JP3730194B2 - Array antenna control method, reception signal signal-to-noise ratio calculation method, and radio receiver adaptive control method - Google Patents

Description

【００２４】
エスパアンテナ装置１００の構造は巡回的な対称性を有しているため、この行列Ｚの４９個の要素のうち独立な要素は６個の要素となる。これらはその物理的意味からそれぞれ以下のように呼ばれるべき複素パラメータである。
【００２５】
【表１】
―――――――――――――――――――――――――――――――――――
ｚ_００：励振素子の自己入力インピーダンス
ｚ_０１：励振素子と非励振素子との間の結合インピーダンス
ｚ_１１：非励振素子の自己入力インピーダンス
ｚ_１２：互いに隣接する２つの非励振素子間の結合インピーダンス
ｚ_１３：次に隣接する（１つ間をおいて隣接する）２つの非励振素子間の結合インピーダンス
ｚ_１４：互いに対向する２つの非励振素子間の結合インピーダンス
―――――――――――――――――――――――――――――――――――
【００２６】
なお、後述する実施例で用いた各インピーダンス値は以下の通りである。
（ａ）ｚ_００＝＋５２．０−５．７ｊ
（ｂ）ｚ_０１＝＋２３．９−２９．２ｊ
（ｃ）ｚ_１１＝＋６４．０−３．４ｊ
（ｄ）ｚ_２１＝＋２９．７−２９．８ｊ
（ｅ）ｚ_３１＝−１３．９−２７．６ｊ
（ｆ）ｚ_４１＝−２６．０−１６．７ｊ
ここで、インピーダンス値の単位は全てΩである。バラクタダイオードであるリアクタンス素子１２−１乃至１２−６のリアクタンス値をｘ_１，ｘ_２，…，ｘ_６とすると、エスパアンテナ装置１００の指向性（アレーファクタ）Ｄ_ａ（θ，φ）は次式で表される（例えば、従来技術文献２参照）。
【００２７】
【数２】
Ｄ_ａ（θ，φ）
＝ａ（θ，φ）^Ｔｉ（ｘ_１，ｘ_２，…，ｘ_６）
【００２８】
ここで、ａ（θ，φ）は、エスパアンテナ装置１００の位相中心を中央の非励振素子Ａ０にとった場合のステアリングベクトルであり、仰角θと方位角φの関数として次式で表される。
【００２９】
【数３】

【００３０】
ここで、ｄは半径ｒに等しい素子間隔であり、βは自由空間中の伝播定数である。また、ｉ（ｘ_１，ｘ_２，…，ｘ_６）はエスパアンテナの等価ウエイトベクトルであり、次式で表される。
【数４】
ｉ（ｘ_１，ｘ_２，…，ｘ_６）
＝Ｚ^−１（ｖ_ｓｕ_０−Ｘｉ）
＝ｖ_Ｓ（Ｚ＋Ｘ）^−１ｕ_０
ここで、ｕ_０は次式で表される単位ベクトルである。
【数５】
ｕ_０＝［１，０，…，０］^Ｔ
また、Ｘは、ＲＦ受信機の入力インピーダンスｚ_ｓと可変リアクタンス素子１２−１乃至１２−６のリアクタンス値を成分とする次式の対角行列であるリアクタンス行列である。
【数６】
Ｘ＝ｄｉａｇ［ｚ_ｓ，ｊｘ_１，ｊｘ_２，…，ｊｘ_６］
【００３１】
従って、エスパアンテナ装置１００の指向性（アレーファクタ）Ｄ_ａ（θ，φ）は次式で表される。
【数７】
Ｄ_ａ（θ，φ）
＝ｚ_ｓａ(θ，φ)^Ｔ｛Ｚ＋ｄｉａｇ[ｚ_ｓ，ｊｘ_１，ｊｘ_２，・・・，ｊｘ_６]｝^−１ｕ_０
【００３２】
複数の信号波が到来する場合にはそれらの信号波形を成分とするベクトル
【数８】
ｓ（ｔ）＝［ｓ_１（ｔ），ｓ_２（ｔ），…，ｓ_Ｋ（ｔ）］
を定義する。ここで、Ｋは信号の数である。これらを同時に受信した場合のエスパアンテナ装置１００の出力信号は次式で表される。
【数９】
ｙ（ｔ）＝ｉ（ｘ_１，ｘ_２，…，ｘ_６）^ＴＡ（θ，Φ）ｓ（ｔ）＋ｎ（ｔ）
ここで、Ａ（θ，Φ）はアレーマニホールドであり、次式で表される。
【数１０】
Ａ（Θ，Φ）
＝［ａ（θ_１，φ_１），ａ（θ_２，φ_２），…，ａ（θ_Ｋ，φ_Ｋ）］
ここで、
【数１１】
Θ＝｛θ_１，θ_２，…，θ_Ｋ｝
【数１２】
Φ＝｛φ_１，φ_２，…，φ_Ｋ｝
であり、ｎ（ｔ）は加算的雑音波形である。
【００３３】
従って、エスパアンテナ装置１００の受信信号ｙ（ｔ）は次式で表される。
【数１３】

【００３４】
ここで、ｓ_ｋ（ｔ）とθ_ｋ，φ_ｋはそれぞれ、第ｋ番目の信号の時間波形と、到来方向である。
【００３５】
次いで、本実施形態で用いる「ブラインド適応ビーム形成」について説明する。適応ビーム形成の目的は上記数１３で導出したアンテナ受信出力信号ｙ（ｔ）に含まれる信号対干渉雑音の電力比ＳＩＮＲを最大化することである。ブラインド制御とは所望波に含まれる信号情報を全く参照することなくアンテナ可変パラメータ（一般的にはウエイトベクトル：ここでは、可変リアクタンス素子１２−１乃至１２−６のリアクタンス値）を更新することである。
【００３６】
適応的にビームを形成するためには、（１）送信パケットのヘッダに参照信号を含ませておき、（２）受信側で予めこの参照信号系列を知っておき、（３）参照信号の同期タイミングを検出して、（４）アレーの重み係数をトレーニングする、というプロセスが通常用いられる。例えばエスパアンテナ装置１００の適応ビーム形成法として受信信号と参照信号との相互相関係数を最大化するアルゴリズム「ＭＣＣＣ：Maximum Cross Correlation Coefficient」がある（例えば、従来技術文献３「神谷ほか，“エスパアンテナの基本検討：適応制御に基づくＳＩＲ特性の統計的規範”，電子情報通信学会技術報告，ＡＰ２０００−１７５，ＳＡＮＥ２０００−１５６，ｐｐ．１７−２４，２００１年１月」参照。）。これに対して、ブラインド適応ビーム形成とは参照信号なしで適応的にビームを形成する機能であり、上記（１）〜（３）のプロセスを省略することができる。
【００３７】
本実施形態においては、ｍ相ＰＳＫ変調信号に特有の性質に着目し、これを利用したブラインド規範を提案する。ここで着目する性質とは、「ｍ相ＰＳＫ変調信号は変調データに関わらずこれをｍ乗すると一定の複素数値となる」ことである。通信路で雑音あるいは干渉を被るとこの一定の複素数値からのゆらぎが受信側で観測される。このゆらぎが小さいほど所望信号が高い純度で抽出できていると考えられる。そこで、上述のごとく導出した受信アンテナの出力信号の第ｍ次モーメントを最大化すること、すなわち、次式を規範関数とすることを提案する。
【００３８】
【数１４】

【００３９】
ここで、Ｅ［・］は引数・のアンサンブル平均（所定の時間における平均値）を表す。分母はｍ乗された信号の平均電力を表している。規範関数Ｊ｛ｙ（ｔ）^ｍ｝の物理的解釈は後述の補足説明で述べる。この規範関数の利点は、上述の「一定の複素数値」を含んでいないことである。すなわち、この値を受信側で予め知っている必要が無い。このことは、アンテナ及び受信回路系の絶対利得や固定的な位相回転量に左右されないことを意味しており、実際の無線システムに用いる際の重要な利点である。上式で表されるように複素信号の第ｍ次モーメントを最大化する規範をここでは「ＭＭＣ:Maximum Moment Criterion」と呼ぶこととする。
【００４０】
次いで、上記規範関数を用いた適応ビーム形成について説明する。「適応ビーム形成」とは、上記数１３で導出した、エスパアンテナ装置１００の受信信号ｙ（ｔ）に含まれる信号対干渉雑音電力比ＳＩＮＲ＝Ｓ／（Ｎ＋Ｉ）を最大化するようにアンテナ可変パラメータ（エスパアンテナ装置１００では各可変リアクタンス素子１２−１乃至１２−６のリアクタンス値）を更新することである。上述の規範関数に基づいてリアクタンス値を反復更新することにより、アンテナ指向性が出力ＳＩＮＲ最大となる最適ビームパターンすなわち所望波の方向へメインビームが形成され干渉波の方向へヌルが形成されるビームパターンとなる。
【００４１】
すなわち、上記規範関数Ｊには目標値Ｃが含まれておらず、受信信号ｙ（ｔ）のみであって、しかも受信信号のｍ乗｛ｙ（ｔ）^ｍ｝を用いて表されて記述されている。この場合、目標値が未知の状態で制御できることが大きなメリットである。この規範に基づいてリアクタンス値を、例えば最急勾配法などの非線形計画法における反復的な数値解法を用いて反復更新することにより、アンテナ出力の信号対干渉雑音電力比（ＳＩＮＲ）が最大となるように、すなわち、エスパアンテナ装置１００の主ビームを所望波の方向に向けかつ干渉波の方向にヌルを向けるように最適ビームが形成される。
【００４２】
次いで、最急勾配法を用いたアンテナビームの適応制御について説明する。最急勾配法を用いるときの可変リアクタンス素子１２−１乃至１２−６のリアクタンス値のセット（リアクタンスベクトル）ｘに対する漸化式は次式で表される。
【００４３】
【数１５】
ｘ（ｎ＋１）＝ｘ（ｎ）＋μ∇Ｊｎ
【数１６】

