Paypal Express checkout(PHP): Transaction id is invalid(DoAuthorization) - php

Question

I'm using Paypal Express Checkout method for my shopping cart. the paypal payment is working correctly.
i used the correct TRANSACTIONID from my sandbox account after the transaction but the given code always returns the error Transaction id is invalid.
$request_params = array
(
'METHOD' => 'DoAuthorization',
'USER' => $api_username,
'PWD' => $api_password,
'VERSION' => $api_version,
'TRANSACTIONID'=>$payment['transaction_id'],
'AMT' => $order['sub_total'],
'CURRENCYCODE' => 'USD',
);
$nvp_string = '';
foreach ($request_params as $var => $val)
{
$nvp_string .= '&' . $var . '=' . urlencode($val);
}
$certFile = 'C:\xampp\htdocs\my_project\certificate\cert_key_pem.txt';
$curl = curl_init();
curl_setopt($curl, CURLOPT_VERBOSE, 1);
curl_setopt($curl, CURLOPT_SSL_VERIFYPEER, FALSE);
curl_setopt($curl, CURLOPT_TIMEOUT, 10);
curl_setopt($curl, CURLOPT_URL, $api_endpoint);
curl_setopt($curl, CURLOPT_RETURNTRANSFER, 1);
curl_setopt($curl, CURLOPT_SSLCERT, $certFile);
curl_setopt($curl, CURLOPT_POSTFIELDS, $nvp_string
$result = curl_exec($curl);
curl_close($curl);
$result_array = $this->NVPToArray($result);
echo "<pre>"; print_r($result_array); die();
the array gives the value as below
Array
(
[TIMESTAMP] => 2015-08-10T07:45:36Z
[CORRELATIONID] => deb2f549572b0
[ACK] => Failure
[VERSION] => 85.0
[BUILD] => 000000
[L_ERRORCODE0] => 10609
[L_SHORTMESSAGE0] => Invalid transactionID.
[L_LONGMESSAGE0] => Transaction id is invalid.
[L_SEVERITYCODE0] => Error
)
if you have any idea about such type of errors on Paypal Express Checkout DoAuthorization then please help me. thanks