Lightweight Asymmetric encryption algorithm I'm an embedded systems researcher, and new in the crypto field. Actually, I need to know if there are any lightweight asymmetric encryption algorithm especially considering the time needed for key generation.

I found that NTRU is considered one of the most lightweight asymmetric crypto systems, is this correct?
When an embedded device needs asymmetric crypto to encrypt, (e.g. measurements it makes) or check authenticity (e.g. of commands or firmware updates it receives), there is no need for a private key or key generation in the device, and nothing beats RSA and Rabin on simplicity and speed (for RSA: with $e=3$, which is safe when used with proper padding); plus RSA and Rabin are well known, and patent-free. In these applications, RSA and Rabin main drawbacks are that cryptograms are at least the size of the private key (e.g. 256 bytes for 2048-bit RSA); however only a fraction of that needs to be overhead not conveying actual data (e.g. 66 bytes for RSA-OAEP with SHA-256).

When and if a device needs a private key (see final note), Elliptic Curve Crypto (e.g. ECDSA, ed25519) has many advantages, including very easy key generation, significantly faster computations for the private-key operation (e.g. signature generation), smaller keys, and smaller minimum size of cryptograms. But there is debate about if some particular implementations are patent-encumbered in some jurisdictions, or not.

On the RSA vs ECC debate: RSA private-key (except perhaps its key generation) can be made fast, using dedicated hardware, as used in many Smart Cards. Dedicated hardware is also used in all modern Common-Criteria security-certified embedded devices using ECC that I am aware of, thus if ECC might allow to do without the burden of dedicated hardware in some contexts, that's uncommon in such security-certified devices.

NTRU can also be considered, but is alleged to be patent-encumbered in some jurisdictions, and is a relatively recent player, thus is of less recognized security, in no FIPS standard, nor endorsed by ANSSI (French) or BSI (German). In particular the signature part of it (NTRUSign) was broken in 2006 (Phong Q. Nguyen and Oded Regev, Learning a Parallelepiped: Cryptanalysis of GGH and NTRU Signatures, in Journal of Cryptology, 2009; preliminary version in proceedings of Eurocrypt 2006); and the break and fix cycle on NTRUSign has hardly stabilized (Léo Ducas and Phong Q. Nguyen, Learning a Zonotope and More: Cryptanalysis of NTRUSign countermeasures, in proceedings of AsiaCrypt 2012).

Note: having a private key in a device is useful only when some of the other entities that have to authenticate such device, or send it confidential data, can not be trusted to hold and properly use a common secret key. If all such other entities can be trusted, symmetric crypto with device-unique diversified keys (derived from a master key and device serial number) can be made functionally equivalent to full-blown asymmetric crypto everywhere (when combined with asymmetric crypto, restricted to public-key operation on the devices, to authenticate said other entities, and encipher to them); that solution is much simpler and faster on the device side.