【００４４】
ここで、ｎはｘの更新の次数、パラメータμは試行錯誤的に定められるステップサイズである。ここで、最急勾配法は、最急降下法を含む方法の概念であるが、本実施形態では、規範関数の値を最大するように最適解を求める方法を用いる。
【００４５】
さらに、最急勾配法による具体的な、最適解を求める手順について説明する。上記数１５を用いた最急勾配法によって規範関数Ｊｎを可能な限り大きくするような良好なリアクタンスベクトルｘを発見するためには、以下の手順を用いる。
（ｉ）最初に、反復数パラメータｎ（すなわち、ｎ回目の反復）を１に設定し、予め決められたリアクタンスベクトルの初期値ｘ（１）（例えば、当該エスパアンテナ装置１００をオムニアンテナに設定にするときのリアクタンスベクトル）によって処理を開始する。
（ｉｉ）次いで、この初期値（ｎ＝１のとき）又は現在の推定値（ｎ≧２のとき）を使用して、反復数パラメータｎ（すなわち、ｎ回目の反復）における規範関数Ｊｎの勾配ベクトル∇Ｊｎを計算する。
（ｉｉｉ）勾配ベクトル∇Ｊｎの方向と同一の方向に初期値又は現在の推定値を変更することで、リアクタンスベクトルｘにおける次の推定値を計算する。
（ｉｖ）反復数パラメータｎを１だけインクリメントし、ステップ（ｉｉ）に戻って処理を繰り返す。この繰り返し処理は、リアクタンスベクトルｘが実質的に収束する反復数まで実行される。
【００４６】
図４は、図１の適応制御型コントローラ２０によって実行される、最急勾配法によるより具体的な適応制御処理を示すフローチャートである。
【００４７】
図４のステップＳ１において、まず、反復数パラメータｎを１にリセットし、リアクタンスベクトルｘ（１）にその初期値を設定挿入し、ステップＳ２において素子パラメータｋを１にリセットする。次いで、ステップＳ３において受信信号ｙ（ｔ）を測定し、ステップＳ４において数１４を用いて規範関数Ｊの値を計算し、Ｊ^（０）に設定挿入する。さらに、ステップＳ５においてリアクタンス値ｘ_ｋに所定の摂動値Δｘ_ｋを加算し、その加算値をリアクタンス値ｘ_ｋとして設定した後、ステップＳ６において受信信号ｙ（ｔ）を測定し、ステップＳ７において数１４を用いて規範関数Ｊの値を計算する。そして、ステップＳ８においてＪ−Ｊ^（０）の値を計算して∂Ｊｎ／∂ｘ_ｋに代入し、ステップＳ９においてリアクタンス値ｘ_ｋに所定の摂動値Δｘ_ｋを減算しその減算値をリアクタンス値ｘ_ｋとして設定することにより摂動前の値に戻した後、ステップＳ１０において素子パラメータｋはＫ（＝６）以上であるか否かが判断される。ステップＳ１０でＮＯであれば、ステップＳ１１で素子パラメータｋを１だけインクリメントしてステップＳ５に戻り、上述の処理を繰り返す。一方、ステップＳ１０でＹＥＳであるときは、ステップＳ１２において、数１５の漸化式を用いて、リアクタンスベクトルｘの次の推定値ｘ（ｎ＋１）を計算した後、ステップＳ１３において反復数パラメータｎが所定の反復数Ｎに到達しているか否かを判断し、ＮＯであれば、ステップＳ１４において反復数パラメータｎを１だけインクリメントした後、ステップＳ２からの処理を繰り返す。一方、ステップＳ１３でＹＥＳであるときは、十分に収束しているものと判断し、計算されたリアクタンスベクトルｘの値を有するリアクタンス値信号を可変リアクタンス素子１２−１乃至１２−６に出力して設定する。
【００４８】
以上説明したように、本実施形態によれば、適応制御型コントローラ２０は、エスパアンテナ装置１００の励振素子Ａ０によって受信された受信信号ｙ（ｔ）に基づいて、非線形計画法における反復的な数値解法である、例えば、最急勾配法を用いて、上記受信信号ｙ（ｔ）のみであって受信信号ｙ（ｔ）のｍ乗を用いて表された規範関数（数１４）の値が最大となるように、上記エスパアンテナ装置１００の主ビームを所望波の方向に向けかつ干渉の方向にヌルを向けるための各可変リアクタンス素子１２−１乃至１２−６のリアクタンス値を計算して設定する。従って、参照信号を必要とせずに、アレーアンテナの指向性を所望波の方向に主ビームを向けかつ干渉波の方向にヌルを向けるように適応制御することができる。ここで、参照信号を必要としないので、当該装置の構成を簡単化できる。また、規範関数Ｊは受信信号ｙ（ｔ）のみで記述されているので、適応制御コントローラ２０の計算処理をきわめて簡単に実行できる。
【００４９】
以上の実施形態においては、６本の非励振素子Ａ１乃至Ａ６を用いているが、その本数は少なくとも複数本あれば、当該アレーアンテナ装置の指向特性を電子的に制御することができる。それに代わって、６個よりも多くの非励振素子を備えてもよい。また、非励振素子Ａ１乃至Ａ６の配置形状も上記の実施形態に限定されず、励振素子Ａ０から所定の距離だけ離れていればよい。すなわち、各非励振素子Ａ１乃至Ａ６に対する間隔は一定でなくてもよい。
【００５０】
以上の実施形態においては、最急勾配法を用いて各可変リアクタンス素子１２のリアクタンス値を計算しているが、本発明はこれに限らず、以下に示す順次ランダム法、ランダム法、高次元二分法などの非線形計画法における反復的な数値解法を用いてもよい。
【００５１】
なお、順次ランダム法においては、以下の手順を用いる。
（ｉ）最初に、反復数パラメータｎ（すなわち、ｎ回目の反復）を１に設定し、リアクタンスベクトルの所定の初期値ｘ（１）（例えば、当該エスパアンテナ装置１００をオムニアンテナに設定にするときのリアクタンスベクトル）によって処理を開始する。
（ｉｉ）次いで、この初期値（ｎ＝１のとき）又は現在の推定値（ｎ≧２のとき）を使用して、反復数パラメータｎ（すなわち、ｎ回目の反復）における推定値への加算値を所定の存在範囲内で乱数を発生させて計算する。
（ｉｉｉ）計算された加算値を上記推定値に加算することにより、リアクタンスベクトルにおける次の推定値を計算する。
（ｉｖ）反復数パラメータｎを１だけインクリメントし、ステップ（ｉｉ）に戻って処理を繰り返す。この繰り返し処理は、規範関数Ｊの値が所定のしきい値（例えば０．９）以上になるまで実行される。
【００５２】
また、ランダム法においては、以下の手順を用いる。
（ｉ）最初に、リアクタンスベクトルの所定の初期値ｘ（１）（例えば、当該エスパアンテナ装置１００をオムニアンテナに設定にするときのリアクタンスベクトル）によって処理を開始する。
（ｉｉ）次いで、この初期値を使用して、当該初期値への加算値を所定の存在範囲内で乱数を発生させて計算する。
（ｉｉｉ）計算された加算値を上記初期値に加算することにより、リアクタンスベクトルにおける推定値を計算する。
（ｉｖ）計算された推定値における規範関数Ｊの値が所定のしきい値（例えば０．９）以上であれば、当該推定値を設定すべきリアクタンスベクトルとするが、ＮＯであれば、ステップ（ｉｉ）に戻って処理を繰り返す。
【００５３】
さらに、高次元二分法においては、以下の手順を用いる。
（ｉ）最初に、反復数パラメータｎ（すなわち、ｎ回目の反復）を１に設定して処理を開始する。
（ｉｉ）次いで、リアクタンスベクトルの各リアクタンス値の所定の存在範囲（なお、２回目以降は、前に選択された推定値の存在範囲）を均等に二分し、二分された各存在範囲の平均値（各可変リアクタンス素子１２−１乃至１２−６に対して２つの平均値）を計算する。
（ｉｉｉ）この２つの平均値に対する規範関数Ｊの値を計算し、規範関数Ｊの値が大きい方を、リアクタンスベクトルにおける次の推定値とする。
（ｉｖ）反復数パラメータｎを１だけインクリメントし、ステップ（ｉｉ）に戻って処理を繰り返す。この繰り返し処理は、規範関数Ｊの値が所定のしきい値（例えば０．９）以上になるまで実行される。
【００５４】
以上の実施形態においては、規範関数Ｊを適応制御のためのリアクタンス値を求めるための規範関数とし、それを最大となるようにリアクタンスベクトルの最適解を計算しているが、本発明はこれに限らず、規範関数Ｊの逆数を適応制御のためのリアクタンス値を求めるための規範関数とし、それを最小となるようにリアクタンスベクトルの最適解を計算してもよい。
【００５５】
以上の実施形態においては、６本の非励振素子Ａ１乃至Ａ６と、それに対応した可変リアクタンス素子１２−１乃至１２−６とを備えているが、本発明はこれに限らず、少なくとも１つの非励振素子Ａ１と、それに対応した可変リアクタンス素子１２−１を備えてもよい。また、それぞれの個数は複数でもよい。
【００５６】
＜第２の実施形態＞
図５は、本発明に係る第２の実施形態であるアレーアンテナの制御装置の構成を示すブロック図である。
【００５７】
この実施形態では、アレーアンテナ５０の各アンテナ素子５１−１乃至５１−Ｐで受信した信号を、可変移相器５３−１乃至５３−Ｐと加算器である合成器５４によって構成されたＲＦ帯のＢＦＮ(Beam Forming Network)回路で合成する構成を採用し、このアレーアンテナの制御装置は、複数Ｐ個のアンテナ素子５１−１乃至５１−Ｐが互いに所定の間隔で配置されてなるアレーアンテナ５０（例えば、リニアアレーであり、２次元形状又は３次元形状で配置されてもよい。）のビームを制御するための適応制御型制御装置であり、適応制御型コントローラ６０を備えたことを特徴としている。ここで、送信された無線信号はｍ相ＰＳＫ変調され（ｍは２以上の整数である。）、適応制御型コントローラ６０は、合成後の受信信号に基づいて、非線形計画法における反復的な数値解法である、例えば、最急勾配法を用いて、上記受信信号ｙ（ｔ）のｍ乗を用いて表された規範関数（数１４）の値が最大となるように、当該アレーアンテナ５０の主ビームを所望波の方向に向けかつ干渉の方向にヌルを向けるための可変移相器５３−１乃至５３−Ｐの移相量に対応する各移相制御電圧ｖ_ｐ（ｐ＝１，２，…，Ｐ）を計算して設定することを特徴としている。
【００５８】
以下、図５に示すアレーアンテナの制御装置の構成について説明する。図５において、複数Ｐ個のアンテナ素子５１−１乃至５１−Ｐが互いに所定の間隔で１直線上に並置されてなるアレーアンテナ５０によって無線信号が受信され、各アンテナ素子５１−１乃至５１−Ｐで受信された無線信号はそれぞれ、低雑音増幅器（ＬＮＡ）５２−１乃至５２−Ｐを介して可変移相器５３−１乃至５３−Ｐに入力される。各可変移相器５３−１乃至５３−Ｐはそれぞれ、入力される無線信号を、適応制御型コントローラ６０から出力される各移相制御電圧ｖ_ｐ（ｐ＝１，２，…，Ｐ）に対応した各移相量だけ移相した後、合成器５４に出力する。合成器５４は入力されるＰ個の無線信号を電力合成して、合成後の無線信号を、受信信号ｙ（ｔ）として図１の無線受信機１０と同様の構成を有する無線受信機１０に出力する。
【００５９】
次いで、無線受信機１０は、入力される合成された受信信号ｙ（ｔ）に基づいて、図１の無線受信機１０と同様に、互いに直交した受信信号からの２つのデジタルベースバンド信号を得て、適応制御型コントローラ６０に出力する。適応制御型コントローラ６０は、入力される２つのデジタルベースバンド信号に基づいて、非線形計画法における反復的な数値解法である、例えば、最急勾配法を用いて、図４の適応制御処理と同様の処理を実行することにより、上記受信信号ｙ（ｔ）のみであって受信信号ｙ（ｔ）のｍ乗を用いて表された規範関数（数１４）の値が最大となるように、当該アレーアンテナ５０の主ビームを所望波の方向に向けかつ干渉の方向にヌルを向けるための可変移相器５３−１乃至５３−Ｐの移相量に対応する各移相制御電圧ｖ_ｐ（ｐ＝１，２，…，Ｐ）を計算し、それを可変移相器５３−１乃至５３−Ｐに印加することにより対応する各移相量を設定する。
【００６０】
この実施形態に係る適応制御型コントローラ６０においても、第１の実施形態に係る適応制御型コントローラ２０と同様に、参照信号を必要とせずに、アレーアンテナの指向性を所望波の方向に主ビームを向けかつ干渉波の方向にヌルを向けるように適応制御することができる。ここで、参照信号を必要としないので、当該装置の構成を簡単化できる。また、規範関数Ｊは受信信号ｙ（ｔ）のみで記述されているので、適応制御コントローラ６０の計算処理をきわめて簡単に実行できる。
【００６１】
以上の実施形態においては、最急勾配法を用いて各可変移相器５３−１乃至５３−Ｐの移相量に対応する移相制御電圧ｖ_ｐを計算しているが、本発明はこれに限らず、上述の順次ランダム法、ランダム法、高次元二分法などの非線形計画法における反復的な数値解法を用いてもよい。また、規範関数Ｊはその逆数を用いてもよい。
【００６２】
【実施例】
図６は、図１のエスパアンテナ装置１００を用いて実行された、ブラインド適応ビーム形成のシミュレーションのフローを示す図である。このシミュレーションでは、上述の定式化モデルと同様に、非励振素子Ａ０として半波長ダイポールアンテナを用い、非励振素子Ａ１乃至Ａ６として円形アレー配列された６本のダイポールアンテナを用いる。また、エスパアンテナ装置１００に到来する所望波と干渉波の到来方向は未知（適応制御）とし、トレーニング信号も用いないこと（ブラインド処理）とする。
【００６３】
図６のシミュレーションフローにおいては、干渉波ステアリングベクトル、所望波ステアリングベクトル、アンテナ構造のパラメータ、到来波信号、及び雑音に基づいて、ステップＳＳ１乃至ＳＳ５の処理を行うことにより当該アンテナビームの適応制御を行い、最後に、指向性アレーファクタ及び出力ＳＩＮＲを計算して出力する（ステップＳＳ６，ＳＳ７）。このステップＳＳ１乃至ＳＳ７の処理では、受信信号ｙ（ｔ）を受信し（ステップＳＳ１）、受信された受信信号ｙ（ｔ）に基づいて規範関数Ｊ｛ｙ（ｔ）^ｍ｝を計算し（ステップＳＳ２）、リアクタンス行列の更新を行って（ステップＳＳ３）リアクタンス行列を計算した後（ステップＳＳ４）、等価ウエイトベクトルを計算する（ステップＳＳ５）。そして、等価ウエイトベクトルから指向性アレーファクタを計算する（ステップＳＳ６）一方、受信信号ｙ（ｔ）と雑音ｎ（ｔ）とから出力ＳＩＮＲを計算している（ステップＳＳ７）。
【００６４】
このシミュレーションにおいては、エスパアンテナ装置１００に到来する所望波と干渉波の到来方向は未知（適応制御）とし、トレーニング信号も用いないこと（ブラインド処理）とする。所望波に加えて干渉波も同時に到来する環境でシミュレーションする。所望波、干渉波ともにＱＰＳＫランダム変調信号、雑音は加算的ガウス雑音とする。これら所望波、干渉波、雑音は相互に無相関とする。簡単のため伝送路における帯域制限フィルタ、遅延広がり、角度広がり、フェージング、ドップラ効果、同期誤差を全て無視する。この条件下で、上述した規範関数に基づいて６個の可変リアクタンス素子１２−１乃至１２−６のリアクタンス値を制御する。シミュレーションに用いたアンテナ構造パラメータは、被制御素子数：６、素子間隔：全て１／４波長、各ダイポール半径：１／１００波長、素子の長さ方向の波長短縮率：０．９２６とした。また、エスパアンテナ装置１００に接続されるＲＦ送受信機の内部インピーダンスはｚ_ｓ＝５０Ωとする。最適化アルゴリズムとしては、純粋ランダム探索法、最急勾配法、高次元二分法、順次ランダム法、回帰ステップ法、ハミルトン力学による方法などの候補があるが、ここでは最急勾配法を用いた計算例を示す。
【００６５】
所望波Ｄ及び干渉波Ｉのレベルはそれぞれ＋６ｄＢｎ、０ｄＢｎ（ｄＢｎは雑音レベルを基準とした電力表示である。）とする。所望波Ｄの到来方位角を０°に固定し、干渉波Ｉの到来方位角が４５°、９０°、１３５°、１８０°とした場合の可変リアクタンス素子の制御結果と指向性パターン（電力パターン）をそれぞれ図７乃至図１０に示す。ポーラチャート周上の記号Ｄ及びＩはそれぞれ所望波と干渉波の到来方位を示す。図７乃至図１０から明らかなように、４つのパターンともほぼ所望波Ｄの到来方向へ主ビームが形成されると同時に干渉波Ｉの方向に深いヌル点が形成されていることがわかる。
【００６６】
以上説明したように、本実施形態によれば、エスパアンテナ装置１００はハードウエア構成が簡単であるにもかかわらず、適切な規範と帰還制御によりブラインドビーム形成が可能であるということをｍ相ＰＳＫ波受信の場合について示した。
【００６７】
以上の実施形態においては、上記数１４の規範関数を用いているが、上記数１４における時間平均Ｅ（・）は、例えば周波数分割多重方式で送信されたデータ信号を一時に受信して並列処理する場合に、例えば１シンボルなどの所定の期間において複数のデータ信号についての平均値であってもよい。
【００６８】
＜補足説明＞
当該補足説明において、ＢＰＳＫ変調信号における規範関数Ｊ｛ｙ（ｔ）^ｍ｝の物理的意味について以下に説明する。
【００６９】
送信信号ｘに雑音ｎが加わり、受信信号ｙ（ｔ）は次式で表されるものとする。
【数１７】
ｙ（ｔ）＝ｘ（ｔ）＋ｎ（ｔ）
【００７０】
ここで、ｎ（ｔ）は熱雑音あるいは多数の干渉波がランダム振幅かつランダム位相に重畳された波形であるとする。これら時間波形信号ｙ（ｔ）、ｘ（ｔ）、ｎ（ｔ）のある標本化時刻での値をそれぞれｙ、ｘ、ｎと書くこととする。また、送受信信号に直流オフセットはないとする。実際の無線受信機１０では直流オフセットが発生することがあるが、受信信号の直流オフセット値はその平均値（期待値）Ｅ[ｙ]が可観測量なのでこれを受信信号から差し引いた値を改めて受信信号とみなすことによりゼロ化することができる。すなわち、次式としても一般性を失わない。
【００７１】
【数１８】
Ｅ[ｙ]＝０
【数１９】
Ｅ[ｘ]＝０
【数２０】
Ｅ[ｎ]＝０
【００７２】
上記数１７をＢＰＳＫ（ｍ＝２）変調信号に対する規範関数Ｊ（ｙ^２）に代入すると次式を得る。
【００７３】
【数２１】

