏈結層(link layer)中順利的傳遞訊息而不會造成過多的碰撞(collision)。為了進一步提升網路輸出(throughput)，我們為通道使用方式進行最佳化的配置，設計可於效能和品質之間達到平衡的混合式通道指定演算法(hybrid channel assignment)。此外我們以VoIP為應用，對IEEE 802.11e標準提出了跨層次的品質保證控制架構(cross-layer QoS control scheme)，使得VoIP有效地應用於此網路。. 二、研究目的為達到上述目標，本子計畫今年度已進行下列三項研究議題: (1) 多通道多天線環境之存取控制協定 (Multi-channel Multi-radio Media Access Control ) 頻寬的共享需要載波偵測來避免碰撞，但無線網路的載波卻有距離上的限制，而造成隱藏節點的問題(hidden terminal problem)，因此 IEEE 802.11 MAC 協定利用分散式協調功能(distributed coordination function, DCF)中的 CTS/RTS 訊息交換，來達成虛擬載波偵測(virtual carrier sensing)的能力[18]。多通道的使用也是為了避免單一通道內的競爭，然而現有的分散式協調機制卻會在此環境下產生新的問題，稱作多重通道隱藏節點問題 (multi-channel hidden terminal problem)[19]，以圖二來加以說明:主機 A 送出 RTS 要求傳資料送至主機 B，而主機 B 回覆 CTS 並指定使用通道 2 進行通訊，但此時主機 C 正利通道 3 與主機 D 通訊而無法偵測到主機 B 已使用了通道 2，因此當主機 C 重新要求與主機 D 傳送時，主機 D 就有可能指定 C 選擇通道 2 而產生碰撞。目前主要的解決方法可分為(1)跳頻模式 [20, 21]和(2)資料通道與控制通道分離[8, 9, 10, 22]以及(3)時間切割 2.

(6) [1]三種方式來達成，本計畫將綜合上述方法，發展新的改進方法，解决多重通道隱藏節點問題，新方法的主要考量則在於避免浪費寬使用率以及減少控制資料的延遲。 A. B. C. D. RTS CTS(2). Channel 3 Time. Channel 2 RTS Collision. ACK. CTS(2). Channel 2. 圖二: 多通道隱藏節點問題. (2) 通道指定之最佳化演算法 (Optimization on Channel Assignment) 在網線網狀網路中，當兩個節點要進行傳輸時，收送的兩端就必需處在一個共同的通道(common channel)才能行進溝通，而通道選擇的也會顯著的影響整體網路的效能，因此我們必需對共同通道的協調方式以及通道的指定方式進行設計，目前已有許多方法被提出，而這些方法大致可分為兩類 (a) 靜態通道指定(Static Channel Assignment): 在這種方式下，每個介面都會被指定一個永久使用的通道。由於通道是固定的，每個節點都能在網路初始時就知道鄰近通道指定的狀況，而不需在傳輸前耗費額外的封包來協調出共同的通道，然而固定的通道同時也意味著缺乏調整的彈性，每個介面只能對擁有相同通道的鄰近介面(neighboring interfaces)進行溝通，而當此通道壅塞時也無法切換至其他負載較輕的通導; (b) 動態通道指定(Dynamic Channel Assignment): 此方法與靜態正好相反，對通道對使用擁有最高的彈性，介面可依週遭或整體網路的使用狀況動態的調整所屬的通道，但相對的需要一個共同通道的協調機制(coordination mechanism)，當通道切換頻繁時，此機制無可避免將造成大量頻寬的浪費。而我們探討的是一種混合通道指定(Hybrid Channel Assignment)方式，這種方式結合了靜態與動態的優點，不儘免除額外的協調機置，也同時擁有高度的調整彈性。我們的目標是對此通道指定方式設計最佳化以及近似的演算法，分析其理論上下界，並進一步以實測數據加以驗證。. (3) VoIP 於 IEEE 802.11e 之跨層次品質保證控制 (Cross-Layer Control Scheme for VoIP over 802.11e) 3.

(7) 從 VoIP 技術發展以來，由於撥打 VoIP 電話的花費比一般電話節省許多，VoIP 漸漸成為一種殺手級的應用(Killer Application)，受到人們廣為使用。再隨著無線網路愈來愈普及，利用無線網路的可移動性，未來的人們不用固定坐在電腦桌前使用 VoIP 電話，而是可以像現在的行動電話這樣隨處講 VoIP 電話，我們稱之 Voice over Wireless LAN(VoWLAN)。 VoIP 這種即時性軟體對於 QoS 需求較嚴格，像是對於傳輸延遲(delay)、封包遺失率(packet loss rate)、延遲變動量(jitter)都有它的限制上限，例如傳輸延遲就不能超過 150 毫秒，超過的話通話品質差到無法容忍。然而無線網路有著頻寬低(lower bandwidth)、頻道變動 (channel variation) 大這 2 種限制。因為無線網路的頻寬低，如果同時網路上有大量的資料在傳輸，就會影響到 VoIP 的通話品質。而頻道變動更是使得 VoIP 處在不穩定的狀態下，也無法保證它的品質。因此要在無線網路上使用 VoIP 的服務，就必須比有線網路付出更大的努力克服這 2 項問題。我們的研究就是針對這二個限制，找出良好的解決方法以提升 VoIP 在無線區域網路中的通話品質。. 三、文獻探討下列分別對這靜態、動態和混合三種通道指定方法探討相關的文獻: A. 靜態通道指定: 此方法是將某個頻道長時間分配給某個天線，為了可以同時使用多個頻道，每台主機必須配備和頻道數量一樣的天線，如此，將需要很高的硬體花費，這三篇文章[8][9][22]都是使用這個方法，不同的是如何決定在哪一個頻道做傳輸的方法， [8]以最近使用過的頻道為優先，若正在使用，則在閒置的頻道列中隨機選用一個，[9] 則是選用最低功率的頻道，而且是由傳送者所決定，不同於[9]，[22]一樣選用最低功率的頻道，但是由接收者所決定。使用這個頻道給予的方法，雖然可以完全解決上面所述的兩個問題，但硬體的花費太高是主要的缺點。 B. 動態通道指定: 此方法是動態的分配某個頻道給某個天線，因此如何解決讓每個相鄰的主機可以互相找到對方是一個困難的問題，在這類方法中，都是使用時間同步的機制來解決這個問題，而[21][19][23][24]都是屬於這類方法，並且都是只使用一個天線，在 [21]中，所有主機都有一個相同的頻道跳躍序列，而且必須隨著這個序列在同一時間作跳躍，當要傳輸封包之前，兩端必須實行接收端初始避免碰撞的交涉，然後留在目前的頻道做傳輸，其他的主機則隨著相同的序列繼續跳躍。[19]則是利用在 IEEE 802.11 節約能源模式中的 ATIM 窗戶，在此段時間裡傳輸控制封包，兩端交涉出要在那一個頻道上傳輸，在 ATIM 結束後，完成交涉的主機就切換到所決定的頻道做傳輸。[23]是將所 4.

