Structured illumination microscopy suffers from the need of sophisticated instrumentation and precise calibration. This makes structured illumination microscopes costly and skill-dependent. We present a novel approach to realize super-resolution structured illumination microscopy using an alignment non-critical illumination system and a reconstruction algorithm that does not need illumination information. The optical system is designed to encode higher order frequency components of the specimen by projecting PSF-modulated binary patterns for illuminating the sample plane, which do not have clean Fourier peaks conventionally used in structured illumination microscopy. These patterns fold high frequency content of sample into the measurements in an obfuscated manner, which are de-obfuscated using multiple signal classification algorithm. This algorithm eliminates the need of clean peaks in illumination and the knowledge of illumination patterns, which makes instrumentation simple and flexible for use with a variety of microscope objective lenses. We present a variety of experimental results on beads and cell samples to demonstrate resolution enhancement by a factor of 2.6 to 3.4 times, which is better than the enhancement supported by the conventional linear structure illumination microscopy where the same objective lens is used for structured illumination as well as collection of light. We show that the same system can be used in SIM configuration with different collection objective lenses without any careful re-calibration or realignment, thereby supporting a range of resolutions with the same system.