【００７４】
上記式の分子の中の第２項は、送信信号ｘと雑音ｎが互い無相関なので、次式のようになる。
【００７５】
【数２２】
２Ｅ[ｘｎ]＝２Ｅ[ｘ]Ｅ[ｎ]＝０
【００７６】
また、同じく第３項は、雑音ｎの実部（Ｉチャンネル成分）と虚部（Ｑチャンネル成分）は等電力かつ互いに無相関なので、次式を得る。
【００７７】
【数２３】
Ｅ[ｎ^２]
＝Ｅ[（ｎ_ｒ＋ｊｎ_ｉ）^２]
＝Ｅ[ｎ_ｒ ^２]−Ｅ[ｎ_ｉ ^２]＋２ｊＥ[ｎ_ｒｎ_ｉ]
＝０
【００７８】
従って、上記数２１の分子は｜Ｅ[ｘ^２]｜^２の項だけとなる。次に、上記数２１の分母を展開すると次式のようになる。
【００７９】
【数２４】
Ｅ［｜ｙ^２｜^２］
＝Ｅ［｜ｘ｜^４］＋４Ｅ［｜ｘ｜^２｜ｎ｜^２］＋Ｅ［｜ｎ｜^４］
＋２Ｒｅ｛２Ｅ［２ｘ^２ｘ^＊ｎ^＊］＋２Ｅ［２ｘｎｎ^２＊］＋Ｅ［ｘ^２ｎ^２＊］｝
【００８０】
上記式において、Ｒｅ（・）は引数の実数部を表し、上付けの記号＊は複素共役を示し、以下同様である。これに上記数２２と上記数２３を用いると次式を得る。
【００８１】
【数２５】
Ｅ［｜ｙ^２｜^２］
＝Ｅ［｜ｘ｜^４］＋４Ｅ［｜ｘ｜^２]Ｅ[｜ｎ｜^２］＋Ｅ［｜ｎ｜^４］
＋２Ｒｅ｛４Ｅ［２ｘ^２ｘ^＊］Ｅ［ｎ^＊］＋４Ｅ［ｘ］Ｅ［ｎｎ^２＊］
＋Ｅ［ｘ^２］Ｅ［ｎ^２＊］｝
＝Ｅ［｜ｘ｜^４］＋４Ｅ［｜ｘ｜^２]Ｅ[｜ｎ｜^２］＋Ｅ［｜ｎ｜^４］
【００８２】
これらの式に登場する
【数２６】
Ｅ［｜ｘ｜^２］＝Ｓ
【数２７】
Ｅ[｜ｎ｜^２］＝Ｎ
はそれぞれ送信信号ｘ及び雑音ｎの平均電力を意味する。雑音の実部（Ｉチャンネル成分）と虚部（Ｑチャンネル成分）は互いに無相関であり、次式のごとく等電力となる。
【００８３】
【数２８】

【００８４】
送信信号ｘはＢＰＳＫ変調信号、すなわち
【数２９】
ｘ∈｛ａ，−ａ｝；ａは複素定数
であるので、その信号平均電力（所定の時間における）は次式で表される。
【数３０】
Ｓ＝Ｅ［｜ｘ｜^２］＝｜ａ｜^２
【００８５】
次いで、上記数２１の分子は、
【数３１】
｜Ｅ［ｘ^２］｜^２＝｜ａ｜^４＝Ｓ^２
となり、雑音ｎがガウス分布の場合、その実部と虚部もそれぞれ正規分布になる。これらに正規分布の４次中心モーメントの公式を適用すると次式を得る。
【００８６】
【数３２】

【００８７】
これを用いれば、上記数２５の末項は次式で表される。
【００８８】
【数３３】

【００８９】
上記数２６、数２７、数３０及び数３３を上記数２５に代入すると次式を得る。
【００９０】
【数３４】
Ｅ［｜ｙ^２｜^２］＝Ｓ^２＋４ＳＮ＋２Ｎ^２
【００９１】
上記数３１と、上記数３４を上記数２１に代入すると次式を得る。
【００９２】
【数３５】

【００９３】
これはＳＮ比のみの関数であり、かつ、単調増加であることを示している。以上で証明を終了する。
【００９４】
＜第３の実施形態＞
図１１は本発明に係る第３の実施形態であるアレーアンテナの制御装置の構成を示すブロック図である。本実施形態に係るアレーアンテナの制御装置は、図１の第１の実施形態に比較して以下の点が異なる。
（１）無線受信機１０に代えて、ｍ相ＰＳＫ信号を受信する無線受信機１０において波形等化器６−１，６−２をさらに備えた無線受信機１０ａを備えたこと。
（２）適応制御型コントローラ２０に代えて、適応制御型コントローラ２０において、上述の規範関数の値を計算し、計算された規範関数に基づいて上記規範関数と信号対雑音電力比との関係を示す式を用いて上記受信信号の信号対雑音電力比を計算し、上記計算された信号対雑音比が実質的に最大となるように波形等化器６−１，６−２を適応制御する適応制御型コントローラ２０ａを備えたこと。
【００９５】
図１１の詳細説明する前に、規範関数である汎関数の定義、及び信号対雑音電力比の計算方法について以下に説明する。
【００９６】
無線受信機において最適受信するために、可変の信号波形等化器や信号フィルタやリニアライザを適応フィードバック制御するには、信号対雑音比の推定が有力な手段となる。特に、トレーニング参照信号や信号レプリカを用いない、図１や図１１の無線受信装置においてはブラインド動作のＳＮ比推定技術を確立する必要がある。これまで、受信データの統計的期待値や分散を用いたブラインド推定関数が例えば、従来技術文献４「T. A. Summers et al., "SNR mismatch and online estimation in turbo decoding", IEEE Transaction on Communications, Vol. COM-46, No. 4, pp.421-423, April. 1998」、従来技術文献５「A. Ramesh et al, "SNR estimation in generalized fading channels and its application to turbo decoding", Proceeding of. IEEE ICC 2001, Helsinki, June 2001」及び従来技術文献６「滝沢ほか，“並列組合せＳＳ通信方式における通信路状態の推定方法に関する一検討（２）”，電子情報通信学会総合全国大会，Ａ−５−６，ｐｐ．１８８，２００２年３月」において提案されている。これらは変調方式としてＢＰＳＫを想定し、かつ、復調においては完全に同期検波が確立したものと仮定している。また、これらの従来技術文献４，５，６では、雑音は実数として扱われているため、雑音による位相ゆらぎが考慮されていない。
【００９７】
本実施形態ではより実用的な無線システムの観点から、多相ＰＳＫに適用でき、かつ、完全同期が確立していない「準同期」状態でも動作するブラインド推定法を提案する。まず、ｍ相ＰＳＫ変調に特有の性質に着目して、受信信号のｍ次モーメントに基づく汎関数を定義する。次に、複素ガウス雑音ならびに多相ＰＳＫ信号のモーメントを高次まで定式化する。これらを用いて本実施形態に係る関数が信号対雑音比の推定指標となることを解析的に示す。さらに、有限データ長の信号と加算的ガウス雑音が混在する系における本汎関数の統計的振舞を計算機シミュレーションにより示す。
【００９８】
まず、汎関数の定義について以下に説明する。ｍ相ＰＳＫ信号ｘ（ｔ）に雑音ｎ（ｔ）が付加され、ある標本化時刻ｔ＝ｔ_ｓで次式の複素数が観測されるとする。
【００９９】
【数３６】
ｓ（ｔ_ｓ）＋ｎ（ｔ_ｓ）＝ｙ（ｔ_ｓ）
【０１００】
ここで、ｍ相ＰＳＫ変調に特有の性質に着目し、これを利用した汎関数を提案する。ここで着目する性質とは、「ｍ相ＰＳＫ信号は変調データに関わらず、ｍ乗すると一定の複素数値となる」ということである。通信路で雑音あるいは干渉を被るとこの一定の複素数値からのゆらぎが受信側で観測される。このゆらぎが小さいほど信号対雑音比が高いと考えられる。そこで、上記の信号ｙ（ｔ_ｓ）を確率変数とみなして、そのｍ乗値のゆらぎの目安として、一定の複素数Ｃとの相互相関係数を採用することを提案する。一般に、二つの関数ｆ_１とｆ_２との相似性は次式の相互相関係数ρ｛ｆ_１，ｆ_２｝で記述される。
【０１０１】
【数３７】

【０１０２】
ここで、Ｅ［・］は所定の期間において変数・のアンサンブル平均（所定の時間における平均値）を計算する演算子を表す。この一般式で次式のようにおき、
【数３８】

かつ、その絶対値自乗をとった次式の汎関数を定義する。
【０１０３】
【数３９】

【０１０４】
この汎関数は受信信号のｍ乗値と任意定数Ｃとの相似性、すなわち、受信信号のｍ乗値がいかにゆらがずに一定値となっているかを示す指標である。また、この汎関数は受信信号の第ｍ次モーメントをｍ乗信号平均電力で正規化したものであるとも解釈できる。このことは、この汎関数がアンテナおよび受信回路系の絶対利得の経時変化や固定的な位相回転に対して不変量であることを意味しており、実際の無線システムに用いる際の重要な利点である。
【０１０５】
さらに、ＰＳＫ信号の高次モーメントについて説明する。ｍ相ＰＳＫ信号を準同期状態で標本化すると、次式の複素変数ｓが観測される。
【０１０６】
【数４０】

【数４１】

【０１０７】
ここで、ａ_ｏは初期振幅、φ_ｏは初期位相、ｄは情報データ、δは同期ずれによる周波数偏差である。ｓを確率変数とみなすと、その第ｋ次モーメントは次式のようになる。
【０１０８】
【数４２】

【０１０９】
ここで、準同期すなわち周波数偏差は平均化操作の時間Ｔに比べて小さいとしてδωの２次項以降は無視し、周波数変動と情報データは無相関であり、かつ、情報データｄが０からｍ−１までの一様分布であるとすると、次式を得る。
【０１１０】
【数４３】

【０１１１】
一方、絶対値についてはｍ値にかかわらず、
【数４４】
｜ｓ｜＝ａ_ｏ
絶対値の高次モーメントは単純に次式となる。
【０１１２】
【数４５】

【０１１３】
ここで、ＳはＰＳＫ信号の平均電力である。
【０１１４】
次いで、ガウス雑音の高次モーメントについて説明する。受信系で発生する熱雑音や多数の波がランダム振幅ランダム位相で重畳された信号はガウス雑音として取り扱うことができる。ＰＳＫ復調系においては、ガウス雑音の標本値を実部（Ｉチャンネル成分）と虚部（Ｑチャンネル成分）からなる複素数として扱う必要がある（なお、従来技術文献４及び５では雑音を実数として扱っている）。ここではこれを複素数として次式のように表現する。
【０１１５】
【数４６】

【０１１６】
ここで、雑音ｎに直流オフセットはなく、その平均電力をＮと書くこととする。実部と虚部は互いに等電力かつ直流バイアスゼロの正規分布である。すなわち、次式を得る。
【０１１７】
【数４７】

【０１１８】
次いで、正規分布の対称性から、その奇数次モーメントは全てゼロすなわち任意の正の整数ｐについて次式を得る。
【０１１９】
【数４８】

【０１２０】
ここで、実部ｎ_ｒと虚部ｎ_ｉに正規分布の偶数次モーメントの漸化式を適用すると次式が得られる。
【０１２１】
【数４９】

【０１２２】
ここで、実部ｎ_ｒと虚部ｎ_ｉは互いに独立であり、かつ、ゼロバイアスであるので、結合モーメントは次式で表される。
【０１２３】
【数５０】

【０１２４】
ガウス雑音は振幅と位相が独立であり、位相は０から２πまで一様に分布する。従ってそのモーメントは任意の次数ｐについて次式で表される。
【０１２５】
【数５１】

【０１２６】
一方、ガウス雑音の絶対値の偶数次モーメントについては上述の漸化式を活用して次式を得る。
【０１２７】
【数５２】

【０１２８】
この計算を繰り返すことにより次式を得る。
【０１２９】
【数５３】

【０１３０】
信号と雑音は互いに独立であること、並びに雑音の高次モーメントがゼロであることから、これらの高次結合モーメントも次式となる。
【０１３１】
【数５４】

【０１３２】
次いで，汎関数の振舞について以下に説明する、上述で定義した次式の汎関数の物理的意味について考察する。
【０１３３】
【数５５】

【０１３４】
以降、簡単のため時間因子（ｔ_ｓ）の記述を省略する。この式に次式を代入し、
【０１３５】
【数５６】
ｙ＝ｓ＋ｎ
分子と分母にわけて二項展開すると次式を得る。
【０１３６】
【数５７】

【０１３７】
上記式の絶対値の中の初項はｍ乗信号電力を意味する。また、当該式の中間項は信号と雑音の結合モーメントなのでゼロである。さらに、当該式の末項は雑音のモーメントであるのでやはりゼロである。結局、初項のみが残り、次式を得る。
【０１３８】
【数５８】

【０１３９】
次に、分母を二項展開すると次式となる。
【０１４０】
【数５９】

【０１４１】
これに、ｍ相ＰＳＫ信号ならびに雑音の高次モーメントを用いると次式を得る。
【０１４２】
【数６０】

【０１４３】
これらにより汎関数は次式で表される。
【０１４４】
【数６１】

【０１４５】
これはＳＮ比のみの関数であり、かつ、単調増加である。これで、この汎関数を用いることにより信号と雑音を分離することなくＳＮ比を推定することが示された。また、この汎関数は受信した信号ｙだけで定義されているので、送信信号レプリカを用いることなくブラインド的に動作する。
【０１４６】
具体例として信号の変調方式が、ＢＰＳＫ、ＴＰＳＫ、ＱＰＳＫの場合の汎関数は、上式でそれぞれ、ｍ＝２，３，４とおいて次式を得る。
【０１４７】
（１）ＢＰＳＫのとき
【数６２】