(8) 有的頻道分成兩類，一個是屬於控制頻道，其他則是屬於資料頻道，要到資料頻道做傳輸前，必須要在控制頻道先做交涉，當兩端選定頻道後，就切換到新的頻道，而為了避免隱藏終端問題，所以做傳輸之前必須等待一段時間，更新自己記載頻道上目前的狀況。在[24]中，每台主機各自擁有一個頻道跳躍序列，但在某個時間縫可以相遇的到，並且每台主機了解鄰近各主機的跳躍序列，所以也可以調整自己的跳躍序列與接收端重疊，而迅速地與接收端作傳輸。以上這些方法雖然只使用一個天線，但在多跳躍的網路環境裡，要維持時間同步是非常困難的。 C.混合的: 此方法兼具靜態和動態的給予頻道，所以屬於此方法的文獻都具備兩個以上的天線，這類文獻主要可分為兩種方法，第一種[10][25]是獨立出一個頻道作為控制頻道，然後將此頻道給予一個專為傳送控制封包的天線，另一個天線則是在其他頻道之間互相轉換，當控制天線在控制頻道上決定了傳輸的頻道，傳輸天線則會切換到這個頻道做傳輸。[26][27]則是給予每台主機一個固定的頻道，若其他鄰近的主機想要與其他主機做傳輸，則會切換到他的固定頻道，所以不會有會面的問題產生，而[26]改變傳送封包的功率，[27]在切換到一個新的頻道時等待一段時間，來解決多頻道隱藏終端的問題，這個方法可以增加頻道和天線的利用率，但這方法還是有些缺點，所以我們的方法是根據[27]的基礎架構，然後加以改進，由實驗得知我們網路的表現比他的方法好。另一方面，IEEE 為了要提供支援服務品質(Quality of Service)的媒介存取控制協定 (Media Access Control Protocol)，成立了工作小組 E(Work Group E)去修訂 IEEE 802.11 媒介存取控制協定以增加支援 QoS 功能，IEEE 稱這個新的協定為 IEEE 802.11e 媒介存取控制協定[28]。這個部份已在 2005 年 11 月完成，現在 802.11e 已是 IEEE 的標準了。雖然藉由 802.11e 中的 EDCA 可有效給予不同種類的資料不同的優先權，然而簡單型的 802.11e 網路沒有使用機制對使用者做控管，會讓一些沒有申請 802.11e QoS 服務的使用者也使用到 802.11e 的服務(只要他有 802.11e 的無線網卡)，這對付費使用者是很不公平的。因此[29]這篇文章提出了一個基於策略(Policy-based)[33]的 802.11e 無線區域網路，在 802.11e 無線區域網路中加入一個伺服器—Wireless QoS Enhancer(WQE)。WQE 存放著使用者申請的服務等級契約(Service Level Agreement,SLA)，每當有一個新的資料流要通過無線基地台，無線基地台就會以一個客戶端(client)的角色向 WQE 詢問這個資料流是否有申請服務品質。如果有才會以 802.11e 的方法對這個資料流(flow)的封包設定存取類型(Acess Category)，否則就把它視為一般的資料流。但是這個架構有一個缺點，它的判斷是採取以資料流為單位的方式，這樣無線基地台要存的服務等級契約很多，對記憶體使用量限制高的無線基地台較不適合，所以我在後面會提出一個以行動工作站為 5.

(9) 單位的方法，可以大幅減少無線基地台要存的使用者資料。在參考論文[30]中提到 802.11e 無線區域網路為即時性(Real-time)應用程式(如 VoIP) 提供了比 802.11 無線區域網路更好的 QoS 功能。但是當某個無線基地台同時服務很多運行高優先權應用程式(如 VoIP)的行動工作站時，便無法保證達到預期的服務品質效果 [31]。特別是當其中某些行動工作站與無線基地台間的連結訊號弱或是受到干擾，就會對網路的效能及 VoIP 的通話品質產生不好的影響。這是因為當行動工作站與無線基地台之間的訊號變弱時，網卡會隨之自動選用資料傳輸速率較低的編碼方式來傳輸封包，希望藉此降低資料傳輸錯誤的機率。跟訊號強時所用高資料傳輸速率的編碼方式相比，傳輸同樣大小的封包，前者需要花費較久的時間，所以會粍費較多的網路資源。這對 VoIP 應用程式會有所影響，所以我們希望藉著加入可隨著網路狀況做調整的機制，來提升 VoIP 應用程式在 802.11e 無線網路中傳輸的通話品質。在參考論文[32]中提到，使用可調變的(Adaptive) Codec – AMR，可改善 VoIP 的品質，所以我們可以利用跨階層調(Cross-layer)的概念設計一個可調變的 VoIP 應用程式 (Adaptive VoIP Application)使它適用於環境多變的無線網路。. 四、研究方法在混合式通道指定法中，每個節點的介面可分為兩類，一類是靜態介面(Fixed Interface)，另一類是可轉換介面(Switchable interface)，當需要傳輸時，送端節點利用其可轉換介面進行傳送，而收端節點則利用其靜態介面進行接收，而所使用的通道則是靜態介可所決定。利用這個方法，節點並不需要在每一次的傳輸都先進行共同通道的協調，因為靜態介面所指定的通道是固定的，並不會雖時間而改變，因此只要在網路初始時廣播一次到其鄰近節點即可。由此可知此方法可免除大量的頻寬浪費，另一方面每個節點仍保有切換通道的彈性，只要利用其可轉換介面就可切換到所以鄰近靜態介面所指定的通道。如下例，紅色方塊為靜態介面，並固定於其所標示的通道上，而綠色為可轉換介面，在時間 t = 1 和 t = 2 時，所有的可轉介面都可直接切換到不同的通道，不需仍何協調機制。. 6.

(10) 圖三 :混合式通道指定法底下(1)和(2)的部分，我們分別為此混合式通定法提出存取控制協定，以及介面和通道配置最化的演算法: (1) 多通道多天線環境之存取控制協定 (Multi-channel Multi-radio Media Access Control ) 在[27]中，為了解決多頻道隱藏終端的問題，當可轉換介面切換通導後會原一段時間來更新 NAV。他們所利用的方法是等待一段最大封包的傳輸時間，然而此時間可能會過長而影響到整個網路的表現，所以我們利用碰撞的機率來計算出每台主機在每個頻道上需等待多少時間，而會產生碰撞主要是因為沒有接收到之前的控制封包，不知道鄰居的固定界面是否正在接收封包，所以我們以在頻道上鄰近的固定介面的個數，來計算出可能產生碰撞的機率，進而決定等待的時間。因為每次轉換頻道時需要耗費時間，所以我們給予每個頻道設立一個行列，用行列來決定轉換頻道的時間，而不是利用每個封包來決定轉換頻道的時機，如果每次相鄰的封包都必須在不同的頻道上傳送，那傳送封包的資源花費是非常高的，且沒有效率，而在我們的協定上，利用轉換至新的頻道時停留一段時間，傳送屬於此頻道的行列裡的封包，來減少轉換頻道所帶來的資源花費。. (2) 通道指定之最佳化演算法 (Optimization on Channel Assignment) 混合式通道指定包含兩大決策因素: A.介面種類選擇; B. 靜態介面通道指定。介面的種類選擇決定了網路的連通性(connectivity)，在實際的網路中每個介面可能有不同的傳輸半徑，因此若較大傳輸半徑的介面被選為靜態介面來進接收，則勢必會造成許多原本可以直接傳送的連通性，而一個節點的介面需有多少為靜態多少為可轉換，較多的可轉換介面可增加其傳送量，但相對的接收能力則會下降，反之亦然，因此因此介面種類的選擇同時需考量整體網路的拓撲和傳輸狀況。此外，介面種類的選擇也決定了主干擾 (Primary Interference)的程度，由於一個介面同時只能進行一個收或送，當一對介面進行收送時，所以與其任一端直接連結的介面皆無法對其在進行收送，如圖四，當 a→b 傳 7.

(11) 輸時，a→c、a→g、d→b、m→b、k→b 皆無法對 a 或 b 進行收送。另一方面，靜態介面通道的指定主要決定了次干擾(Second Interference)的程度，次干擾的產生是由於一塊區域面積內同時有多個傳輸使用相同的通道，這將造成彼此間的碰撞而降低網路的產出，如圖四，a→b、h→i、h→g、n→g、d→g 皆使用通道 2，因此同一時間內最只會有一對介面能成功傳輸。. 圖四: 混合式通道指定之主干擾及次干擾為了降低主干擾及次干擾所造成的影響而又能保有網路的連通性，我們必需對次兩決策因素進行最佳化的分析與設計。我們的目標是要使得每一個傳輸所可能造成平均的干擾最小化，如圖五，在此介面及通道配置下，平均每個傳輸會造成 6.36 個可能的干擾 (2+3+6+7+6+7+8+6+9+10+6+8 +7+5+5+6+8+5+7+7+5)/24。. 圖五: 平均干擾首先，我們利用整數線性規畫(Integer Linear Programming)將此問題公式化，使得此問題可被廣泛使用的簡化法(Simplex Method)所解決，如下線性函式: K ( v ) K (u ). ∑ ∑∑y. Maximize. ( v ,u )∈E i =1. j =1. i, j. (u , v). Subject to. ∑. K ( p )K ( q ). ∑ ∑H. ( p , q )∈E 2 ( u ,v ) k =1 s =1. k ,s ,h. ( p, q ) yk , s ( p, q ) ≤ 1,. ∀i = 1,2,..., K (v), j = 1,2,..., K (u ), h = 1,2,..., H , (v, u ) ∈ E H. ∑x j =1. i, j. kv. ∑x i =1. i, j. (v) ≤ 1, ∀v ∈ V , ∀i = 1,2,..., K (v) (v) ≤ 1, ∀v ∈ V , ∀j = 1,2,..., H. 8.

