private function _generateSignature($parameters = array())
    {
        $this->_headers = [];
        $canonical_uri = '/';

        $parameters['Action'] = $this->_action;
        ksort($parameters);

        $request_parameters = http_build_query($parameters, '', '&', PHP_QUERY_RFC3986);

        $canonical_headers = 'host:' . $this->_host . "\n" . 'x-amz-date:' . $this->_amz_date . "\n";
        $signed_headers = 'host;x-amz-date';
        $payload_hash = hash('sha256', '');

        // task1
        $canonical_request = $this->_method . "\n" . $canonical_uri . "\n" . $request_parameters . "\n" . $canonical_headers . "\n" . $signed_headers . "\n" . $payload_hash;

        // task2
        $credential_scope = $this->_date . '/' . $this->_region . '/' . self::SERVICE . '/aws4_request';
        $string_to_sign =  self::ALGORITHM . "\n" . $this->_amz_date . "\n" . $credential_scope . "\n" . hash('sha256', $canonical_request);

        // task3
        $signing_key = $this->_generateSignatureKey();
        $signature = hash_hmac('sha256', $string_to_sign, $signing_key);
        $this->_headers['Authorization'] = self::ALGORITHM . ' Credential=' . $this->_aws_key . '/' . $credential_scope . ', SignedHeaders=' . $signed_headers . ', Signature=' . $signature;
        $this->_headers['x-amz-date'] = $this->_amz_date;
        $this->_query_parameters = $request_parameters;
    }