（２）ＴＰＳＫのとき
【数６３】

（３）ＱＰＳＫのとき
【数６４】

【０１４８】
これらの式は汎関数とＳＮ比との関係を示す式であり、受信信号レベルを検出することにより、数６１を用いて汎関数の値を計算し、当該汎関数の値を数６２、数６３又は数６４に代入することによりＳＮ比に関する高次方程式となり、これを例えば、ニュートン法などの方程式の数値解法を用いて解であるＳＮ比を計算できる。これらをＳＮ比の関数として描くと図１２の曲線で示すようになる。すなわち、図１２は図１１のアレーアンテナの制御装置において用いる、信号対雑音電力比に対する汎関数Ｊ_２｛ｙ（ｔ）｝，Ｊ_３｛ｙ（ｔ）｝Ｊ_４｛ｙ（ｔ）｝の理論値を示すグラフである。図１２から明かなように、信号対雑音電力比が増加するにつれて汎関数Ｊ_２｛ｙ（ｔ）｝，Ｊ_３｛ｙ（ｔ）｝Ｊ_４｛ｙ（ｔ）｝の理論値が短調増加していることがわかる。
【０１４９】
次いで，有限データ長信号に対するこの汎関数の振舞を計算機シミュレーションする。手順は以下の通りである。
（１）ｍ値の乱数データからｍ相ＰＳＫ信号系列を生成する。
（２）これをＩチャンネルとＱチャンネルとに分離する。
（３）無相関の実数ガウス雑音系列を各チャンネルに加算する。
（４）これらを複素変数として汎関数に代入する。
（５）信号レベルを変えて、上記手順をくり返す。
【０１５０】
図１３乃至図１５はそれぞれ、図１１のアレーアンテナの制御装置において用いる、信号対雑音電力比に対する汎関数Ｊ_２｛ｙ（ｔ）｝，Ｊ_３｛ｙ（ｔ）｝，Ｊ_４｛ｙ（ｔ）｝の理論値及びシミュレーション結果の値を示すグラフである。図１３乃至図１５から明らかなように、有限長の乱数データを用いており、平均化演算Ｅ［・］にゆらぎがあるので、汎関数の計算結果にもばらつきが生じている。特に、低いＳＮ比の領域でばらつきが顕著である。データ長すなわち平均化サンプル数ｐを大きくしていくと単調増加関数に漸近する。ｐが無限大である極限では図１２に示した曲線に一致する。
【０１５１】
さらに、上記の汎関数を用いた無線受信機における適応制御方法について図１１を参照して説明する。
【０１５２】
図１１の無線受信機１０ａにおいて、波形等化器６−１が乗算器２−１とＡ／Ｄ変換機５−１との間に挿入され、波形等化器６−２が乗算器２−２とＡ／Ｄ変換機５−２との間に挿入される。各波形等化器６−１，６−２は例えば公知のトランスバーサルフィルタであり、異なる複数の遅延量で遅延された受信信号を所定の乗算パラメータで乗算することによりＰＳＫ受信信号の波形を制御して等化するものである。適応制御型コントローラ２０ａは、図１の適応制御型コントローラ２０の処理に加えて、Ａ／Ｄ変換器５−１，５−２の出力信号に基づき受信信号レベルを検出し、数６１を用いて汎関数の値を計算し、当該汎関数の値を数６２、数６３又は数６４に代入することによりＳＮ比に関する高次方程式となり、これを例えば、ニュートン法などの方程式の数値解法を用いて解であるＳＮ比を計算する。次いで、適応制御型コントローラ２０ａは、計算したＳＮ比に基づいて、そのＳＮ比が実質的に最大となるように、各波形等化器６−１，６−２の乗算パラメータを適応制御する。なお、複数の乗算パラメータを制御する方法については、例えば、上述の最急勾配法、順次ランダム法、ランダム法、高次元二分法などの非線形計画法における反復的な数値解法を用いることができる。
【０１５３】
以上の実施形態においては、アナログ波形等化器６−１，６−２を用いているが、本発明はこれに限らず、デジタル波形等化器を用いてもよい。この場合、アナログ波形等化器６−１，６−２に代えて、Ａ／Ｄ変換器５−１と適応制御型コントローラ２０ａとの間にデジタル波形等化器を挿入し、Ａ／Ｄ変換器５−２と適応制御型コントローラ２０ａとの間にデジタル波形等化器を挿入する。
【０１５４】
以上の実施形態においては、受信信号のＳＮ比に基づいた適応制御方法の対象として波形等化器６−１，６−２を用いているが、本発明はこれに限らず、受信信号のＳＮ比に対して影響を与える無線受信機の信号等化器、信号ろ波器、リニアライザ、同調器などの信号処理手段を用いてもよい。ここで、例えば、信号ろ波器は、上記アナログ波形等化器６−１，６−２又はデジタル波形等化器の位置に挿入され、所定の帯域の信号ろ波処理を実行する。また、リニアライザは、上記アナログ波形等化器６−１，６−２又はデジタル波形等化器の位置に挿入され、所定の線形等化処理を実行する。さらに、同調器は、例えば適応制御型コントローラ２０ａの制御動作に含まれ、計算されたＳＮ比に基づいて、ＳＮ比が実質的に最大となるように、局部発振器３の局部発振周波数を制御することにより、当該無線受信機１０ａの受信周波数を、所望波の信号周波数に実質的に同一になるように同調する。
【０１５５】
以上の実施形態においては、複素ガウス雑音ならびに多相ＰＳＫ信号のモーメントを高次まで定式化し、ＰＳＫ変調に特有な信号点配置に着目することにより汎関数を定義し、これが信号対雑音比の推定指標となることを上記のモーメントの定式を用いて解析的に示した。さらに、有限データ長の信号と加算的ガウス雑音が混在する系における本汎関数の統計的振舞を計算機シミュレーションにより示した。平均化のデータ数が少ないと特に低ＳＮ比の領域で分散が大きい。データ数を多くしていくと解析的に導出した単調増加曲線に漸近し、高い精度でＳＮ比を推定して計算することができる。本汎関数は演算が容易であり、同期検波も必要としないので、簡易な民生コンシューマ向の適応受信システム等のブラインド制御規範としての利用することができる。
【０１５６】
以上の実施形態においては、６本の非励振素子Ａ１乃至Ａ６と、それに対応した可変リアクタンス素子１２−１乃至１２−６とを備えているが、本発明はこれに限らず、少なくとも１つの非励振素子Ａ１と、それに対応した可変リアクタンス素子１２−１を備えてもよい。また、それぞれの個数は複数でもよい。
【０１５７】
【発明の効果】
以上詳述したように本発明に係るアレーアンテナの制御方法によれば、従来技術のエスパアンテナやリニアアレーアンテナなどのアレーアンテナの制御方法において、当該アレーアンテナによって受信された受信信号に基づいて、非線形計画法における反復的な数値解法を用いて、上記受信信号のｍ乗を用いて表された規範関数の値が最大又は最小となるように、上記アレーアンテナの主ビームを所望波の方向に向けかつ干渉波の方向にヌルを向けるための各可変リアクタンス素子のリアクタンス値を計算して設定する。従って、参照信号を必要とせずに、アレーアンテナの指向性を所望波の方向に主ビームを向けかつ干渉波の方向にヌルを向けるように適応制御することができる。ここで、参照信号を必要としないので、当該装置の構成を簡単化できる。また、規範関数は受信信号のｍ乗値のみで記述されているので、適応制御処理の計算処理をきわめて簡単に実行できる。
【０１５８】
また、本発明に係る受信信号の信号対雑音比の計算方法によれば、ｍ相ＰＳＫ変調された（ここで、ｍは２以上の整数である。）無線信号を受信信号として受信する無線受信機において、所定の期間における、上記受信信号のｍ乗値の平均値の絶対値の二乗値を、上記受信信号のｍ乗値の絶対値の二乗値の平均値で除算した関数である規範関数の値を計算し、計算された規範関数に基づいて上記規範関数と信号対雑音比との関係を示す式を用いて上記受信信号の信号対雑音比を計算する。従って、きわめて簡単な方法で受信信号の信号対雑音比を、リアルタイムで高精度で計算することができる。
【０１５９】
さらに、本発明に係る無線受信機の適応制御方法によれば、上記受信信号の信号対雑音比の計算方法により受信信号の信号対雑音比を計算し、上記計算された信号対雑音比が実質的に最大となるように、無線受信機の信号等化器又は信号ろ波器である信号処理手段を適応制御する。従って、上記計算した信号対雑音比に基づいて、無線受信機の信号処理手段をリアルタイムでかつ高精度で適応制御できる。
【図面の簡単な説明】
【図１】 本発明に係る第１の実施形態であるアレーアンテナの制御装置の構成を示すブロック図である。
【図２】 図１のエスパアンテナ装置１００の詳細な構成を示す断面図である。
【図３】 図１のエスパアンテナ装置１００の非励振素子Ａｎと可変リアクタンス素子１２−ｎの接続点付近の回路を示す回路図である。
【図４】 図１の適応制御型コントローラ２０によって実行される、最急勾配法による適応制御処理を示すフローチャートである。
【図５】 本発明に係る第２の実施形態であるアレーアンテナの制御装置の構成を示すブロック図である。
【図６】 図１のエスパアンテナ装置１００を用いて実行された、ブラインド適応ビーム形成のシミュレーションのフローを示す図である。
【図７】 図６のシミュレーション結果であって、干渉波方向が４５度のときの放射電力パターンを示す指向特性図である。
【図８】 図６のシミュレーション結果であって、干渉波方向が９０度のときの放射電力パターンを示す指向特性図である。
【図９】 図６のシミュレーション結果であって、干渉波方向が１３５度のときの放射電力パターンを示す指向特性図である。
【図１０】 図６のシミュレーション結果であって、干渉波方向が１８０度のときの放射電力パターンを示す指向特性図である。
【図１１】 本発明に係る第３の実施形態であるアレーアンテナの制御装置の構成を示すブロック図である。
【図１２】 図１１のアレーアンテナの制御装置において用いる、信号対雑音電力比に対する汎関数Ｊ_２｛ｙ（ｔ）｝，Ｊ_３｛ｙ（ｔ）｝Ｊ_４｛ｙ（ｔ）｝の理論値を示すグラフである。
【図１３】 図１１のアレーアンテナの制御装置において用いる、信号対雑音電力比に対する汎関数Ｊ_２｛ｙ（ｔ）｝の理論値及びシミュレーション結果の値を示すグラフである。
【図１４】 図１１のアレーアンテナの制御装置において用いる、信号対雑音電力比に対する汎関数Ｊ_３｛ｙ（ｔ）｝の理論値及びシミュレーション結果の値を示すグラフである。
【図１５】 図１１のアレーアンテナの制御装置において用いる、信号対雑音電力比に対する汎関数Ｊ_４｛ｙ（ｔ）｝の理論値及びシミュレーション結果の値を示すグラフである。
【符号の説明】
Ａ０…励振素子、
Ａ１乃至Ａ６…非励振素子、
１…低雑音増幅器（ＬＮＡ）、
２−１，２−２…混合器、
３…局部発振器、
４…９０度移相器、
５−１，５−２…Ａ／Ｄ変換器、
６−１，６−２…波形等化器、
８…給電用同軸ケーブル、
１１…接地導体、
１２−１乃至１２−６…可変リアクタンス素子、
１３…低域通過フィルタ、
１４…抵抗、
１５…キャパシタ、
２０，２０ａ…適応制御型コントローラ、
５０…アレーアンテナ、
５１−１乃至５１−Ｎ…アンテナ素子、
５２−１乃至５２−Ｎ…低雑音増幅器（ＬＮＡ），
５３−１乃至５３−Ｎ…可変移相器、
５４…合成器、
６０…適応制御型コントローラ、
１００…エスパアンテナ装置。[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an array antenna control method capable of changing the directivity of an array antenna apparatus composed of a plurality of antenna elements, and more particularly to an electronically controlled waveguide array antenna apparatus (ESPAR) antenna; Hereinafter, the present invention relates to an array antenna control method capable of adaptively changing the directivity characteristic of ESPAR antenna. The present invention also relates to a method of calculating a signal-to-noise ratio of a wireless receiver that calculates a signal-to-noise ratio of a received signal received by the wireless receiver, and an adaptive control method of the wireless receiver using the calculation method.
[0002]
[Prior art]
Prior art ESPAR antennas are disclosed in, for example, prior art document 1 “T. Ohira et al.,“ Electronically steerable passive array radiator antennas for low-cost analog adaptive beamforming, ”2000 IEEE International Conference on Phased Array System & Technology pp. 101. -104, Dana point, California, May 21-25, 2000 "and Japanese Patent Application Laid-Open No. 2001-24431. The ESPAR antenna is connected to an excitation element to which a radio signal is supplied, at least one non-excitation element that is provided at a predetermined interval from the excitation element and to which no radio signal is supplied, and the non-excitation element. A directivity characteristic of the array antenna can be changed by providing an array antenna including a variable reactance element and changing a reactance value of the variable reactance element.
[0003]
In general, the following method is used as a method of adaptively controlling the ESPAR antenna on the receiving side. That is, a learning sequence signal is included in advance at the beginning of each wireless packet data on the transmission side, the same signal as the learning sequence signal is generated on the reception side, and the received learning sequence signal on the reception side, Using the maximum cross-correlation with the generated learning sequence signal as a standard (standard standard), the reactance value of the variable reactance element is changed to change its directivity. As a result, the directivity of the ESPAR antenna is set to the optimum pattern, that is, a pattern in which the main beam is directed in the desired wave direction and a null is formed in the interference wave direction.
[0004]
[Problems to be solved by the invention]
However, in this conventional example, a reference signal such as a learning sequence signal is necessary, and it is necessary to match this reference signal in advance on both the transmission side and the reception side. There was a problem that the circuit of this became complicated.
[0005]
In addition, in order to adaptively control the signal equalizer and signal filter in a radio receiver, it is necessary to estimate and calculate the signal-to-noise power ratio, but to calculate the received signal received in real time. I couldn't.
[0006]
The object of the present invention is to solve the above-mentioned problems, and can perform adaptive control so that the main beam of the array antenna is directed to the desired wave and the null is directed to the interference wave without requiring a reference signal. It is to provide a method for controlling an array antenna.
[0007]
Another object of the present invention is to solve the above-described problems. For example, in order to adaptively control the signal equalizer and the signal filter in a radio receiver, the signal-to-noise ratio of the received signal is set. It is an object of the present invention to provide a method for calculating a signal-to-noise ratio of a received signal that can be estimated and calculated, and an adaptive control method for a radio receiver using the calculation method.
[0008]
[Means for Solving the Problems]
An array antenna control method according to a first invention includes an excitation element for receiving a radio signal,
At least one non-excitation element provided at a predetermined distance from the excitation element;
A variable reactance element connected to the non-excitation element,
In the array antenna control method of changing the directivity characteristics of the array antenna by operating the non-excited element as a director or a reflector by changing a reactance value of the variable reactance element,
The transmitted radio signal is m-phase PSK modulated (where m is an integer greater than or equal to 2), and an iterative numerical solution in nonlinear programming is performed based on the received signal received by the excitation element. The main beam of the array antenna is directed in the direction of the desired wave and the null is directed in the direction of the interference wave so that the value of the normative function expressed using the m-th power of the received signal is maximized or minimized. And a step of calculating and setting a reactance value of the variable reactance element.
[0009]
Further, the array antenna control method according to the second invention is such that a plurality of P received signals received by an array antenna in which a plurality of P antenna elements are juxtaposed with each other at a predetermined interval are respectively converted into P phase shifts. In the array antenna control method for outputting a received signal after combining after being phase-shifted by a predetermined amount by means,
The transmitted radio signal is m-phase PSK modulated (where m is an integer greater than or equal to 2), and based on the combined received signal, using an iterative numerical solution in nonlinear programming, Each for directing the main beam of the array antenna in the direction of the desired wave and directing the null in the direction of the interference wave so that the value of the normative function expressed using the m-th power of the received signal becomes maximum or minimum The method includes calculating and setting a phase shift amount of the phase shift means.
[0010]
Further, in the array antenna control method according to the first and second inventions, the normative function is preferably a square value of an absolute value of an average value of m-th power values of the received signal in a predetermined period. It is a function obtained by dividing by the average value of the square value of the absolute value of the m-th power value of the received signal.
[0011]
Furthermore, the signal-to-noise ratio calculation method for the received signal according to the third aspect of the invention is a wireless reception for receiving a radio signal that is m-phase PSK modulated (where m is an integer of 2 or more) as a received signal. In the machine
The value of a normative function which is a function obtained by dividing the square value of the absolute value of the average value of the m-th power value of the received signal by the average value of the square value of the absolute value of the m-th value of the received signal in a predetermined period. And calculating a signal-to-noise ratio of the received signal using an expression indicating a relationship between the reference function and a signal-to-noise ratio based on the calculated reference function.
[0012]
Still further, an adaptive control method for a wireless receiver according to a fourth aspect of the present invention is to receive a wireless signal that is m-phase PSK modulated (where m is an integer of 2 or more) as a received signal, and the received signal In a wireless receiver provided with signal processing means for processing
The value of a normative function which is a function obtained by dividing the square value of the absolute value of the average value of the m-th power value of the received signal by the average value of the square value of the absolute value of the m-th value of the received signal in a predetermined period. Calculating a signal-to-noise ratio of the received signal using an equation indicating a relationship between the reference function and a signal-to-noise ratio based on the calculated reference function;
Adaptively controlling the signal processing means so that the calculated signal-to-noise ratio is substantially maximized. Here, the signal processing means is preferably a signal equalizer, a signal filter, a linearizer or a tuner of a radio receiver.
[0013]
DETAILED DESCRIPTION OF THE INVENTION
Embodiments according to the present invention will be described below with reference to the drawings.
[0014]
<First Embodiment>
FIG. 1 is a block diagram showing a configuration of an array antenna control apparatus according to a first embodiment of the present invention. As shown in FIG. 1, the array antenna control apparatus according to this embodiment includes an ESPAR antenna apparatus 100 including one excitation element A0 and six non-excitation elements A1 to A6, a radio receiver 10, and the like. And an adaptive control type controller 20.
[0015]
Here, the transmitted radio signal is m-phase PSK modulated (where m is an integer equal to or greater than 2), and the adaptive control controller 20 is configured by a digital computer such as a computer, for example, and the ESPAR antenna apparatus 100 Based on the received signal y (t) received by the excitation element A0, the received signal y (t) is raised to the m-th power using, for example, the steepest gradient method, which is an iterative numerical method in nonlinear programming. For directing the main beam of the ESPAR antenna apparatus 100 in the direction of the desired wave and directing the null in the direction of interference so that the value of the reference function expressed using The reactance values of the variable reactance elements 12-1 to 12-6 are calculated and set.
[0016]
In FIG. 1, an ESPAR antenna device 100 includes an excitation element A0 and non-excitation elements A1 to A6 provided on a ground conductor 11, and the excitation element A0 includes six excitation elements A0 provided on a circumference of a radius r. They are arranged so as to be surrounded by the non-excitation elements A1 to A6. Preferably, the non-exciting elements A1 to A6 are provided at equal intervals on the circumference of the radius r. The lengths of the excitation elements A0 and the non-excitation elements A1 to A6 are configured to be, for example, about λ / 4 (where λ is the wavelength of the desired wave), and the radius r is λ / 4. Configured. The feeding point of the excitation element A0 is connected to the low noise amplifier (LNA) 1 via the coaxial cable 8, and the non-excitation elements A1 to A6 are connected to the variable reactance elements 12-1 to 12-6, respectively. The reactance values of the reactance elements 12-1 to 12-6 are set by reactance value signals from the adaptive control type controller 20.
[0017]
FIG. 2 is a longitudinal sectional view of the ESPAR antenna device 100. The excitation element A0 is electrically insulated from the ground conductor 11, and the non-excitation elements A1 to A6 are grounded with respect to the ground conductor 11 via the variable reactance elements 12-1 to 12-6. The operation of the variable reactance elements 12-1 to 12-6 will be described. For example, when the longitudinal lengths of the excitation element A0 and the non-excitation elements A1 to A6 are substantially the same, for example, the variable reactance element 12-1 Is inductive (L property), the variable reactance element 12-1 becomes an extension coil, and the electrical lengths of the non-excitation elements A1 to A6 are longer than that of the excitation element A0, and function as a reflector. On the other hand, for example, when the variable reactance element 12-1 has capacitance (C-type), the variable reactance element 12-1 becomes a shortening capacitor, and the electrical length of the non-excitation element A1 becomes shorter than that of the excitation element A0. Acts as a director. The non-excitation elements A2 to A6 connected to the other variable reactance elements 12-2 to 12-6 operate in the same manner.
[0018]
Therefore, in the ESPAR antenna apparatus 100 of FIG. 1, the plane directivity characteristics of the ESPAR antenna apparatus 100 are changed by changing the reactance values of the variable reactance elements 12-1 to 12-6 connected to the non-excitation elements A1 to A6. Can be changed.
[0019]
In the array antenna control apparatus of FIG. 1, the excitation element A0 of the ESPAR antenna apparatus 100 receives a radio signal y (t), and the received signal y (t), which is the received radio signal, passes through the coaxial cable 8. Input to the wireless receiver 10, the wireless receiver 10 performs BPSK demodulation processing on the received signal y (t) to obtain two digital baseband signals from the BPSK demodulated received signals orthogonal to each other. . That is, in the radio receiver 10, the received signal y (t) is first subjected to high frequency amplification by the low noise amplifier (LNA) 1 and then divided into two, and one of the two divided received signals y (t) is mixed by the mixer 2-2. 1 is mixed with the local oscillation signal from the local oscillator 3, and the I signal after direct conversion is A / D converted by the A / D converter 5-1 to obtain a digital baseband I signal. On the other hand, the other received signal y (t) divided into two is mixed by the mixer 2-2 with the local oscillation signal shifted by 90 degrees from the local oscillation signal by the 90 degree phase shifter 4, and then directly The converted Q signal is A / D converted by the A / D converter 5-2 to obtain a digital baseband Q signal. These two digital baseband signals are output as data signals and also output to the adaptive control type controller 20. Next, the adaptive control type controller 20 uses the steepest gradient method, for example, based on the two digital baseband signals representing the received signal y (t) received by the excitation element A0 of the ESPAR antenna apparatus 100. The main beam of the ESPAR antenna apparatus 100 is set to the desired wave so that the value of the reference function (Expression 14) represented only by the signal m (t) and the mth power of the received signal y (t) is maximized. Reactance values x of the variable reactance elements 12-1 to 12-6 for directing null in the direction of the interference and in the direction of interference_k(K = 1, 2,..., 6) is calculated, and reactance value signals indicating the calculated values are output to the variable reactance elements 12-1 to 12-6, so that the reactance value x_kSet.
[0020]
FIG. 3 is a circuit diagram showing a circuit near the connection point between the non-excitation element An and the variable reactance element 12-n of the ESPAR antenna apparatus 100 of FIG. In FIG. 3, a DC bias voltage, which is a reactance value signal from the adaptive control type controller 20, passes through an L-type low-pass filter 13 composed of a resistor 14 and a capacitor 15, for example, a variable reactance element 12 that is a varactor diode. −n (n = 1, 2,..., 6), whereby the reactance values x of the variable reactance elements 12-1 to 12-6 are applied._k(K = 1, 2,..., 6) is controlled.
[0021]
Next, the ESPAR antenna device 100 is formulated. In this formulation model, a half-wave dipole antenna is used as the non-exciting element A0, and six dipole antennas arranged in a circular array are used as the non-exciting elements A1 to A6. All the element intervals are λ / 4, and each dipole is a conductive cylinder having a radius λ / 100. The wavelength shortening rate in the length direction of the element is 0.926. Varactor diodes, which are variable reactance elements 12-1 to 12-6, are loaded in series with respect to the central part of each of the non-excitation elements A1 to A6, and the directivity is determined by the combination of these reactance values. .
[0022]
The mutual coupling between elements is obtained from the structural parameters of the antenna by using electromagnetic field analysis by the method of moments, and this is expressed by the impedance matrix Z as shown in the following equation (for example, the prior art document 2 “Takashi Ohira,“ Espa. A method for easily obtaining reactance for forming a main beam of an antenna into a desired method: quasi-synchronous synthesis and steepest gradient method ", IEICE Technical Report, AP2001-48, pp.1-6, 20017 See "Month".)
[0023]
[Expression 1]