(12) K (v) H. ∑∑ x i =1 j =1. K (v). ⎛. i, j. (v) > 0, ∀v ∈ V. H. ∑ ⎜⎜1 − ∑ x i =1. ⎝. j =1. i, j. ⎞ (v) ⎟⎟ > 0, ∀, v ∈ V ⎠. xi , j (v) = 0 or 1, ∀i = 1,2,..., K (v), j = 1,2,..., H , v ∈ V. yi , j (v, u ) = 0 or 1, ∀i = 1,2,..., K (v), j = 1,2,..., H , (v, u ) ∈ E 為了更有效率地解決此問題，我們提出了具有常數上界的近似解演算法. (c-Approximation)，主要的概念是用問題轉換的法式(Problem Transformation)，我們將此問題在多項式時間內轉換到最小獨立佔有集合(Minimum Independent Dominiating Set. Problem)問題上，使我們可以將現存的近似解演算法經過轉換後就可用來解決我們的問題，以目前最佳的解過，當網路拓撲的支度(degree)為B時，我們的問題可近似到B2內。下圖為一示意圖，一個原本有五個節點的無線網狀網路可經由我們所提出的公式轉換成最小獨立佔有集合問題的輸入，因此我們可利用已存在的演算法經由反轉來近似原本問題的輸入。. 圖六: 問題轉換與近似解演算法. (3) VoIP 於 IEEE 802.11e 之跨層次品質保證控制 (Cross-Layer Control Scheme for VoIP over 802.11e) 9.

(13) 此研究方法分為兩個部份，第一部份是改進 WQE[29]的方法，建構一個基於策略[33] 的 802.11e 無線區域網路。第二部份提出一個跨階層調變 VoIP 應用程式(Cross-layer. Adaptive VoIP application)來提升 VoIP 在 802.11e 無線區域網路運行的通話品質。 . 第一部份 WQE[29]是以資料流為單位判斷是否符合策略規則(policy rule)，這種方法類似於 InterServ 的概念，它們的缺點就是需要儲存的策略資訊太多了，無法達到. scalable。所以我們設計了一個系統類似 DiffServ 的方法，以行動工作站的存取類別 (Access Category)為單位，以減少無線基地台需要儲存的策略資訊數量。我們的方法如下圖所示:. 圖七：主要架構行動工作站連上無線基地台後，附在無線基地台上的 hostap daemon 會先幫工作站去和 RADIUS Server 做認證。認證完後，工作站申請的服務等級契約(Service Level. Agreement,SLA)會附在 Access-Accept 中帶給無線基地台。我們是去修改 RADIUS Server，使之可以利用 RADIUS Message[34]中的 Vendor Specific Attribute 將服務等級契約傳給無線基地台，無線基地台收到服務等級契約後，每當有認證成功的行動工作站要傳送封包，無線基地台會去看 IP 封包的 DSCP 欄位的值判斷封包的類型，如果是 VoIP 的封包，無線基地台會再去服務等級契約中查看這個行動工作站是否有申請 AC_VO 的服務，如果有申請才將封包設成 AC_VO 的型態，使之擁有較高的傳送優先權。 . 第二部份 : 這個部份我們修改一個在 Window 平台上運行的開放原始碼 VoIP. application—RAT(Robust Audio Tool)[9]。在 RAT 中新加入可根據行動工作站和無線基地台間訊號的強度值 (RSSI(Receiver Signal Strength Indicator)) 來調整 VoIP 10.

(14) codec 的方法。. 圖八：. 選擇 codec 的方法. 將RSSImin~RSSImax分為四個區段，每收集n個封包後就計算一次平均的RSSI值，若平均RSSI值落在某個區段A，就選擇用區段A對應到codec。. 五、結果與討論(含結論與建議) (1) 多通道多天線環境之存取控制協定 (Multi-channel Multi-radio Media Access Control ) 實驗平台式使用 ns2 來做模擬，圖 9 是在線型的拓撲上所做的實驗，總共有六個點，有兩條 UDP 流量，分別從兩端流向另一端，如此可測出隱藏終端的問題是否獲得紓解，圖 9 的橫軸為封包到達的速率，縱軸為網路的平均延遲，與[27]比較(HMCP)可發現我們的協定(HMCP_enb)在網路上的延遲是有改善的。圖 10 的橫軸是封包到達的速率，縱軸是網路的總輸出量，由圖可看出我們的總輸出量都比[27]改善許多。. 圖九：線型拓撲之平均延遲. 圖十：線型拓撲之總輸出量. 圖 11 和圖 12 是在利用亂數所取得的拓撲上所做的實驗，總共有二十個點，有十條. UDP 流量，如此可測出我們的協定在實際狀況下是否真有改善，圖 11 的橫軸是封包到達的速率，縱軸是網路的平均延遲，與[27]做比較可發現我們在網路上的延遲是有改善的，且當封包到達的速率越快，所改善的幅度越大。. 11.

(15) 圖十一：隨機拓墣之平均延遲. 圖十二：隨機拓墣之總輸出量. (2) 通道指定之最佳化演算法 (Optimization on Channel Assignment) 此部分之成果主要以理論分析為主，當拓撲的支度最大為一常數B時，我們的演算法可近似到B2 倍內，而當拓撲可被一等徑圓盤圖(unit disk graph)表示時，則可進似至 5 倍最佳解內。在未來的研究，我們將利用數據分析來驗驗理論的結果，並推導Relaxed ILP 線性規畫公式以作為數據分析時的理論下界。最後我們會把通道指定以及存取控制兩邊的結果加以結合，也就是以此通道指定演算法規畫網路初始時間的配置(包含介面種類決定以及靜態介面通道指定)，並以多通道多天線存取控制協定作為網路運作時的碰撞避免機制。 (3) VoIP 於 IEEE 802.11e 之跨層次品質保證控制 (Cross-Layer Control Scheme for VoIP over 802.11e) 下表中，我們分別測試 VoIP 應用程式在 802.11 與 802.11e 網路上運行的傳輸延遲，. TCP 使用 Best Effort，而 VoIP 分別使用 Best Effort 和 Voice Priority，此外我們分別測試 5.3kbps 以及 64kbps 兩種 codec 傳輸的延遲: 表一: VoIP 於 802.11, 802.11e 以及不同 codec 大小之延遲. MAC 資料流優先權設定方式. 64kbps 5.3kbps. 802.11 VoIP：Best Effort. 140ms. 104ms. 11ms. 9ms. TCP：Best Effort VoIP：Voice Priority 802.11e TCP：Best Effort (1)802.11e 與 802.11 效能比較由橫的兩列來看 802.11e 與 802.11 效能比較，我們可以看到不管是使用資料傳輸率大的 codec 或是資料傳輸率小的 codec，VoIP 應用程式在 802.11e 網路上傳輸的延遲都會遠小於 802.11 網路，由此可以得知 802.11e 確實可以讓 VoIP 應用程式獲得較好的通. 12.

