Deployment of Long Term Evolution (LTE) in unlicensed spectrum has been a candidate feature to meet the explosive growth of traffic demand since 3GPP release 13. To further explore the advantage of unlicensed bands, in this context the operation of both uplink and downlink has been supported and studied in the subsequent releases. However, it has been identified that scheduled uplink transmission performance in unlicensed spectrum is significantly degraded due to the double listen-before-talk (LBT) requirements at both eNB when sending the uplink grant, and at the scheduled UEs before transmission. In this paper, in order to overcome this issue, a novel uplink transmission scheme, which does not require any grant, is proposed, and the details regarding the system design are provided. By modeling the dynamics in time of the LBT for both a system that employs a conventional uplink scheme, as well as the proposed scheme, it is verified through analytical evaluation that the double LBT scheme for uplink transmission greatly reduces the channel access probability for the UE, and leads consequently to performance loss, while the proposed scheme is able to alleviate this issue. System level simulation results, compliant with the LTE standard, show that the proposed scheme can achieve a significant performance gain in terms of throughput with negligible performance loss for the downlink, and other technologies operating in the same spectrum.