[0024]
Since the structure of the ESPAR antenna device 100 has cyclic symmetry, the independent elements of the 49 elements of the matrix Z are 6 elements. These are complex parameters that should be called as follows from their physical meanings.
[0025]
[Table 1]
―――――――――――――――――――――――――――――――――――
z₀₀: Self-input impedance of excitation element
z₀₁: Coupling impedance between excitation element and non-excitation element
z₁₁: Self-input impedance of non-excited element
z₁₂: Coupling impedance between two non-excited elements adjacent to each other
z₁₃: Next, the coupling impedance between two non-excited elements (adjacent to each other)
z₁₄: Coupling impedance between two non-excited elements facing each other
―――――――――――――――――――――――――――――――――――
[0026]
In addition, each impedance value used in the Example mentioned later is as follows.
(A) z₀₀= + 52.0-5.7j
(B) z₀₁= + 23.9-29.2j
(C) z₁₁= + 64.0-3.4j
(D) z₂₁= + 29.7-29.8j
(E) z₃₁= -13.9-27.6j
(F) z₄₁= -26.0-16.7j
Here, the unit of the impedance value is all Ω. The reactance values of the reactance elements 12-1 to 12-6, which are varactor diodes, are expressed as x.₁, X₂, ..., x₆Then, the directivity (array factor) D of the ESPAR antenna device 100_a(Θ, φ) is expressed by the following equation (see, for example, Prior Art Document 2).
[0027]
[Expression 2]
D_a(Θ, φ)
= A (θ, φ)^Ti (x₁, X₂, ..., x₆)
[0028]
Here, a (θ, φ) is a steering vector when the phase center of the ESPAR antenna device 100 is taken as the central non-excitation element A0, and is expressed by the following equation as a function of the elevation angle θ and the azimuth angle φ. .
[0029]
[Equation 3]

[0030]
Here, d is an element interval equal to the radius r, and β is a propagation constant in free space. I (x₁, X₂, ..., x₆) Is an equivalent weight vector of the ESPAR antenna and is expressed by the following equation.
[Expression 4]
i (x₁, X₂, ..., x₆)
= Z^-1(V_su₀-Xi)
= V_S(Z + X)^-1u₀
Where u₀Is a unit vector expressed by the following equation.
[Equation 5]
u₀= [1, 0, ..., 0]^T
X is the input impedance z of the RF receiver._sAnd a reactance matrix that is a diagonal matrix of the following equation having reactance values of the variable reactance elements 12-1 to 12-6 as components.
[Formula 6]
X = diag [z_s, Jx₁, Jx₂, ..., jx₆]
[0031]
Therefore, directivity (array factor) D of ESPAR antenna apparatus 100_a(Θ, φ) is expressed by the following equation.
[Expression 7]
D_a(Θ, φ)
= Z_sa (θ, φ)^T{Z + diag [z_s, Jx₁, Jx₂, ..., jx₆]}^-1u₀
[0032]
When multiple signal waves arrive, a vector whose components are those signal waveforms
[Equation 8]
s (t) = [s₁(T), s₂(T), ..., s_K(T)]
Define Here, K is the number of signals. The output signal of ESPAR antenna apparatus 100 when these are received simultaneously is expressed by the following equation.
[Equation 9]
y (t) = i (x₁, X₂, ..., x₆)^TA (θ, Φ) s (t) + n (t)
Here, A (θ, Φ) is an array manifold and is expressed by the following equation.
[Expression 10]
A (Θ, Φ)
= [A (θ₁, Φ₁), A (θ₂, Φ₂), ..., a (θ_K, Φ_K]]
here,
## EQU11 ##
Θ = {θ₁, Θ₂, ..., θ_K}
[Expression 12]
Φ = {φ₁, Φ₂, ..., φ_K}
And n (t) is an additive noise waveform.
[0033]
Therefore, the received signal y (t) of the ESPAR antenna apparatus 100 is expressed by the following equation.
[Formula 13]

[0034]
Where s_k(T) and θ_k, Φ_kAre the time waveform and direction of arrival of the kth signal, respectively.
[0035]
Next, “blind adaptive beamforming” used in the present embodiment will be described. The purpose of adaptive beamforming is to maximize the signal-to-interference noise power ratio SINR included in the antenna reception output signal y (t) derived by Equation (13). Blind control is to update antenna variable parameters (generally weight vectors: here reactance values of variable reactance elements 12-1 to 12-6) without referring to any signal information contained in the desired wave. is there.
[0036]
In order to form a beam adaptively, (1) the reference signal is included in the header of the transmission packet, (2) the reference signal sequence is known in advance on the receiving side, and (3) the reference signal is synchronized. The process of detecting timing and (4) training the array weighting factors is typically used. For example, there is an algorithm “MCCC: Maximum Cross Correlation Coefficient” that maximizes the cross-correlation coefficient between a received signal and a reference signal as an adaptive beam forming method of the ESPAR antenna apparatus 100 (for example, the conventional art document 3 “Kamiya et al.,“ ESPAR (Refer to "Basic Study of Antenna: Statistical Standard of SIR Characteristics Based on Adaptive Control", IEICE Technical Report, AP2000-175, SANE2000-156, pp.17-24, January 2001)). On the other hand, blind adaptive beam forming is a function of adaptively forming a beam without a reference signal, and the processes (1) to (3) can be omitted.
[0037]
In this embodiment, paying attention to the characteristic peculiar to the m-phase PSK modulation signal, a blind standard using this is proposed. The property to be noted here is that “the m-phase PSK modulation signal becomes a constant complex value when raised to the mth power regardless of the modulation data”. When receiving noise or interference on the communication channel, fluctuations from this constant complex value are observed on the receiving side. It is considered that the desired signal can be extracted with higher purity as the fluctuation is smaller. Therefore, it is proposed to maximize the m-th moment of the output signal of the receiving antenna derived as described above, that is, to use the following equation as a reference function.
[0038]
[Expression 14]