(16) 話品質。. (2)VoIP 應用程式 codec 效能比較由第二列的資料來看，在 VoIP 應用程式在 802.11e 網路使用資料傳輸率小的 codec 可以減少傳輸延遲，這是因為使用資料傳輸率小的 codec 時，傳輸封包長度短，而且網路資料量也變少，所以傳輸延遲會變小。但是用資料傳輸率小的 codec 會使得聲音聽起來不是很清晰，所以我們不可以永遠都只用資料傳輸率小的 codec，我們的方法是將. 802.11e 無線網路搭配跨階層調變的 VoIP 應用程式，讓 VoIP 應用程式隨著網路狀況調整 codec，以減小傳輸延遲，提升 VoIP 通話品質。這種方法在很多 VoIP 應用程式使用者位於訊號弱的狀況時，讓它們換用資料傳輸率小的 codec 可以減少對網路資源的浪費。. 六、第二年工作計畫無線網線透過繞徑機制將資料經由多重節點轉送至目地端，在實作中通道的指定會影響網路負載，繞徑的結果亦會改變個別虛擬連線的負載，因此指定的結果必需使多數的傳送競爭到足夠的頻寬，但頻寬的分佈又會進一步影響繞徑結果，而形成雙向相依的特性。另一方面，在對等式網路中，資料的繞徑經常透過尋找最少轉送點路徑來達成，以降低多重傳送所造成的延遲，可是在考量具有多重速率的環境時，雖然選取較遠的相鄰點的方法，可減少路徑轉送點的個數，但長距離的傳送意味著較低的傳輸速度，對持續性的傳輸未必能得到好處，因此繞徑的設計必需在延遲和速率之間取得平衡。而對於不同的模式，受到傳輸功率以及編碼模式的影響，距離與最大速度之遞減關係亦有不同的定義，此時若再使用不同的模式傳輸，將會再度提升繞徑設計之複雜度。因此，第二年我們將可先分別對多天線多通道無線網狀網路，以及多模多速率無線網狀網路，設計動態之繞徑演算法，並依此推導有用的性質、函式、和定理，作為M4無線網狀網路動態繞徑研究的基礎。. 七、參考文獻 [1] K. Jain, J. Padhye and V. N. Padmanabhan, “Impact of interference on multi-hop wireless network performance”. MobiCom, 2003. [2] “IEEE 802.11b Standard”. standards.ieee.org/getieee802/download/802.11b-1999.pdf [3] “IEEE 802.11a Standard”. standards.ieee.org/getieee802/download/802.11a-1999.pdf [4] IEEE 802.11 Working Group, “Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY)specifications,” 1997 13.

(17) [5] A. Raniwala, K. Gopalan and T.C. Chiueh, “Centralized channel assignment and routing algorithms for multi-channel wireless mesh network”. Mobile Computing and Communications Review, 8, 2, 2004, pp. 50–65. [6] R.Poor, “Wireless mesh networks”. Intelligent System Wireless, February 2003 [7] P. Whitehead, “Mesh networks; a new architecture for broadband wireless access systems”. Radio and Wireless Conference IEEE , 2000, pp. 43–46. [8] A. Nasipuri, J. Zhuang and S. R. Das, “A Multichannel CSMA MAC Protocol for Multihop Wireless Networks”. Proc. of IEEE Wireless Communications and Networking Conference (WCNC), September 1999. [9] A. Nasipuri and S. R. Das, “Multichannel CSMA with Signal Power-based Channel Selection for Multihop Wireless Networks”. Proc. of IEEE Vehicular Technology Conference (VTC), September 2000. [10] S.-L. Wu, C.-Y. Lin, Y.-C. Tseng and J.-P. Sheu, “A New Multi-Channel MAC Protocol with On-Demand Channel Assignment for Multi-Hop Mobile Ad Hoc Networks”. Int’l Symposium on Parallel Architectures, Algorithms and Networks (I-SPAN), 2000. [11] B. Vucetic, “An adaptive coding scheme for time-varying channels”, IEEE Transactions on Communications 39, 1991, pp. 653–663. [12] J. Williams, L. Hanzo and R. Steele, “Channel-adaptive modulation”. Proc. 6th Internat. Conference Radio Receivers and Associated Systems, 1995, pp. 344–147. [13] C. Andren and J. Boer, “Draft text for the high speed extension of the Standard”. doc: IEEE P802.11-98/314 (1998). [14] C. Andren and M. Webster, “CCK Modulation Delivers 11 Mbps for High Rate 802.11 Extension”. Proc. Wireless Symposium/Portable by Design Conference, Spring 1999. [15] M.E. Barton, “Baseband system design for a multi-mode 802.11 a/b wireless LAN adapter”. Proc. SoutheastCon, IEEE , April 2002, pp. 322–325. [16] M. Maeng, Y.S. Hur, N. Lal, E. Gebara, S.W. Yoon and J. Laskar, “Combined digital/wireless link over the multi-mode fiber with a vertical cavity surface emitting laser Microwave Symposium Digest”, IEEE MTT-S International, 1, 11, June 2003, pp. 265–268 . [17] S. Zhongming and R. Rofougaran, ”A single-chip and multi-mode 2.4/5GHz RF transceiver for IEEE 802.11 wireless LAN Microwave and Millimeter Wave Technology”. Proc. ICMMT 3rd International Conference, Aug. 2002, pp. 17–19. [18] F. A. Tobagi and L. Kleinrock, “Packet Switching in Radio Channels: Part II - the hidden terminal problem in carrier sense multiple-access modes and the busy tone solution”. IEEE Transactions on Communications, COM-23, 1975. 14.

(18) [19] J. So and N. Vaidya; “Multi-Channel MAC for Ad Hoc Networks: Handling Multi-Channel Hidden Terminals Using a Single Transceiver”. ACM MobiHoc, May 2004. [20] Z. Tang and J.J. Garcia-Luna-Aceves, “Hop-Reservation Multiple Access (HRMA) for Ad-Hoc Networks”. Proc. of IEEE INFOCOM, 1999. [21] A. Tzamaloukas and J.J. Garcia-Luna-Aceves, “A Receiver-Initiated Collision Avoidance Protocol for Multi-Channel Networks”. Proc. of IEEE INFOCOM, 2001. [22] N. Jain and S. Das, “A Multichannel CSMA MAC Protocol with Receiver-Based Channel Selection for Multihop Wireless Networks”. Proc. of the 9th Int.Conf. on Computer Communications and Networks (IC3N), October 2001. [23] Nakjung Choi, Yongho Seok and Yanghee Choi, “Multi-Channel MAC Protocol for Mobile Ad Hoc Networks,” in IEEE VTC 2003-Fall, 2003. [24] Paramvir Bahl, Ranveer Chandra and John Dunagan, “SSCH: Slotted Seeded Channel Hopping for Capacity Improvement in IEEE 802.11 Ad-Hoc Wireless Networks,” in ACM MobiCom’04, 2004. [25] Yu-Chee Tseng, Shih-Lin, Chih-Yu Lin and Jang-Ping Sheu, “A Multi-Channel MAC Protocol with Power Control for Multi-Hop mobile Ad Hoc Networks,” in International Conference on Distributed Computing Systems Workshop, 2001. [26] Jaya Shankar Pathmasuntharam, Amitabha Das and Anil Kumar Gupta, “Primary Channel Assignment based MAC (PCAM) – A Multi-Channel MAC Protocol for Multi-Hop Wireless Networks,” in IEEE WCNC, 2004. [27] Pradeep Kyasanur and Nitin H. Vaidya, “Routing and Interface Assignment in Multi-Channel Multi-Interface Wireless Networks,” in IEEE WCNC, 2005. [28] IEEE Work Group: “IEEE Standard for Information technology— Telecommunications and information exchange between systems— Local and metropolitan area networks— Specific requirements Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) specifications Amendment 8: Medium Access Control (MAC) Quality of Service Enhancements”, IEEE, Nov 2005. [29] Pauy, D.Maniezzo, S.Das, Y.Lim, J.Pyon, H.Yu, M. Gerla:” A Cross-Layer Framework for Wireless LAN QoS Support”, IEEE, 2003. [30] Q.Ni, L.Romdhani, T.Turletti, and I.Aad: “ QoS Issues and Enhancements for IEEE 802.11 Wireless LAN”, INRIA, Nov 2002. [31] M.Matsumoto and T.Itoh:” QoS-guarantee Method for Public Wireless LAN Access Environments”, IEEE, 2005. [32] Seo J W, Woo S J and Bae K S: “A Study of the Application of an AMR Speech Codec 15.

(19) to VoIP”, IEEE, 2001. [33] J. Strassner, ”Policy-Based Network Management : Solution for the Next Generation”, O’REILLY, April 2002. [34] C. Rigney, S. Willens, A. Rubens, and W. Simpson, ”Remote Authentication Dial In User Service (RADIUS)”, RFC-2865, June 2000 [35] C. Rigney, W. Willats, P. Calhoun, ”RADIUS Extensions”, RFC-2869, June 2000 [36] RAT,. Robust. Audio. Tool,. available. from University. College. London. —. http://www-mice.cs.ucl.ac.uk/multimedia/software/rat/ 本年度本計畫衍生之論文如下：附件一 :A.-K. Jeng and R.-H. Jan, “Optimization on Hybrid Channel Assignment for. Multi-channel Multi-radio Wireless Mesh Networks”, submit to Globecom 2006. 附件二 :A.-K. Jeng and R.H Jan, The r-neighborhood Graph: A Novel Structure for. Topology Control in Wireless Networks, accepted and to appear in IEEE Transactions on Parallel and Distributed Systems, 2005 (SCI). 附件三:Hsiao-Po Lin, Shih-Chang Huang and Rong-Hong Jan, "A Power-Saving Scheduling. for Infrastructure-Mode 802.11 Wireless LANs," accepted and to appear in Computer Communications. 附件四:Yu-He Gau, Hung-Chi Chu, and Rong-Hong Jan, "A Weighted Multilateration. Positioning Method for Wireless Sensor Networks" accepted and to appear in International Journal of Pervasive Computing and Communications, 2006.. 16.

