The past may be a foreign country, but not in Iraq; to paraphrase Faulkner, it's not even past.

As the repercussions of the 2003 invasion continue to play out on the streets of Baghdad and in the deserts around Tikrit, the war is still vividly and violently present. If it has never really gone away for ordinary Iraqis, then for the American poet Brian Turner it remains a source of continuing anxiety and inspiration, 11 years after he first led his men into combat.

A former sergeant in the US Army, Turner channelled his experiences into two celebrated volumes of poetry. Here, Bullet (published in the US in 2005) focused on the brutal disorientation of the fighting, while his follow-up, Phantom Noise (2010), dwelled on the immense challenges of coming home still haunted by what he had seen and done as a professional soldier.

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As the title of this innovative and extraordinary memoir suggests, Turner is adapting LP Hartley's aphorism into a way of framing the savagery and confusion of his own past, exploring its strange customs and baffling traditions, and everything about it that now seems both familiar and unrecognisable. Recapitulating in prose many of the same ideas, characters and incidents of those earlier volumes, the book isn't an expanded version of the poems but a companion piece that addresses the same material from a different angle.

"I am a drone aircraft plying the darkness above my body," he writes, and this idea of an elevated perspective is the key to the memoir. If his lyric poetry moves between the voices of the self and of a numbed observer, each giving witness to what he has seen, then Turner's prose comes from a cooler, more detached position. From above, the self is positioned not as an isolated unit, but as part of a history of violence that stretches back for generations, across countries and continents.

In 136 numbered sections, articulating discrete moments, observations and epiphanies, Turner follows a rough narrative from initial combat operations to his post-war travels and his attempts to purge himself of his experiences. As this narrative unspools, he is free to follow digressions into his childhood, into the brutality of human history, and into his own family's history of combat, from the Pacific campaign of the Second World War and the jungles of Vietnam, to the 1862 Civil War battlefield of Antietam.

Without judgement, Turner reflects on how his whole upbringing has reinforced a particular notion of masculinity, that to be a man is "to travail through fire and return again". Different generations have found different ways to re-engage with civilian life; his grandfather through alcohol, and his father through a fascination with the metaphysics of violence, constructing a dojo and initiating his son into the discipline and control of the martial arts.

As simultaneously delicate and hard-edged as his poetry, Turner's memoir recalls not so much conventional accounts of military service as it does David Shields's polemic Reality Hunger. In form and structure, its combination of autobiography, military history, poetry and the opaque mythology of men united in the "hunt for souls" seems to answer Shields's call for a literature free of the bounds of linear narrative and the contrived demands of fiction, while still retaining the persuasive power of both.

If occasionally a little portentous, over-reaching for a resonant phrase here or settling for a misplaced Hemingwayesque reticence there, this is still a profound, impressionistic meditation on the nature of war and the difficulty of bringing yourself home as a human being afterwards. What lifts it above mere confession is Turner's imaginative generosity, his empathy for those he fought against as well as for those innocents indifferently destroyed by the fighting. To even attempt to understand the emotions of a female suicide bomber, for example, as she prepares to kill herself and others, is to gesture towards a kind of grace.

At the end of the book, as the drone settles its perspective once more on the sleeping figure of the author, it feels entirely fitting that its invisible pilot is revealed as the spirit of Sgt Brian Turner, who died over there in Iraq, and who never really made it home.