[0039]
Here, E [•] represents an ensemble average (an average value at a predetermined time) of the argument •. The denominator represents the average power of the m-th signal. Canonical function J {y (t)^m} Will be described later in the supplementary explanation. The advantage of this normative function is that it does not include the “constant complex value” described above. That is, it is not necessary for the receiving side to know this value in advance. This means that it does not depend on the absolute gain and fixed phase rotation amount of the antenna and the receiving circuit system, and is an important advantage when used in an actual radio system. Here, the criterion for maximizing the m-th moment of the complex signal as expressed by the above equation is referred to as “MMC: Maximum Moment Criterion”.
[0040]
Next, adaptive beam forming using the reference function will be described. “Adaptive beamforming” means that the antenna is variable so as to maximize the signal-to-interference noise power ratio SINR = S / (N + I) included in the received signal y (t) of the ESPAR antenna apparatus 100, which is derived by Equation 13 above. The parameter (reactance values of the variable reactance elements 12-1 to 12-6 in the ESPAR antenna apparatus 100) is updated. By repetitively updating the reactance value based on the above-described normative function, an optimum beam pattern in which the antenna directivity is maximum in output SINR, that is, a beam in which a main beam is formed in the desired wave direction and a null is formed in the interference wave direction. It becomes a pattern.
[0041]
That is, the normative function J does not include the target value C, only the received signal y (t), and the mth power of the received signal {y (t)^m} Is used to express the description. In this case, it is a great merit that the target value can be controlled in an unknown state. Based on this criterion, the reactance value is repeatedly updated using an iterative numerical method in a nonlinear programming method such as the steepest gradient method, thereby maximizing the signal-to-interference noise power ratio (SINR) of the antenna output. In other words, the optimum beam is formed so that the main beam of the ESPAR antenna apparatus 100 is directed toward the desired wave and the null is directed toward the interference wave.
[0042]
Next, adaptive control of the antenna beam using the steepest gradient method will be described. A recurrence formula for the set of reactance values (reactance vectors) x of the variable reactance elements 12-1 to 12-6 when using the steepest gradient method is expressed by the following equation.
[0043]
[Expression 15]
x (n + 1) = x (n) + μ∇Jn
[Expression 16]

[0044]
Here, n is the update order of x, and the parameter μ is a step size determined by trial and error. Here, the steepest gradient method is a concept of a method including the steepest descent method, but in the present embodiment, a method for obtaining an optimal solution so as to maximize the value of the normative function is used.
[0045]
Further, a specific procedure for obtaining the optimum solution by the steepest gradient method will be described. In order to find a good reactance vector x that makes the normative function Jn as large as possible by the steepest gradient method using Equation 15, the following procedure is used.
(I) First, the iteration number parameter n (that is, the nth iteration) is set to 1, and an initial value x (1) of a predetermined reactance vector (for example, the ESPAR antenna device 100 is set as an omni antenna). The process is started by the reactance vector).
(Ii) This initial value (when n = 1) or current estimate (when n ≧ 2) is then used to determine the slope of the normative function Jn in the iteration number parameter n (ie, the nth iteration) Calculate the vector ∇Jn.
(Iii) The next estimated value in the reactance vector x is calculated by changing the initial value or the current estimated value in the same direction as the direction of the gradient vector ∇Jn.
(Iv) The iteration number parameter n is incremented by 1, and the process returns to step (ii) to repeat the process. This iterative process is executed up to the number of iterations at which the reactance vector x substantially converges.
[0046]
FIG. 4 is a flowchart showing more specific adaptive control processing by the steepest gradient method, which is executed by the adaptive control type controller 20 of FIG.
[0047]
In step S1 of FIG. 4, first, the iteration number parameter n is reset to 1, the initial value is set and inserted in the reactance vector x (1), and the element parameter k is reset to 1 in step S2. Next, the received signal y (t) is measured in step S3, and the value of the normative function J is calculated using equation 14 in step S4.⁽⁰⁾Insert set to. Further, in step S5, the reactance value x_kA predetermined perturbation value Δx_kAnd add the value to reactance value x_kAfter that, the received signal y (t) is measured in step S6, and the value of the normative function J is calculated using equation 14 in step S7. In step S8, JJ⁽⁰⁾To calculate ∂Jn / ∂x_kAnd reactance value x in step S9_kA predetermined perturbation value Δx_kAnd subtract the subtracted value to reactance value x_kAfter returning to the value before the perturbation, it is determined in step S10 whether or not the element parameter k is K (= 6) or more. If “NO” in the step S10, the element parameter k is incremented by 1 in a step S11, the process returns to the step S5, and the above-described processing is repeated. On the other hand, if YES in step S10, the next estimated value x (n + 1) of the reactance vector x is calculated in step S12 using the recurrence formula of equation 15, and then the iteration number parameter n is determined in step S13. It is determined whether or not the predetermined number of iterations N has been reached. If NO, the number of iterations parameter n is incremented by 1 in step S14, and then the processing from step S2 is repeated. On the other hand, if YES in step S13, it is determined that the signal has sufficiently converged, and a reactance value signal having the calculated reactance vector x value is output to the variable reactance elements 12-1 to 12-6. Set.
[0048]
As described above, according to the present embodiment, the adaptive control type controller 20 is based on the received signal y (t) received by the excitation element A0 of the ESPAR antenna apparatus 100, and is an iterative numerical value in nonlinear programming. For example, by using the steepest gradient method, which is a solution method, the value of the reference function (Equation 14) represented only by the received signal y (t) and the mth power of the received signal y (t) is maximized. The reactance values of the variable reactance elements 12-1 to 12-6 for directing the main beam of the ESPAR antenna apparatus 100 in the desired wave direction and the null in the interference direction are calculated and set so that . Therefore, the directivity of the array antenna can be adaptively controlled so that the main beam is directed in the direction of the desired wave and null is directed in the direction of the interference wave without requiring a reference signal. Here, since no reference signal is required, the configuration of the apparatus can be simplified. Further, since the normative function J is described only by the received signal y (t), the calculation process of the adaptive controller 20 can be executed very easily.
[0049]
In the above embodiment, six non-excitation elements A1 to A6 are used. However, if there are at least a plurality of the non-excitation elements A1 to A6, the directivity of the array antenna apparatus can be electronically controlled. Alternatively, more than six non-exciting elements may be provided. In addition, the arrangement shape of the non-excitation elements A1 to A6 is not limited to the above-described embodiment, and it is sufficient that the non-excitation elements A1 to A6 are separated from the excitation element A0 by a predetermined distance. In other words, the intervals with respect to the non-excitation elements A1 to A6 may not be constant.
[0050]
In the above embodiment, the reactance value of each variable reactance element 12 is calculated using the steepest gradient method, but the present invention is not limited to this, and the following sequential random method, random method, high-dimensional bisection An iterative numerical method in nonlinear programming such as the method may be used.
[0051]
In the sequential random method, the following procedure is used.
(I) First, the iteration number parameter n (that is, the nth iteration) is set to 1, and a predetermined initial value x (1) of the reactance vector (for example, the ESPAR antenna apparatus 100 is set to an omni antenna). The process starts with the reactance vector at the time.
(Ii) The initial value (when n = 1) or the current estimate (when n ≧ 2) is then used to add to the estimate in the iteration number parameter n (ie, the nth iteration) The value is calculated by generating a random number within a predetermined range.
(Iii) The next estimated value in the reactance vector is calculated by adding the calculated added value to the estimated value.
(Iv) The iteration number parameter n is incremented by 1, and the process returns to step (ii) to repeat the process. This iterative process is executed until the value of the normative function J becomes a predetermined threshold value (for example, 0.9) or more.
[0052]
In the random method, the following procedure is used.
(I) First, processing is started by a predetermined initial value x (1) of a reactance vector (for example, a reactance vector when the ESPAR antenna device 100 is set to an omni antenna).
(Ii) Next, using this initial value, a value added to the initial value is calculated by generating a random number within a predetermined existence range.
(Iii) The estimated value in the reactance vector is calculated by adding the calculated addition value to the initial value.
(Iv) If the value of the normative function J in the calculated estimated value is equal to or greater than a predetermined threshold value (for example, 0.9), the estimated value is set as the reactance vector to be set. Return to (ii) and repeat the process.
[0053]
Further, in the high-dimensional bisection method, the following procedure is used.
(I) First, the iteration number parameter n (that is, the nth iteration) is set to 1 and the process is started.
(Ii) Next, a predetermined existence range of each reactance value of the reactance vector (in the second and subsequent times, the existence range of the estimated value selected before) is equally divided into two, and the average value of each of the two existence ranges divided into two (Two average values for each variable reactance element 12-1 to 12-6) is calculated.
(Iii) The value of the normative function J for these two average values is calculated, and the one with the larger value of the normative function J is set as the next estimated value in the reactance vector.
(Iv) The iteration number parameter n is incremented by 1, and the process returns to step (ii) to repeat the process. This iterative process is executed until the value of the normative function J becomes a predetermined threshold value (for example, 0.9) or more.
[0054]
In the above embodiment, the norm function J is a norm function for obtaining the reactance value for adaptive control, and the optimum solution of the reactance vector is calculated so as to maximize it. Not limited to this, the reciprocal of the normative function J may be a normative function for obtaining a reactance value for adaptive control, and an optimal solution of the reactance vector may be calculated so as to minimize it.
[0055]
In the above embodiment, the six non-excitation elements A1 to A6 and the corresponding variable reactance elements 12-1 to 12-6 are provided. However, the present invention is not limited to this, and at least one non-excitation element is included. An excitation element A1 and a variable reactance element 12-1 corresponding to the excitation element A1 may be provided. Moreover, the number of each may be plural.
[0056]
<Second Embodiment>
FIG. 5 is a block diagram showing the configuration of the array antenna control apparatus according to the second embodiment of the present invention.
[0057]
  In this embodiment, signals received by the antenna elements 51-1 to 51-P of the array antenna 50 are converted into RF bands formed by variable phase shifters 53-1 to 53-P and a combiner 54 that is an adder. The BFN (Beam Forming Network) circuit is used to synthesize, and the array antenna control device has a plurality of P antenna elements.51-1 to 51-PAre adaptive control controllers for controlling the beams of array antennas 50 (for example, linear arrays, which may be arranged in a two-dimensional shape or a three-dimensional shape) arranged at predetermined intervals from each other, An adaptive control type controller 60 is provided. Here, the transmitted radio signal is m-phase PSK modulated (m is an integer equal to or greater than 2), and the adaptive control type controller 60 repeats numerical values in nonlinear programming based on the synthesized received signal. For example, by using the steepest gradient method, which is a solution method, the value of the reference function (Equation 14) expressed using the m-th power of the received signal y (t) is maximized. Each phase shift control voltage v corresponding to the amount of phase shift of the variable phase shifters 53-1 to 53-P for directing the main beam in the direction of the desired wave and directing null in the direction of interference_p(P = 1, 2,..., P) is calculated and set.
[0058]
The configuration of the array antenna control apparatus shown in FIG. 5 will be described below. In FIG. 5, a radio signal is received by an array antenna 50 in which a plurality of P antenna elements 51-1 to 51-P are arranged in parallel on a straight line at a predetermined interval, and each antenna element 51-1 to 51-P is received. The radio signals received by P are input to variable phase shifters 53-1 to 53-P through low noise amplifiers (LNA) 52-1 to 52-P, respectively. Each of the variable phase shifters 53-1 to 53-P receives the input radio signal from each of the phase shift control voltages v output from the adaptive control type controller 60._pAfter the phase shift amount corresponding to (p = 1, 2,..., P), the phase is output to the synthesizer 54. The synthesizer 54 synthesizes the power of the input P radio signals, and the synthesized radio signal is received signal y (t) to the radio receiver 10 having the same configuration as the radio receiver 10 in FIG. Output.
[0059]
Next, the wireless receiver 10 obtains two digital baseband signals from the received signals orthogonal to each other based on the input combined received signal y (t), similarly to the wireless receiver 10 of FIG. To the adaptive control type controller 60. The adaptive control type controller 60 is an iterative numerical method in nonlinear programming based on two input digital baseband signals, for example, using the steepest gradient method, similar to the adaptive control processing of FIG. By executing the processing of the above, the value of the normative function (Equation 14) expressed by using the mth power of the received signal y (t) only and the received signal y (t) is maximized. Each phase shift control voltage v corresponding to the amount of phase shift of variable phase shifters 53-1 to 53-P for directing the main beam of array antenna 50 in the direction of the desired wave and directing null in the direction of interference_p(P = 1, 2,..., P) is calculated and applied to the variable phase shifters 53-1 to 53-P to set the corresponding phase shift amounts.
[0060]
Also in the adaptive control type controller 60 according to this embodiment, as in the adaptive control type controller 20 according to the first embodiment, the directivity of the array antenna is set in the direction of the desired wave without requiring a reference signal. Can be adaptively controlled so that the null is directed toward the interference wave. Here, since no reference signal is required, the configuration of the apparatus can be simplified. Further, since the normative function J is described only by the received signal y (t), the calculation process of the adaptive controller 60 can be executed very easily.
[0061]
In the above embodiment, the phase shift control voltage v corresponding to the amount of phase shift of each of the variable phase shifters 53-1 to 53-P using the steepest gradient method._pHowever, the present invention is not limited to this, and an iterative numerical method in the above-described nonlinear programming method such as the sequential random method, the random method, or the high-dimensional bisection method may be used. The normative function J may use the reciprocal thereof.
[0062]
【Example】
FIG. 6 is a diagram showing a simulation flow of blind adaptive beamforming executed using the ESPAR antenna apparatus 100 of FIG. In this simulation, as in the above-described formulation model, a half-wave dipole antenna is used as the non-exciting element A0, and six dipole antennas arranged in a circular array are used as the non-exciting elements A1 to A6. Further, the arrival directions of the desired wave and the interference wave arriving at the ESPAR antenna apparatus 100 are unknown (adaptive control), and no training signal is used (blind processing).
[0063]
In the simulation flow of FIG. 6, adaptive control of the antenna beam is performed by performing steps SS1 to SS5 based on the interference wave steering vector, the desired wave steering vector, the antenna structure parameter, the incoming wave signal, and the noise. Finally, the directivity array factor and the output SINR are calculated and output (steps SS6 and SS7). In the processing of steps SS1 to SS7, the reception signal y (t) is received (step SS1), and the reference function J {y (t) is based on the received reception signal y (t).^m} (Step SS2), the reactance matrix is updated (step SS3), the reactance matrix is calculated (step SS4), and the equivalent weight vector is calculated (step SS5). Then, the directivity array factor is calculated from the equivalent weight vector (step SS6), while the output SINR is calculated from the received signal y (t) and the noise n (t) (step SS7).
[0064]
In this simulation, it is assumed that the arrival directions of the desired wave and the interference wave arriving at the ESPAR antenna apparatus 100 are unknown (adaptive control) and that no training signal is used (blind processing). Simulation is performed in an environment in which interference waves simultaneously arrive in addition to desired waves. QPSK random modulation signal and noise are both additive and Gaussian noise for both the desired wave and the interference wave. These desired wave, interference wave, and noise are uncorrelated with each other. For simplicity, the band limiting filter, delay spread, angular spread, fading, Doppler effect, and synchronization error are all ignored in the transmission path. Under this condition, the reactance values of the six variable reactance elements 12-1 to 12-6 are controlled based on the above-described normative function. The antenna structure parameters used in the simulation were the number of controlled elements: 6, element spacing: all 1/4 wavelength, each dipole radius: 1/100 wavelength, and the wavelength shortening rate in the length direction of the element: 0.926. The internal impedance of the RF transceiver connected to the ESPAR antenna device 100 is z_s= 50Ω. Optimization algorithms include candidates such as the pure random search method, steepest gradient method, high-dimensional bisection method, sequential random method, regression step method, and Hamilton mechanics method. An example is shown.
[0065]
The levels of the desired wave D and the interference wave I are +6 dBn and 0 dBn (dBn is a power display based on the noise level), respectively. Control result and directivity pattern (power pattern) of variable reactance element when arrival azimuth of desired wave D is fixed at 0 ° and arrival azimuth of interference wave I is 45 °, 90 °, 135 °, 180 ° ) Are shown in FIGS. Symbols D and I on the polar chart circumference indicate the arrival directions of the desired wave and the interference wave, respectively. As is apparent from FIGS. 7 to 10, it can be seen that the main beam is formed in the direction of arrival of the desired wave D in all four patterns, and at the same time, a deep null point is formed in the direction of the interference wave I.
[0066]
As described above, according to the present embodiment, the ESPAR antenna apparatus 100 is capable of blind beam formation by an appropriate standard and feedback control even though the hardware configuration is simple. The case of wave reception is shown.
[0067]
In the above embodiment, the normative function of the above equation 14 is used. The time average E (•) in the above equation 14 is obtained by receiving a data signal transmitted by, for example, a frequency division multiplexing method in parallel and performing parallel processing. In this case, for example, an average value for a plurality of data signals in a predetermined period such as one symbol may be used.
[0068]
<Supplementary explanation>
In the supplementary explanation, the reference function J {y (t) in the BPSK modulated signal^m} Will be described below.
[0069]
It is assumed that noise n is added to the transmission signal x and the reception signal y (t) is expressed by the following equation.
[Expression 17]
y (t) = x (t) + n (t)
[0070]
Here, it is assumed that n (t) is a waveform in which thermal noise or multiple interference waves are superimposed on a random amplitude and a random phase. The values of these time waveform signals y (t), x (t), and n (t) at a certain sampling time are written as y, x, and n, respectively. Further, it is assumed that there is no DC offset in the transmission / reception signal. In the actual radio receiver 10, a DC offset may occur. However, since the average value (expected value) E [y] of the received signal is an observable amount, the value obtained by subtracting this from the received signal is revised. It can be zeroized by considering it as a received signal. That is, generality is not lost even if it is a following formula.
[0071]
[Expression 18]
E [y] = 0
[Equation 19]
E [x] = 0
[Expression 20]
E [n] = 0
[0072]
Equation 17 above can be used as a reference function J (y for a BPSK (m = 2) modulated signal.²Substituting for), we get
[0073]
[Expression 21]