(20) Optimization on Hybrid Channel Assignment for Multi-channel Multi-radio Wireless Mesh Networks Andy An-Kai Jeng and Rong-Hong Jan Department of Computer Science National Chiao Tung University Hsinchu, 300, Taiwan, R.O.C. Abstract-The emergence of multi-channel multi-radio wireless mesh networks has given us many new opportunities and challenges. Particularly, the issue on how to appropriately assign channels to interfaces has gathered great importance in the recent publications. To efficiently utilize the channels diversity, the communicating channels should be negotiated between interfaces, which however would cause considerable overhead. To conquer this, a hybrid scheme was proposed to rule the way for assigning channels in literatures. In this paper, we formally model the hybrid scheme into an integer linear programming formulation. We provide the necessary as well as sufficient conditions of any feasible assignment which is not restricted to some specific goals. To for optimizing the linking-layer performance, we suggest a superior objective function which can minimize the potential interference of any transmission on average. We also show that a special case of the considered problem is APX-complete. I. INTRODUCTION The wireless broadband technique has been continually grown in the last years. To extend the broadband access to the last mile, the deployment and research issues of the wireless mesh networks (WMNs) has attracted more and more attentions recently. In WMNs, a node can be either a mesh router or a mesh client [1]. By relaying packets thought multiple hops, the mesh clients, connecting to some mesh routers with AP functionality, are able to communicate to other nodes or access to the Internet. Different from the traditional multi-hop networks, the WMNs put more stress on exploiting multiple non-overlapping channels to improve the network performance. By transmitting on different channels, the interferences among nodes can be greatly mitigated. However, for the time being, the available channels are still limited. In IEEE 802.11b/g (2.4GHz) and IEEE 802.11a (5GHz), at most 3 and 12 orthogonal channels are available only. Even in the further, wasting on the channels may not be a promising way. Therefore, the channel utilization should be properly spread among nodes to gain better spatial reusability. On the other hand, researches [1, 2, 5] have suggested that a mesh node. should equip with more than one radio to increase its throughput in parallel. A node having multiple radios is able to transmit and receive packets simultaneously using non-overlapped channels. In this paper, we consider the multi-channel multi-radio wireless mesh networks (MCMR-WMNs). Our goal is to assign channels on radios such that a link layer performance measurement can be optimized. A number of algorithms have been proposed to the channel assignment problem. According to Kyasanur and Vaidya [3], these algorithms can be categorized into threefold (scheme): 1) Static Scheme: In this scheme, the channels assigned on interfaces or links are fixed permanently or over a long period of time. The benefit of this scheme is that it requires no overhead for negotiating the communicating channel before transmission. All channels are decided in advance. However, as the traffic profile is changed, the bandwidth requirement on links may change. When this happens, the links or interfaces are not able to adequate to this change. Examples are [4, 5]. In [4], the channels assigned on the interfaces of each node are in the same pattern. Das et al. [5] provided a two optimization models for a link layer measurement. The channels are assigned on links rather than interfaces in [5]. 2) Dynamic Scheme: This scheme allows the channels used by interfaces or links to be continually changed. However, to achieve this, communicating overhead for negotiating a common channel would be very heavy, if the traffic patterns are frequently changed. 3) Hybrid Scheme: This scheme is suggested by [3]. It combines the benefits of both static and dynamic schemes. In this scheme, an interface can be either fixed or switchable. For any fixed interface, a channel must be assigned on it in advance and can not be changed later. All transmission are initiated by switchable interfaces and received by fixed interfaces. When a switchable interface attempt to transmit to a target interface, it transmits using the channel assigned on the target interface. Because the channels of neighboring fixed interfaces of a switchable interface are always unchanged, the switchable interface can switch to the communicating channel immediately without any communicating overhead In this paper, we propose an optimization model for the hybrid scheme. We formulate the channel assignment using.

(21) hybrid scheme into an ILP formulation. A link layer performance measurement, named average potential interference per switchable link, will be given. The optimization models for the channel assignment problem with static and/or dynamic scheme for on MCMR-WMNs were discussed in [5, 6, 7, 8, 9]. Especially, [5] is most similar to our work. It concerns a link layer performance measure for the static scheme in the worst case. To the best of knowledge, there is no preview works concerning the optimization problem for the hybrid scheme. II. NETWORK MODEL AND ASSUMPTIONS In this section, we formally describe the networks under study. Some necessary assumptions and considerations are also explained. A given MCMR-WMN can be symbolically modeled as the following instance. 1) The mesh nodes correspond to a set V of n fixed nodes. 2) Each node v has K(v) interfaces, where K(v) ≥ 2. The set of interfaces equipped on v is represented by I(v) = {Ii(v) | i, =1, 2, … , K(v)}, where Ii(v) is the ith interface on v. Whether an interface is fixed or switchable is our decision variable either, rather than specifying in the instance. The rationale will be explained later. 3) Each interface Ii(v) has its won transmission range, detonated by Ri(v). The set of neighboring nodes, in the transmission range of Ii(v) is denoted by Ni(v). i.e. Ni(v) = { u | u ∈ V, u is covered by Ri(v)}. All neighboring nodes of v, reachable from some interface of v, is denoted by Ni(v). i.e. N(v) = { u | u ∈ Ni(v) for some i}.(Note that N(v)=∪1≤i≤K(v)Ni(v)). In other words, by using different interfaces, the reachability of a node can be varied. This consideration is reasonable, since in the near further, multiple radios in different modes, like IEEE 802.11 a, b and g, can be equipped together on a single node to integrate heterogeneous networks. This will lead to unequal converge on each interface. Besides, even all interfaces are on the same mode, the topological control in MCMR architecture would result in diverse ranges on interfaces, which is beyond our scope. 4) Further, NIi(v) and NI(v) are the sets of neighboring interfaces reachable from Ii(v) and v, respectively. i.e NIi(v) = { Ij(u) | u ∈ Ni(v), j = 1, 2, …, K(u)} and NI(v) = { Ij(u) | Ij(u) ∈ NIi(v), for some i}. 5) The transmission range Ri(v) of each interfaces Ii(v) can be variant according the hardware feature or preliminary network planning. The neighboring interfaces NIi(v) of Ii(v) is the set of interfaces which are within Ri(v), not include Ii(v) itself. 6) We assume for simplicity that all available channels are homogeneous to the entire deployment region. That is, H orthogonal channels are equally available to each node. To neglect trivial instance, we assume that H ≥ 2. Actually, the assumption on the homogenous distribution of available channels can be released further. We will mention this in our discussion. Then the linking status among nodes can be represented by a digraph RG = (V, E), named reachability graph on nodes,. where two nodes v and u has directed edge (v, u) in E if and only if u is reachable by some interface on v. i.e. u ∈ N(v). Similarly, RGI = (VI, EI) is the reachability graph on interfaces, where VI = {Ii(v) | v ∈ V, i = 1, 2, …, K(v)}, representing all interfaces in the networks, and an directed (Ii(v), Ij(u)) in EI, if and only if v = u or Ij(u) ∈ NIi(v). In this paper, we assume that any given instance of MCMR-WMN corresponding to RG is strongly connected. That is, for any two nodes v and u in V, there is some path in RG from v to u and vice versa 1 . Obviously, the connectivity of RG and RGI are equivalent. In hybrid scheme, nodes should have at least on fixed interface for transmitting and at least one interface for receiving. Therefore, the assumption that K(v) ≥ 2, ∀ v ∈ V, is for the connectivity of instance either. III. DESIGN PRINCIPLES In the hybrid scheme, compared to the static scheme, the transmitting channels used by switchable interfaces can be dynamically chosen from those channels assigned on the neighboring interfaces which are fixed. So it is not necessary to determine a channel for any switchable interface before transmission. However, a new issue rises from this scheme: whether an interface is fixed or switchable? In the previous works [4], they generally assume that the roles of interfaces are given in advance. This assumption may however restrict the optimality within a specific consideration. We can treat the possible combinations of the transmitting channels used by all links in RGI, including using no channel, as the whole solution space. Specifying the roles of interfaces in advance confines the solution space to a specific subgraph of RGI, since those links, except between fixed and switchable, interfaces can be no longer in RGI. Contrarily, unlike the dynamic scheme, the channels assigned on fixed interfaces are unchanged overtime, which means that for a fixed interface, it always uses the same channel to receive messages from different switchable interfaces. Therefore, we do not have to decide channels based on links. Instead, assigning a single channel on each fixed interface is representative enough. Accordingly, in this paper, the channel assignment problem on the hybrid scheme consists of the following two decisions 1) For each interface, decide whether it is fixed or switchable. 2) If an interface is fixed, assign a channel to it. After an assignment is decided, a switchable interface can initiate an transmission with all neighboring interfaces which are fixed by switching to their channels. So, for any two interface Ii(v) and Ij(u), we say that a switchable link is from Ii(v) to Ij(u) if and only if the following three conditions are satisfied 1. v ≠ u; 2. Ij(u) ∈ Ni(v); 3. Ii(v) is switchable and Ii(v) is fixed. By this, the switchability among interfaces of an assignment 1. The path from v to u and that from u to v are not necessarily the same..