[0074]
The second term in the numerator of the above equation is as follows because the transmission signal x and the noise n are uncorrelated with each other.
[0075]
[Expression 22]
2E [xn] = 2E [x] E [n] = 0
[0076]
Similarly, since the real part (I channel component) and imaginary part (Q channel component) of noise n are equal power and uncorrelated with each other, the third term is obtained as follows.
[0077]
[Expression 23]
E [n²]
= E [(n_r+ Jn_i)²]
= E [n_r ²] -E [n_i ²] + 2jE [n_rn_i]
= 0
[0078]
Accordingly, the numerator of Equation 21 is |²] ｜²It becomes only the term. Next, when the denominator of Equation 21 is expanded, the following equation is obtained.
[0079]
[Expression 24]
E [| y²｜²]
= E [| x |⁴] + 4E [| x |²| N |²] + E [| n |⁴]
+ 2Re {2E [2x²x^*n^*] + 2E [2xnn^{2 *}] + E [x²n^{2 *}]}
[0080]
In the above equation, Re (•) represents the real part of the argument, the superscript symbol * represents the complex conjugate, and so on. If the above Equation 22 and Equation 23 are used for this, the following equation is obtained.
[0081]
[Expression 25]
E [| y²｜²]
= E [| x |⁴] + 4E [| x |²] E [| n |²] + E [| n |⁴]
+ 2Re {4E [2x²x^*] E [n^*] + 4E [x] E [nn^{2 *}]
+ E [x²] E [n^{2 *}]}
= E [| x |⁴] + 4E [| x |²] E [| n |²] + E [| n |⁴]
[0082]
Appear in these formulas
[Equation 26]
E [| x |²] = S
[Expression 27]
E [| n |²] = N
Means the average power of the transmission signal x and noise n, respectively. The real part (I channel component) and the imaginary part (Q channel component) of the noise are uncorrelated with each other and have equal power as shown in the following equation.
[0083]
[Expression 28]

[0084]
The transmission signal x is a BPSK modulated signal, i.e.
[Expression 29]
x∈ {a, -a}; a is a complex constant
Therefore, the signal average power (at a predetermined time) is expressed by the following equation.
[30]
S = E [| x |²] = | A |²
[0085]
Next, the molecule of the number 21 is
[31]
| E [x²] ｜²= | A |⁴= S²
When the noise n has a Gaussian distribution, the real part and the imaginary part also have a normal distribution. Applying the formula of the fourth-order central moment of normal distribution to these gives the following equation.
[0086]
[Expression 32]

[0087]
If this is used, the last term of the above formula 25 is expressed by the following equation.
[0088]
[Expression 33]

[0089]
Substituting Equation 26, Equation 27, Equation 30 and Equation 33 into Equation 25 yields the following equation.
[0090]
[Expression 34]
E [| y²｜²] = S²+ 4SN + 2N²
[0091]
Substituting the above formula 31 and the above formula 34 into the above formula 21, the following formula is obtained.
[0092]
[Expression 35]

[0093]
This is a function of only the S / N ratio and indicates a monotonous increase. This completes the proof.
[0094]
<Third Embodiment>
FIG. 11 is a block diagram showing the configuration of the array antenna control apparatus according to the third embodiment of the present invention. The array antenna control apparatus according to this embodiment differs from the first embodiment of FIG. 1 in the following points.
(1) In place of the wireless receiver 10, the wireless receiver 10 that further includes waveform equalizers 6-1 and 6-2 is provided in the wireless receiver 10 that receives the m-phase PSK signal.
(2) Instead of the adaptive control type controller 20, the adaptive control type controller 20 calculates the value of the above standard function, and based on the calculated standard function, the relationship between the standard function and the signal to noise power ratio is obtained. The signal-to-noise power ratio of the received signal is calculated using the equation shown, and the waveform equalizers 6-1 and 6-2 are adaptively controlled so that the calculated signal-to-noise ratio is substantially maximized. An adaptive control type controller 20a is provided.
[0095]
Prior to the detailed description of FIG. 11, a functional definition that is a reference function and a method for calculating a signal-to-noise power ratio will be described below.
[0096]
For adaptive feedback control of variable signal waveform equalizers, signal filters, and linearizers for optimal reception at a wireless receiver, signal-to-noise ratio estimation is an effective means. In particular, it is necessary to establish an S / N ratio estimation technique for blind operation in the wireless receivers of FIGS. 1 and 11 that do not use a training reference signal or a signal replica. Up to now, blind estimation functions using statistical expectation values and variances of received data have been described in, for example, the prior art document 4 “TA Summers et al.,“ SNR mismatch and online estimation in turbo decoding ”, IEEE Transaction on Communications, Vol. COM-46, No. 4, pp.421-423, April. 1998 ”, Prior Art Document 5“ A. Ramesh et al, “SNR estimation in generalized fading channels and its application to turbo decoding”, Proceeding of. IEEE ICC 2001, Helsinki, June 2001 ”and prior art document 6“ Takizawa et al., “A Study on Estimating Channel State in Parallel Combination SS Communication Method (2)”, IEICE General Conference, A-5-6 , Pp. 188, March 2002 ”. These assume that BPSK is assumed as a modulation method, and that synchronous detection is completely established in demodulation. In these prior art documents 4, 5, and 6, noise is handled as a real number, and therefore phase fluctuation due to noise is not considered.
[0097]
In the present embodiment, from the viewpoint of a more practical wireless system, a blind estimation method that can be applied to multiphase PSK and that operates even in a “quasi-synchronization” state in which perfect synchronization is not established is proposed. First, focusing on the characteristics peculiar to m-phase PSK modulation, a functional based on the m-th moment of the received signal is defined. Next, the complex Gaussian noise and the moment of the polyphase PSK signal are formulated up to higher order. Using these, it is analytically shown that the function according to the present embodiment is an estimation index of the signal-to-noise ratio. Furthermore, the statistical behavior of this functional in a system with a mixture of finite data length signals and additive Gaussian noise is shown by computer simulation.
[0098]
First, the definition of the functional will be described below. Noise n (t) is added to the m-phase PSK signal x (t), and a sampling time t = t_sSuppose that the following complex number is observed.
[0099]
[Expression 36]
s (t_s) + N (t_s) = Y (t_s)
[0100]
Here, paying attention to the characteristic peculiar to m-phase PSK modulation, a functional using this is proposed. The property to be noted here is that “the m-phase PSK signal becomes a constant complex value when raised to the mth power regardless of the modulation data”. When receiving noise or interference on the communication channel, fluctuations from this constant complex value are observed on the receiving side. It is considered that the signal-to-noise ratio is higher as the fluctuation is smaller. Therefore, the signal y (t_s) Is regarded as a random variable, and it is proposed to adopt a cross-correlation coefficient with a certain complex number C as a measure of fluctuation of the m-th power value. In general, the two functions f₁And f₂Is the cross-correlation coefficient ρ {f₁, F₂}.
[0101]
[Expression 37]

[0102]
Here, E [•] represents an operator that calculates an ensemble average (an average value at a predetermined time) of a variable • during a predetermined period. In this general formula,
[Formula 38]

In addition, a functional of the following equation that takes the absolute value square is defined.
[0103]
[39]

[0104]
This functional is an index indicating the similarity between the m-th power value of the received signal and the arbitrary constant C, that is, how much the m-th power value of the received signal does not fluctuate and is a constant value. This functional can also be interpreted as a normalization of the m-th moment of the received signal by the m-th signal average power. This means that this functional is invariant to changes over time and fixed phase rotation of the absolute gain of the antenna and receiver circuit system, and is an important advantage when used in an actual radio system. It is.
[0105]
Further, the high-order moment of the PSK signal will be described. When the m-phase PSK signal is sampled in a quasi-synchronized state, a complex variable s of the following equation is observed.
[0106]
[Formula 40]

[Expression 41]

[0107]
Where a_oIs the initial amplitude, φ_oIs an initial phase, d is information data, and δ is a frequency deviation due to synchronization deviation. When s is regarded as a random variable, the k-th moment is as follows.
[0108]
[Expression 42]

[0109]
Here, assuming that the quasi-synchronization, that is, the frequency deviation is smaller than the time T of the averaging operation, the second and subsequent terms of δω are ignored, the frequency fluctuation and the information data are uncorrelated, and the information data d is from 0 to m−. Assuming a uniform distribution up to 1, the following equation is obtained.
[0110]
[Equation 43]

[0111]
On the other hand, regardless of the m value,
(44)
| S | = a_o
The high-order moment of the absolute value is simply given by
[0112]
[Equation 45]

[0113]
Here, S is the average power of the PSK signal.
[0114]
Next, the high-order moment of Gaussian noise will be described. A thermal noise generated in the receiving system or a signal in which a large number of waves are superimposed with a random amplitude and a random phase can be handled as Gaussian noise. In the PSK demodulation system, it is necessary to treat the sample value of Gaussian noise as a complex number consisting of a real part (I channel component) and an imaginary part (Q channel component) (In the prior art documents 4 and 5, noise is treated as a real number. ing). Here, this is expressed as a complex number as follows.
[0115]
[Equation 46]

[0116]
Here, there is no DC offset in the noise n, and the average power is written as N. The real part and the imaginary part are normally distributed with equal power and zero DC bias. That is, the following formula is obtained.
[0117]
[Equation 47]

[0118]
Then, from the symmetry of the normal distribution, the odd moment is all zero, that is, for any positive integer p:
[0119]
[Formula 48]

[0120]
Where real part n_rAnd imaginary part n_iApplying the recurrence formula of the even-order moment of the normal distribution to
[0121]
[Formula 49]

[0122]
Where real part n_rAnd imaginary part n_iAre independent of each other and zero biased, so the coupling moment is expressed by the following equation.
[0123]
[Equation 50]

[0124]
Gaussian noise is independent in amplitude and phase, and the phase is uniformly distributed from 0 to 2π. Therefore, the moment is expressed by the following equation for an arbitrary order p.
[0125]
[Formula 51]

[0126]
On the other hand, for the even-order moment of the absolute value of Gaussian noise, the following equation is obtained by utilizing the above recurrence equation.
[0127]
[Formula 52]

[0128]
By repeating this calculation, the following equation is obtained.
[0129]
[53]

[0130]
Since the signal and the noise are independent from each other and the high-order moment of the noise is zero, these high-order coupling moments are also expressed by the following equation.
[0131]
[Formula 54]

[0132]
Next, the physical meaning of the functional of the following formula defined above will be discussed, which will be described below for the behavior of the functional.
[0133]
[Expression 55]

[0134]
Hereinafter, for simplicity, the time factor (t_s) Is omitted. Substituting the following into this formula,
[0135]
[Expression 56]
y = s + n
Dividing the numerator and denominator into a binomial expansion yields:
[0136]
[Equation 57]

[0137]
The first term in the absolute value of the above equation means m-th power signal power. The intermediate term of the equation is zero because it is a coupling moment of signal and noise. Furthermore, since the last term of the equation is the moment of noise, it is still zero. Eventually, only the first term remains, and the following equation is obtained.
[0138]
[Formula 58]

[0139]
Next, when the denominator is expanded into two terms, the following equation is obtained.
[0140]
[Formula 59]

[0141]
If an m-phase PSK signal and a high-order moment of noise are used for this, the following equation is obtained.
[0142]
[Expression 60]

[0143]
As a result, the functional is expressed by the following equation.
[0144]
[Equation 61]