(22) can be represented by a digraph SGI = (VI, EIS), named switchability graph, where EIS corresponds to all switchable links between interfaces. Likewise, for an assignment, the corresponding connectivity of nodes, can be represented by a digraph SG = (V, ES), where a directed edge (u, v) is in ES if and only if some switchable link is from u to v. Given any instance, the feasibility of an assignment should be further constrained. In our work, any feasible assignment satisfies the following three considerations. 1) About interfaces: By definition, the channels assigned on fixed interfaces are always unchanged. Besides, the switchable interfaces are unnecessarily associated with any channel before transmission. So in a feasible assignment, any interface can be assigned at most one interface. 2) About channels: In MCMR architecture, multiple interfaces are available to exploit the usage of channels on separated spectrums simultaneously. Yet if two fixed interfaces are on the same channel as well as the same node, then there must be one of them useless, since they can never receive simultaneously at any time. In this case, for either of them, altering the channel or turning the role to switchable can never worsen. Consequently, all channels assigned on the same node should be distinct. The constraint can be expressed as 3) About connectivity: Clearly, SG is always a subgraph of RG. Therefore, the assumption on the connectivity of RG is only a necessary condition for that of SG. We should further define the necessary as will sufficient condition for the connectivity (strongly connected) of any SG. We say that a switchable link is active if it is used for transmission. For two reasons, a switchable link can not be active. First, the link is blocked, which means that the interfaces on either or both of the ends are occupied by other links for transmission. Obviously, any adjacent links can not be active simultaneously due to this reason. Second, the link is interfered by other transmissions. When a switchable link (Ii(v), Ij(u)) is active, the switchable links adjacent to the interfaces in Ni(v) can not be active on the same channel of Ij(u), since either transmitting or receiving of them can be interfered by Ii(v)’s transmitting (Note that some link could be blocked as well as interfered. In this case, we say the link is being blocked only, since no matter what channel is used by the link, it can not be active). See Figure 1 for example in which all interfaces transmit using channel 1: when the switchable link (a, b) is active , (a, c) and (g, b) are blocked, because their transmitting and receiving interfaces respectively are used by (a, b). On the other hand, (d, c), (d, f) and (e, c) can not be active either, since there are adjacent to c and/or d, which are within the transmission range of a.. Figure 1: The links blocked or interfered by the transmission of (a, b). In [5], they considered the static scheme. To optimize the link-layer throughput in the worst case traffic, in which all links contend for transmission at the same time, they set their goal to be maximizing the number of simultaneous transmissions between interfaces. Similarly, an institutive objective function for our consideration can be maximizing the number of switchable links which can be active simultaneously. However, this objective has many weaknesses. First, such goal would be more interesting for the hardest traffic profile, while ignore the most cases where only a pairs need transmit. Second, maximizing the simultaneous transmissions does not guarantee that any transmissions has the minimal interference to the other links A transmission causing high interference would lead to considerable degradation on throughput. Third, this objective does not take the channel diversity into consideration. In the hybrid scheme, a switchable interface can utilize varied channels to conquer dynamic traffic profiles by switching channels. Therefore, the higher switchability of interfaces could bring more channel diversity, where the switchability of an interface means the number of neighboring interfaces it can switch to. Third, this objective does not take the channel diversity into consideration. For any switchable interface, the channel diversity is the number of distinct channels it can switch to. An interface with higher channel diversity can be more adequate to dynamic traffic demands, since it has more choices to keep away from the intensively interfered channel. From these viewpoints, in this paper, we aim to minimize an average-case linking-layer performance measure, named the average potential interference per switchable link, abbreviated as APS. Given an assignment, the potential interference of a switchable link Ii(v) is the number of switchable links that are interfered by Ii(v) on the same channel. Let us see Figure 2 (a): the potential interference of (a, b) is 4, including (h, i), (h, g), (d, g) and (f, g). Let TI be the total number of potential interferences and TS be the total number of switchable links. The APS is defined as AIS =. TI . TS. (1). This objective function provides an upper bound on the average number of interferences which would be caused by an arbitrary transmission. Figure 2 (b) illustrated a fully example, where totally has 21 switchable links and averagely no more than 1.19 transmissions (1.19 = 29 /21) could be interfered as a switchable interface is active.. (a). (b).

(23) Figure 2: (a) the potential interference of a link (b) the potential interferences of all links.. IV. PROBLEM FORMULATION The following, we are going to introduce the symbolic terms defining an assignment. Then, we discuss and formulize all essential constraints for characterizing a feasible assignment. Finally, an objective function dedicatedly tailored for the hybrid scheme will be presented. A. Decision variables First, we define the following binary variables to constitute an assignment based on interfaces: ⎧1 if channel h is assigned on the i th interface of node v xi , h (v) = ⎨ ⎩0 Otherwise. ,where v ∈ V, i = 1, 2, … , K(v) and h = 1, 2, … , H. These variables are sufficient to model the two decisions. First, they dedicate the channels assign on interfaces. Secondary, an interface is switchable if there is no channel assigned on it, i.e i.e ∑1≤h≤Hxi,h(v) = 0, otherwise, it must be fixed. B. Constraints The considerations of any feasible assignment have been verbally described previously. Now we formally define the sufficient and necessary conditions of the feasibility for any assignment. Constraints on interfaces: For each interface, no matter being fixed or switchable, at most one channel can be assigned on it. Thus we have H. ∑x. i,h. h =1. (v) ≤ 1, ∀v ∈V , ∀ i = 1,2,..., K (v). (2). Constraint on channels: To ensure that there is no channel assigned to any node for the second times, the constraint can be expressed as K (v). ∑x. i,h. i =1. (v) ≤ 1, ∀v ∈ V , ∀h = 1,2,..., H. (3). Constraint on connectivity: In the hybrid scheme, a node can communicate with other nodes only if it has at least one fixed interface for receiving and has at least one switchable interface for transmitting. As a sequel, the obviously necessary conditions for connectivity can be given by K (v ) H. ∑∑ x i =1 h =1. i,h. (v) > 0, ∀v ∈ V. (4). and K (v). ⎛. H. ∑ ⎜⎝1 − ∑ x i =1. h =1. i,h. ⎞ (v) ⎟ > 0, ∀v ∈V ⎠. (5). Equations (3) and (4) indicate respectively that all nodes should have at least one fixed and switchable interfaces. However, they are not sufficient either. In RG, some neighboring node u of an interface Ii(v) may be no longer reachable in an assignment if Ii(v) is assigned to be fixed and. no other interface of v can reach u. Fortunately, when all transmission ranges on a node are equal (i.e. ∀ v ∈V, Ri(v) = Rk(v), ∀ i, j ≤ K(v)), equations (3) and (4) can be sufficient either: In the reachability graph RG, for any two nodes v and u, there is a path π from v to u. Considering any median node w and w’s next hop t on π, if the transmission ranges on w are all equal, w can reach t by any interface. Therefore, if some interface on w is switchable and some interface on t is fixed, w must be able to reach to v. Continuing the same argue on each w, the correctness follows. C. Objective function Now, we formulate our link-layer measure performance measurement APS, the average potential interference per switchable link. Let ri,j(u, v) = 1 if Ij(u) ∈ NIi(u), 0, otherwise. A function Si,j(v,u) that indicates whether a switchable link is in SG, i.e. Si,j(v,u) = 1 if (Ii(v), Ij(u)) ∈ SG, and Si,j(v,u) = 0, otherwise, can be defined as follows. 2. H H ⎛ ⎞⎛ H ⎞ Si , j (v, u ) = ⎜1 − ∑ xi ,h (v) ⎟⎜ ∑ xi ,h (v) − ∑ x j ,h (u ) ⎟ ri , j (u , v) (6) h =1 ⎝ h=1 ⎠⎝ h=1 ⎠ The first parenthesis returns 1 i.f.f. the two interfaces are not assigned the same role, the second returns 1 i.f.f. Ii(v) is switchable, the last term indicates whether Ij(u) can be reached by Ii(v). So, the three conditions defining a switchable link is characterized by equation (6). By this, the total number of switchable links can be obtained by K (v). TS = ∑ ∑. K (u ). ∑ ∑S. v∈V i =1 u∈N ( v ) j =1. i, j. ( v, u ). (7). Next, we consider the number of potential interference per link. Consider two pairs of interfaces (Ii(v), Ij(u)) and (Is(p), It(q)). First, we define a function Fi,j,s,t(u, v, p, q) to indicate whether they are switchable on the same channel. Fi,j,s,t(u, v, p, q) =1, if it is, 0, otherwise. The function can be given as Fi , j , s ,t (v, u, p, q) = ∑ (x j , h (u ) Si , j (v, u ) )(xt , h (q) S s ,t ( p, q) ) H. (8). h =1. Then, we need to identify whether (Is(p), It(q)) is in the interference range of (Ii(v), Ij(u)). As shown by figures 1 and 2, (Is(p), It(q)) can be interfered by (Ii(v), Ij(u)) only if either end of (Is(p), It(q)) is reachable from Ii(v) in RG. So, let EIi(v) denote the set of links in RGI which are adjacent to some interface in NIi(v), all possible links which can be interfered by (Ii(v), Ij(u)) are in EIi(v). However, (Is(p), It(q)) can be interfered, rather than be blocked, by (Ii(v), Ij(u)), only if either end is neither Ii(v) nor Ij(u). So, let EI–i(v, u) be the subset of EIi(v) removing all links adjacent to neither Ii(v) nor Ij(u). The number of potential interference of (Ii(v), Ij(u)) can be defined as TI i , (u, v) =. ∑F. (v , u , p, q ). i , j ,s ,t ( I s ( p ), I t ( q ))∈EIi− ( u ,v ). , and the total number of potential interference links is. (9).

(24) K (v ). TI = ∑ ∑. ∑. K (u ). ∑ PI i, j (v, u ). (10). v∈V i =1 u∈N ( v ) j =1. Finally, the average potential interference per switchable link can be obtained by AIS =. TI TS. We name the channel assignment problem with the goal of minimizing AIS as AISP. D. The ILP formulation The final form of the ILP model is summarized below, which consists of totally nH∑v∈VK(v) decision variables and (H + 1)(n∑v∈VK(v) + 1) + 1 constraints. Minimize AIS subject to H. ∑x. i,h. (v) ≤ 1, ∀v ∈ V , ∀ i = 1,2,..., K (v). h =1. K (v). ∑x. i,h. i =1. (v) ≤ 1, ∀v ∈ V , ∀h = 1,2,..., H. K (v ) H. ∑∑ x i =1 h =1. K (v). ⎛. i,h. (v) > 0, ∀v ∈ V. H. ∑ ⎜⎝1 − ∑ x i =1. h =1. i,h. ⎞ (v) ⎟ > 0, ∀v ∈V ⎠. xi , h (v), ∀v ∈V , ∀ i = 1,2,..., K (v), ∀h = 1,2,..., H Notice that in equation (1), the value of TI is determined by the two decisions, while the number of switchable links is solely determined by the roles of interfaces. Therefore, if the role of each interface is given in advance, we can concentrate on minimizing TI. We named this specialized problem as TIP.. IV. APPROXIMATION In this section, we will show that in some reasonable consideration of network topology, TIP is APX-complete. In other words, in those cases, there is some polynomial-time algorithm such that the performance ratio of TIP can be bounded by a constant. Given a graph G, a dominating set D of G is subgraph of vertices such that for each vertex v in G, S contains either v itself or some neighbor of v in G. An independent dominating set T of a graph is a dominating set such that no two vertices of T are connected an edge in G. The minimum independent dominating set problem (MIDP) is to minimize the vertices of T [13]. Let P = (V, R, I, H) be an instance of TIP, where R, I and H are the sets of transmission ranges, interfaces and available channels, as defined in Section II, respectively. We show that there is a strict-reduction (f, g) from TIP to MIDP. That is, we shall prove the following 1) For every instance P in TIP, f(P) is an instance in MIDP.. 2) For every feasible solution T to f(P), g(T) is a feasible solution to P. 3) TI(g(T)) – TI(P) = MID(T) – MID(f(P)), where TI(g(T)) (MID(T)) and TI(P) (MID(f(P))) are the result of T (g(T)) and optimal result of P (f(P)) respectively. We now illustrate the transformation f from P to f(P) (1) For any two interfaces Ii(v) and Ij(u) having a switchable link from Ii(v) to Ij(u) in S, we create H components Ci,j,h(v, u), h = 1, 2, … , H. (2) For any two components Ci,j,h(v, u) and Cs,t,h(p, q) having the same subscript h, if either Is(p) or It(q) or both are within the Ri(v), we have a node Ni,j,s,f,h(v, u, p, q) in f(P). (3) For any two nodes Ni1,j1,s1,f1,h1(v1, u1, p1, q1) and Ni2,j2,s2,f2,h2(v2, u2, p2, q2) in f(P), an edge is between then if and only if one of the following conditions is satisfied. i. Ij1(u1) = Ij2(u2) and h1 ≠ h2. ii. Ih1(q1) = Ih2(q2) and h1 ≠ h2. iii. u1 = u2, j1 ≠ j2 and h1 = h2. iv. q1 = q2, f1 ≠ f2 and h1 = h2. Next, we show the function g which maps a independent dominating set T of f(P) to an assignment g(T) of P. An assignment is represented by binary matrix yi,h(v) such that yi,h(v) = 1 means that the Ii(v) is assigned channel h, and 0, otherwise. Then the function is defined as, for any v ∈ V, i = 1,2,… , K(v) and h =1,2, … ,H, yi,h(v) = 1 if there is some node Nik,jk,sk,fk,h(vk, uk, pk, qk) in T such that either Ijk(uk) = Ii(v) or Ifk(qk) = Ii(v), 0, otherwise. Then, we can show that if T is feasible to MIDP, then g(T) is feasible to TIP. Compared to AISP, the conditions of defining the feasibility of TIP are equivalent, except for the connectivity, since this condition is determined solely be the roles of interfaces and these roles in TIP are given in advance. Besides, an additional condition for the feasibility is that all fixed interfaces are assigned at least one channel. 1) Each fixed interface has at most one channel: In f(P), if a node Ni1,j1,s1,f1,h1(v1, u1, p1, q1) is in T, which means that the two fixed interfaces Ijk(uk) and Ifk(qk) are assigned channel h1 in g(T) , then any other node Ni2,j2,s2,f2,h2(v2, u2, p2, q2) such that Ij1(u1) = Ij2(u2) and h1 ≠ h2 or Ih1(q1) = Ih2(q2) and h1 ≠ h2 can not be in T, since an edge is between each of them an all nodes in T should be impendent. 2) Each fixed interface has at least one channel: It can see that the combinations of all fixed interfaces and channels are elaborated by nodes in f(P). Besides, by virtue of the dominating set, each node should be either in T or adjacent to some node T. Therefore, for each fixed Ii(v), there must be some node in T with a subscript h consisting it. i.e. there must be some h such that yi,h(v) = 1. 3) All channels assigned on a node are distinct: The conditions that u1 = u2, j1 ≠ j2 and h1 = h2 (q1 = q2, f1 ≠ f2 and h1 = h2) in above avoid that any two interfaces j1 and j2 on the same node u1 (f1 and f2 on q1) being assigned the same channel h1. Consequently, we can conclusion that any feasible solution of f(P) can be translated to a feasible assignment to P through a.