[0145]
This is a function of only the S / N ratio and is monotonically increasing. It has been shown that the signal-to-noise ratio is estimated without separating the signal and noise by using this functional. Since this functional is defined only by the received signal y, it operates blindly without using a transmission signal replica.
[0146]
As a specific example, when the signal modulation method is BPSK, TPSK, or QPSK, the following functions are obtained when m = 2, 3, and 4 respectively in the above equation.
[0147]
(1) For BPSK
[62]

(2) For TPSK
[Equation 63]

(3) For QPSK
[Expression 64]

[0148]
These expressions are expressions showing the relationship between the functional and the S / N ratio. By detecting the received signal level, the value of the functional is calculated using Expression 61, and the value of the functional is expressed by Expression 62. By substituting into 63 or Equation 64, a high-order equation relating to the SN ratio is obtained, and the SN ratio that is a solution can be calculated using a numerical solution of an equation such as Newton's method. These are plotted as a function of the signal-to-noise ratio, as shown by the curve in FIG. That is, FIG. 12 shows the functional J for the signal-to-noise power ratio used in the array antenna control apparatus of FIG.₂{Y (t)}, J₃{Y (t)} J₄It is a graph which shows the theoretical value of {y (t)}. As apparent from FIG. 12, the functional J increases as the signal-to-noise power ratio increases.₂{Y (t)}, J₃{Y (t)} J₄It can be seen that the theoretical value of {y (t)} is increasing in minor.
[0149]
Next, we simulate the behavior of this functional for a finite data length signal. The procedure is as follows.
(1) An m-phase PSK signal sequence is generated from m-value random number data.
(2) This is separated into an I channel and a Q channel.
(3) Add an uncorrelated real Gaussian noise sequence to each channel.
(4) Substituting these into the functional as complex variables.
(5) Repeat the above procedure while changing the signal level.
[0150]
FIGS. 13 to 15 respectively show the functional J with respect to the signal-to-noise power ratio used in the array antenna control apparatus of FIG.₂{Y (t)}, J₃{Y (t)}, J₄It is a graph which shows the theoretical value of {y (t)}, and the value of a simulation result. As apparent from FIGS. 13 to 15, random number data of a finite length is used, and the averaging operation E [•] fluctuates, so that the functional calculation results also vary. In particular, the variation is remarkable in the low SN ratio region. As the data length, that is, the number of averaged samples p is increased, it gradually approaches a monotonically increasing function. In the limit where p is infinite, it matches the curve shown in FIG.
[0151]
Further, an adaptive control method in the radio receiver using the above functional will be described with reference to FIG.
[0152]
In the radio receiver 10a of FIG. 11, the waveform equalizer 6-1 is inserted between the multiplier 2-1 and the A / D converter 5-1, and the waveform equalizer 6-2 is the multiplier 2-. 2 and the A / D converter 5-2. Each of the waveform equalizers 6-1 and 6-2 is, for example, a known transversal filter, and controls the waveform of the PSK reception signal by multiplying the reception signal delayed by a plurality of different delay amounts by a predetermined multiplication parameter. And equalize. The adaptive control type controller 20a detects the received signal level based on the output signals of the A / D converters 5-1 and 5-2 in addition to the processing of the adaptive control type controller 20 of FIG. By calculating the value of the functional and substituting the value of the functional into Equation 62, Equation 63, or Equation 64, a higher-order equation relating to the S / N ratio is obtained, and this is expressed by using a numerical solution of an equation such as Newton's method. The S / N ratio that is the solution is calculated. Next, the adaptive control type controller 20a adaptively controls the multiplication parameters of the waveform equalizers 6-1 and 6-2 based on the calculated S / N ratio so that the S / N ratio is substantially maximized. As a method for controlling a plurality of multiplication parameters, for example, an iterative numerical solution method in the nonlinear programming method such as the steepest gradient method, the sequential random method, the random method, or the high-dimensional bisection method can be used.
[0153]
  In the above embodiment, the analog waveform equalizers 6-1 and 6-2 are used. However, the present invention is not limited to this, and a digital waveform equalizer may be used. In this case, instead of the analog waveform equalizers 6-1 and 6-2, a digital signal is inserted between the A / D converter 5-1 and the adaptive control type controller 20a.WaveformAn equalizer is inserted and digitally connected between the A / D converter 5-2 and the adaptive control type controller 20a.WaveformInsert an equalizer.
[0154]
In the above embodiment, the waveform equalizers 6-1 and 6-2 are used as targets of the adaptive control method based on the SN ratio of the received signal. However, the present invention is not limited to this, and the SN of the received signal is not limited thereto. Signal processing means such as a signal equalizer, a signal filter, a linearizer, and a tuner that affect the ratio may be used. Here, for example, the signal filter is inserted at the position of the analog waveform equalizers 6-1 and 6-2 or the digital waveform equalizer, and executes signal filtering processing of a predetermined band. The linearizer is inserted at the position of the analog waveform equalizers 6-1 and 6-2 or the digital waveform equalizer, and executes a predetermined linear equalization process. Further, the tuner is included in the control operation of the adaptive control type controller 20a, for example, and controls the local oscillation frequency of the local oscillator 3 based on the calculated SN ratio so that the SN ratio is substantially maximized. Thus, the reception frequency of the radio receiver 10a is tuned so as to be substantially the same as the signal frequency of the desired wave.
[0155]
In the above embodiment, the complex Gaussian noise and the moment of the polyphase PSK signal are formulated to a higher order, and the functional is defined by focusing on the signal point arrangement peculiar to PSK modulation, which is an estimation of the signal-to-noise ratio. It was analytically shown to be an index using the above moment formula. Furthermore, the statistical behavior of this functional in a system with a finite data length signal and additive Gaussian noise is shown by computer simulation. When the number of data to be averaged is small, the variance is large particularly in the low SN ratio region. As the number of data is increased, the curve gradually approaches an analytically derived monotonically increasing curve, and the SN ratio can be estimated and calculated with high accuracy. Since this functional is easy to calculate and does not require synchronous detection, it can be used as a blind control standard for a simple adaptive reception system for consumer consumers.
[0156]
In the above embodiment, the six non-excitation elements A1 to A6 and the corresponding variable reactance elements 12-1 to 12-6 are provided. However, the present invention is not limited to this, and at least one non-excitation element is included. An excitation element A1 and a variable reactance element 12-1 corresponding to the excitation element A1 may be provided. Moreover, the number of each may be plural.
[0157]
【The invention's effect】
As described above in detail, according to the array antenna control method according to the present invention, in the array antenna control method such as the ESPAR antenna or the linear array antenna of the prior art, based on the received signal received by the array antenna, Using an iterative numerical method in nonlinear programming, the main beam of the array antenna is moved in the direction of the desired wave so that the value of the reference function expressed using the m-th power of the received signal is maximized or minimized. The reactance value of each variable reactance element for directing and directing null toward the interference wave is calculated and set. Therefore, the directivity of the array antenna can be adaptively controlled so that the main beam is directed in the direction of the desired wave and null is directed in the direction of the interference wave without requiring a reference signal. Here, since no reference signal is required, the configuration of the apparatus can be simplified. Further, since the normative function is described only with the m-th power value of the received signal, the calculation process of the adaptive control process can be executed very easily.
[0158]
Further, according to the method for calculating the signal-to-noise ratio of a received signal according to the present invention, wireless reception for receiving a radio signal that has been m-phase PSK modulated (where m is an integer of 2 or more) as a received signal. Machine, a normative function which is a function obtained by dividing the square value of the absolute value of the mean value of the m-th power value of the received signal by the average value of the square value of the absolute value of the m-th value of the received signal in a predetermined period. And the signal-to-noise ratio of the received signal is calculated using an equation indicating the relationship between the normative function and the signal-to-noise ratio based on the calculated normative function. Therefore, the signal-to-noise ratio of the received signal can be calculated with high accuracy in real time by a very simple method.
[0159]
Furthermore, according to the adaptive control method of a radio receiver according to the present invention, the signal-to-noise ratio of the received signal is calculated by the signal-to-noise ratio calculation method of the received signal, and the calculated signal-to-noise ratio is substantially equal. Therefore, the signal processing means which is a signal equalizer or a signal filter of the wireless receiver is adaptively controlled so as to be maximized. Accordingly, the signal processing means of the wireless receiver can be adaptively controlled in real time and with high accuracy based on the calculated signal-to-noise ratio.
[Brief description of the drawings]
FIG. 1 is a block diagram showing a configuration of an array antenna control apparatus according to a first embodiment of the present invention.
FIG. 2 is a cross-sectional view showing a detailed configuration of the ESPAR antenna device 100 of FIG. 1;
3 is a circuit diagram showing a circuit near a connection point between a non-excitation element An and a variable reactance element 12-n of the ESPAR antenna apparatus 100 of FIG. 1;
4 is a flowchart showing an adaptive control process by the steepest gradient method, which is executed by the adaptive control type controller 20 of FIG. 1. FIG.
FIG. 5 is a block diagram showing a configuration of an array antenna control apparatus according to a second embodiment of the present invention;
FIG. 6 is a diagram showing a flow of blind adaptive beam forming simulation executed using the ESPAR antenna apparatus 100 of FIG. 1;
7 is a directivity characteristic diagram showing a radiated power pattern when the interference wave direction is 45 degrees, which is the simulation result of FIG. 6; FIG.
FIG. 8 is a directivity characteristic diagram showing a radiated power pattern when the interference wave direction is 90 degrees, which is the simulation result of FIG. 6;
9 is a directivity characteristic diagram showing the radiated power pattern when the interference wave direction is 135 degrees, which is the simulation result of FIG. 6; FIG.
10 is a directivity characteristic diagram showing a radiated power pattern when the interference wave direction is 180 degrees, which is the simulation result of FIG. 6; FIG.
FIG. 11 is a block diagram showing a configuration of an array antenna control apparatus according to a third embodiment of the present invention.
12 is a functional J for the signal-to-noise power ratio used in the array antenna control apparatus of FIG.₂{Y (t)}, J₃{Y (t)} J₄It is a graph which shows the theoretical value of {y (t)}.
13 is a functional J for the signal-to-noise power ratio used in the array antenna control apparatus of FIG.₂It is a graph which shows the theoretical value of {y (t)}, and the value of a simulation result.
14 is a functional J for the signal-to-noise power ratio used in the array antenna control apparatus of FIG.₃It is a graph which shows the theoretical value of {y (t)}, and the value of a simulation result.
15 is a functional J for the signal-to-noise power ratio used in the array antenna control apparatus of FIG.₄It is a graph which shows the theoretical value of {y (t)}, and the value of a simulation result.
[Explanation of symbols]
A0: Excitation element,
A1 to A6 ... non-excited elements,
1 ... Low noise amplifier (LNA),
2-1, 2-2 ... mixer,
3 ... Local oscillator,
4 ... 90 degree phase shifter,
5-1, 5-2 ... A / D converter,
6-1, 6-2 ... waveform equalizer,
8 ... Coaxial cable for feeding,
11: Ground conductor,
12-1 to 12-6 ... variable reactance element,
13 ... Low-pass filter,
14 ... resistance,
15: Capacitor,
20, 20a ... adaptive control type controller,
50 ... Array antenna,
51-1 to 51-N ... antenna elements,
52-1 to 52 -N: Low noise amplifier (LNA),
53-1 to 53 -N ... variable phase shifter,
54. Synthesizer,
60: Adaptive control type controller,
100: ESPAR antenna device.

Claims (8)

An excitation element for receiving a radio signal;
At least one non-excitation element provided at a predetermined distance from the excitation element;
A variable reactance element connected to the non-excitation element,
In the array antenna control method, by changing the reactance value of the variable reactance element, the non-excited element is operated as a director or a reflector, respectively, and the directivity characteristics of the array antenna are changed.
The transmitted radio signal is m-phase PSK modulated (where m is an integer greater than or equal to 2), and an iterative numerical solution in nonlinear programming is performed based on the received signal received by the excitation element. The main beam of the array antenna is directed in the direction of the desired wave and the null is directed in the direction of the interference wave so that the value of the normative function expressed using the m-th power of the received signal is maximized or minimized. look including the step of setting a reactance value by the calculation of the variable reactance element for,
The normative function is a function obtained by dividing the square of the absolute value of the average value of the m-th power value of the received signal in the predetermined period by the average value of the square value of the absolute value of the m-th value of the received signal. A method for controlling an array antenna. A plurality of P received signals received by an array antenna in which a plurality of P antenna elements are juxtaposed at a predetermined interval are phase-shifted by a predetermined amount of phase by P phase-shifting means, and then synthesized. In the array antenna control method for outputting the combined received signal,
The transmitted radio signal is m-phase PSK modulated (where m is an integer greater than or equal to 2), and based on the combined received signal, using an iterative numerical solution in nonlinear programming, Each for directing the main beam of the array antenna in the direction of the desired wave and directing the null in the direction of the interference wave so that the value of the normative function expressed using the m-th power of the received signal becomes maximum or minimum the step of setting calculates the amount of phase shift of the phase shifting means seen including,
The normative function is a function obtained by dividing the square of the absolute value of the average value of the m-th power value of the received signal in the predetermined period by the average value of the square value of the absolute value of the m-th value of the received signal. A method for controlling an array antenna. In a radio receiver that receives an m-phase PSK modulated radio signal (where m is an integer greater than or equal to 2) as a received signal,
The value of a normative function which is a function obtained by dividing the square value of the absolute value of the average value of the m-th power value of the received signal by the average value of the square value of the absolute value of the m-th value of the received signal in a predetermined period. Calculating a signal-to-noise ratio of the received signal using an expression indicating a relationship between the normative function and the signal-to-noise ratio based on the calculated normative function. Signal to noise ratio calculation method. In a radio receiver including a signal processing unit that receives an m-phase PSK-modulated radio signal (where m is an integer of 2 or more) as a received signal and processes the received signal.
The value of a normative function which is a function obtained by dividing the square value of the absolute value of the average value of the m-th power value of the received signal by the average value of the square value of the absolute value of the m-th value of the received signal in a predetermined period. Calculating a signal-to-noise ratio of the received signal using an equation indicating a relationship between the reference function and a signal-to-noise ratio based on the calculated reference function;
Adaptive control of the signal processing means such that the calculated signal-to-noise ratio is substantially maximized. 5. The wireless receiver adaptive control method according to claim 4 , wherein the signal processing means is a signal equalizer of the wireless receiver. 5. The radio receiver adaptive control method according to claim 4 , wherein the signal processing means is a radio receiver signal filter. 5. The wireless receiver adaptive control method according to claim 4 , wherein the signal processing means is a linearizer of the wireless receiver. 5. The adaptive control method of a radio receiver according to claim 4 , wherein the signal processing means is a tuner of the radio receiver.

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