(25) function g. A node Ni,j,s,f,h(v, u, p, q) in f(P) corresponds to a interference that the activity on (Ii(v), Ij(u)) interferes the possible transmission on (Is(p), It(q)). Thus TI(g(T)) is always equal to MID(T). As we show above, for every feasible solution T to f(P), g(T) is a feasible solution to P. On the other hand, it can be easily evaluated that any feasible solution g(T) to P can also be transformed to a feasible solution T to f(P). Therefore, we have g(T) is feasible if and only if T is feasible, which implies that that TI(P) can be no worse than MID(f(P)) So, we can get that TI(g(T)) – TI(P) = MID(T) – MID(f(P)). Halldorsson [10] show that for general n-vertex graphs, MIDP is not approximable within n1- ε, for any ε > 0. Kann [11] show that MIDP, when restricted to graph of bounded degree, is APX-complete. Thus by the strict-reduction, if any instance P to IPP can be transformed to f(P) having bounded degree, TIP is APX-complete. Moreover, we can observe that if all interfaces in P have bounded neighboring interfaces, the degrees in transformed instance re also bounded. So we can conclusion that TIP is APX-complete when considered bounded neighboring interfaces. In wireless environment, the transmission power would exponential grown by distance. So, we usually hope to control the topology in advance so that each node covers a limited number neighboring nodes [12]. For this reason, the restricted consideration for P is quite reasonable. Kann [11] also show that for d-regular graph, MIDP is approximable within (d+1)/2. As a sequel, TIP can also be approximable within (d+1)/2. V. CONCLUSION In this paper, we have studied the optimization model for the hybrid scheme of channel assignment problem on MCMR-WMNs. We have discussed and formulated the feasibility of an assignment into a set of necessary as well as sufficient constraints. To optimize the link layer performance, we have introduced an objective function AIS. A small AIS means that less interferences will be caused by an arbitrary transmission. We also show that TIP, a special case of AISP, is APX-complete for topology with bounded degree. For the future research, it would be worth to investigate the optimization mode for the network layer performance measurement for the hybrid scheme. Besides, an efficient algorithm or distributed protocol for the hybrid channel assignment is attractive. In addition, whether the general problem AISP is also APX-complete or NPO-complete should be verified further. ACKNOWLEDGEMENT This research was supported in part by Intel and in part by the National Science Council of the ROC, under grant NSC 93-2752-E-009-005-PAE REFERENCES [1]. I. F. Akyildiz and X. Wang, Weilin, “wireless mesh networks: a suvery,” Computer Network, vol. 47, pp. 445-487, 2005. [2]. A. Raniwala, K. Gopalan, and T. C. Chiueh,. [3].. [4].. [5].. [6].. [7].. [8].. [9].. [10].. [11].. [12].. [13].. “Centralized channel assignment and routing algorithm for multi-channel wireless mesh networks,” ACM Mobile Computing and Communications Review (MC2R), vol. 8(2), pp. 50-55, 2004. P. Kyasanur and N.H. Vaidya, “Routing and interface assignment in multi-channel multi-interface wireless networks,” IEEE Communications Society WCNC, pp. 2051-2056, 2005. R. Draves, J. Padhye, and B. Zill, “Routing in multi-radio, multi-hop wireless mesh networks,” ACM Mobicom, 2004. A.K. Das, H.M.K Alazemi, R. Vijayakumar and S. Roy, “Optimization models for fixed channel assignment in wireless mesh networks with multiple radios,” IEEE SECON, 2005. M. Alicherry, R. Bhatia, and L. Li, “Join channel assignment and routing for throughput optimization in multi-radio wireless mesh networks”, ACM MobiCom, 2005. P. Kyasanur, and N.H. Vaidya, “Capacity of multi-channel wireless networks: Impact of number of channels and interfaces,” ACM MobiCom, 2005. J. Tang, G. Xue, and W. Zhang, “Interference-aware topology control and QoS routing in multi-channel wireless Mesh networks,” ACM MobiCom, 2005. M. Kodialam, and T. Nandagopal, “Characterizing the capacity region in multi-radio multi-channel wireless mesh networks,” ACM MobiCom, 2005. M. M. Halldorsson, “Approximating the minimum maximal independence number,” Information Process Letters, 46(4), pp. 169-172, 1993. V. Kann, “On the approximability of NP-complete optimization problems,” Ph.D. thesis, Department of Numerical Analysis, Royal Institute of Technology, Stockholm, 1992. A.A.K Jeng and R.H. Jan, “r-neighborhood graph: A novel structure for topology control in wireless ad hoc network,” unpublished. M.R. Garey and D.S. Johnson, Computers and intractability: A guide to the theory of NP-completeness. Freeman, San Francisco, 1979..

(26) The r - Neighborhood Graph: An Adjustable Structure for Topology Control in Wireless Ad hoc Networks # Andy An-Kai Jeng and Rong-Hong Jan * Department of Computer and Information Science, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, 300, Taiwan, R.O.C. {andyjeng, rhjan}@cis.nctu.edu.tw. Abstract: In wireless ad hoc networks, constructing and maintaining a topology with lower nodes degrees is usually intended to mitigate excessive traffic load on wireless nodes. However, keeping lower nodes degrees often prevents nodes from choosing better routes that consume less energy. Therefore, a tradeoff is between the node degree and the energy efficiency. In this paper, an adjustable structure, named the r-neighborhood graph, is proposed to control the topology. This structure has the flexibility to be adjusted between the two objectives through a parameter r, 0 ≤ r ≤ 1. More explicitly, for any set of n nodes, the maximum node degree and power stretch factor can be bounded from above by some decreasing and increasing functions of r, respectively. Specifically, the bounds can be constants in some ranges of r. Even more, the r-neighborhood graph is a general structure of both RNG and GG, two well-known structures in topology control. Compared with YGk, another famous adjustable structure, our method can always results a connected planar with symmetric edges. To construct this structure, we investigate a localized algorithm, named PLA, consuming less transmitting power during construction and execute efficiently in O(nlogn) time.. #. This research was supported in part by the National Science Council, Taiwan, under Grant NSC 94-2219-E-009-005 and NSC 94-2752-E-009-005-PAE, in part by the communication software technology of III, Taiwain, and in part by the Intel. * Corresponding author: Tel: +886-3-5712121 ext.31539. 1.

(27) Index Terms: Wireless ad hoc networks, topology control, energy-efficient, localized algorithm.. I. Introduction Wireless ad hoc networks enhance the conventional deployment of communicating environments for many applications, such as conferences, hospitals, battlefields, search and rescue teams, etc. In these environments, the performance of network operations heavily depends upon the underlying topology [4]. For instance, the delivery rate would be significantly lower down as the underlying topology breaks. Therefore, appropriately controlling the topology is a crucial stage in communication. The topology control problem in wireless ad hoc networks has been widely studied in recent years [3, 15, 18, 19, 20, 23, 29, 32]. Generally speaking, the core of this problem is to determine set of wireless links such that the composed topology is able to achieve certain goals [23]. These goals would be variant depending upon the circumstances and could be either qualitative features or quantitative objectives. Since wireless nodes usually struggle with limited bandwidth and computation power, a genius way should be able to simultaneously achieve several goals. In this paper, we aim to control the topology with the following goals which are extremely desired in wireless environments. 1. Symmetry: The existence of asymmetric links may complicate many communication primitives. For instance, the MAC layer’s ACK is hard to implement when some links are not bidirectional [21]. Besides, asymmetric links in topology would also cause inconsistent routing qualities at two ends. 2. Connectivity: Connectivity is unquestionably the most essential prerequisite in any communicable topology [23]. Two nodes u and v are strongly connected if there is a directed path from u to v and vice versa. A directed topology is strongly connected if all pairs of nodes are strongly connected. If the links are symmetric, we should aim at the connectivity of an undirected topology instead. 3. Energy efficiency: Energy is the most crucial resource in wireless nodes. Due to the severe path loss in radio carriers, transmitting with large ranges would exponentially run out of nodes’ energy. Therefore, relaying messages through multiple hops with shorter ranges could usually consume less energy [24].How to choice the links between nodes for relaying is a 2.